{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# *Density Matrices and Path Integrals*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`Doruk Efe Gökmen -- 14/08/2018 -- Ankara`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stationary states of the quantum harmonic oscillator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The 1-dimensional (1D) quantum mechanical harmonic oscillator with characteristic frequency $\\omega$ is described by the same potential energy as its classical counterpart acting on a mass $m$: $V(x)=\\frac{1}{2}m\\omega^2x^2$. The physical structure of the allowed states subjected to this potential is governed by the time independent Schrödinger equation (TISE) $\\mathcal{H}\\psi=\\left(-\\frac{\\hbar^2}{2m}\\frac{\\text{d}^2}{\\text{d}x^2}+\\frac{1}{2}m\\omega^2x^2\\right)\\psi=E\\psi$, where $E$ is an energy eigenvalue. Note that here we have taken $\\hbar=1$, $m=1$, $\\omega=1$ for simplicity. The stationary states $\\psi_n(x)$ (Hermite polynomials) and the corresponding energy eigenvalues $E_n$ are calculated by the following program." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%pylab inline\n", "import math, pylab\n", "\n", "n_states = 20 #number of stationary states to be plotted\n", "grid_x = [i * 0.1 for i in range(-50, 51)] #define the x-grid\n", "psi = {} #intialise the list of stationary states\n", "for x in grid_x:\n", " psi[x] = [math.exp(-x ** 2 / 2.0) / math.pi ** 0.25] # ground state\n", " psi[x].append(math.sqrt(2.0) * x * psi[x][0]) # first excited state\n", " # other excited states (through Hermite polynomial recursion relations):\n", " for n in range(2, n_states): \n", " psi[x].append(math.sqrt(2.0 / n) * x * psi[x][n - 1] -\n", " math.sqrt((n - 1.0) / n) * psi[x][n - 2])\n", "\n", "# graphics output\n", "for n in range(n_states):\n", " shifted_psi = [psi[x][n] + n for x in grid_x] # vertical shift\n", " pylab.plot(grid_x, shifted_psi)\n", "pylab.title('Harmonic oscillator wavefunctions')\n", "pylab.xlabel('$x$', fontsize=16)\n", "pylab.ylabel('$\\psi_n(x)$ (shifted)', fontsize=16)\n", "pylab.xlim(-5.0, 5.0)\n", "pylab.savefig('plot-harmonic_wavefunction.png')\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following section checks whether the above results are correct (normalisation, ortanormality and TISE). TISE condition is verified by a discrete appoximation of the second derivative." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import math\n", "\n", "def orthonormality_check(n, m):\n", " integral_n_m = sum(psi[n][i] * psi[m][i] for i in range(nx)) * dx\n", " return integral_n_m\n", "\n", "nx = 1000\n", "L = 10.0\n", "dx = L / (nx - 1)\n", "x = [- L / 2.0 + i * dx for i in range(nx)]\n", "n_states = 4\n", "psi = [[math.exp(-x[i] ** 2 / 2.0) / math.pi ** 0.25 for i in range(nx)]] \n", "psi.append([math.sqrt(2.0) * x[i] * psi[0][i] for i in range(nx)]) \n", "for n in range(2, n_states):\n", " psi.append([math.sqrt(2.0 / n) * x[i] * psi[n - 1][i] - \\\n", " math.sqrt((n - 1.0) / n) * psi[n - 2][i] for i in range(nx)])\n", "n = n_states - 1\n", "print 'checking energy level', n\n", "#discrete approximation for the second derivative\n", "H_psi = [0.0] + [(- 0.5 * (psi[n][i + 1] - 2.0 * psi[n][i] + psi[n][i - 1]) /\n", " dx ** 2 + 0.5 * x[i] ** 2 * psi[n][i]) for i in range(1, nx - 1)]\n", "for i in range(1, nx - 1): \n", " print n, x[i], H_psi[i] / psi[n][i]" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math, pylab\n", "\n", "nx = 300 # nx is even, to avoid division by zero\n", "L = 10.0\n", "dx = L / (nx - 1)\n", "x = [- L / 2.0 + i * dx for i in range(nx)]\n", "# construct wavefunctions:\n", "n_states = 4\n", "psi = [[math.exp(-x[i] ** 2 / 2.0) / math.pi ** 0.25 for i in range(nx)]] # ground state\n", "psi.append([math.sqrt(2.0) * x[i] * psi[0][i] for i in range(nx)]) # first excited state\n", "for n in range(2, n_states):\n", " psi.append([math.sqrt(2.0 / n) * x[i] * psi[n - 1][i] - \\\n", " math.sqrt((n - 1.0) / n) * psi[n - 2][i] for i in range(nx)])\n", "# local energy check:\n", "H_psi_over_psi = []\n", "for n in range(n_states):\n", " H_psi = [(- 0.5 * (psi[n][i + 1] - 2.0 * psi[n][i] + psi[n][i - 1])\n", " / dx ** 2 + 0.5 * x[i] ** 2 * psi[n][i]) for i in range(1, nx - 1)]\n", " H_psi_over_psi.append([H_psi[i] / psi[n][i+1] for i in range(nx - 2)])\n", "\n", "# graphics output:\n", "for n in range(n_states):\n", " pylab.plot(x[1:-1], [n + 0.5 for i in x[1:-1]], 'k--', lw=1.5)\n", " pylab.plot(x[1:-1], H_psi_over_psi[n], '-', lw=1.5)\n", " pylab.xlabel('$x$', fontsize=18)\n", " pylab.ylabel('$H \\psi_%i(x)/\\psi_%i(x)$' % (n, n), fontsize=18)\n", " pylab.xlim(x[0], x[-1])\n", " pylab.ylim(n, n + 1)\n", " pylab.title('Schroedinger equation check (local energy)')\n", " #pylab.savefig('plot-check_schroedinger_energy-%i.png' % n)\n", " pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Quantum statistical mechanics - Density matrices" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In a thermal ensemble, the probability of being in $n$th energy eigenstate is given by the Boltzmann factor $\\pi(n)\\propto e^{-\\beta E_n}$, where $\\beta=\\frac{1}{k_BT}$. Hence, e.g the probability $\\pi(x,n)$ to be in state $n$ and in position $x$ is proportional to $e^{-\\beta E_n}|\\psi_n(x)|^2$.\n", "\n", "We can consider the diagonal density matrix $\\rho(x,x,\\beta)=\\sum_n e^{\\beta E_n}\\psi_n(x)\\psi_n^*(x)$, which is the probability $\\pi(x)$ of being at position $x$. This is a special case of the more general density matrix $\\rho(x,x',\\beta)=\\sum_n e^{\\beta E_n}\\psi_n(x)\\psi_n^*(x')$, which is the central object of quantum statistical mechanics. The partition function is given by $Z(\\beta)=\\text{Tr}\\rho_u=\\int_{-\\infty}^\\infty \\rho_u(x,x,\\beta)\\text{d}x$, where $\\rho_u=e^{-\\beta \\mathcal{H}}$ is the unnormalised density matrix. It follows that $\\rho(\\beta)=\\frac{e^{-\\beta\\mathcal{H}}}{\\text{Tr}(e^{-\\beta\\mathcal{H}})}$.\n", "\n", "Properties of the density matrix:\n", "* *The convolution property*: $\\int \\rho(x,x',\\beta_1) \\rho(x',x'',\\beta_2) \\text{d}x' = \\int \\text{d}x' \\sum_{n,m} \\psi_n(x)e^{-\\beta_1 E_n} \\psi_n^*(x')\\psi_m(x')e^{-\\beta_2 E_m}\\psi_m^*(x'')$ $ = \\sum_{n,m} \\psi_n(x)e^{-\\beta_1 E_n} \\int \\text{d}x' \\psi_n^*(x')\\psi_m(x')e^{-\\beta_2 E_m}\\psi_m^*(x'') = \\sum_n \\psi_n(x)e^{-(\\beta_1+\\beta_2)E_n}\\psi_n^*(x'')=\\rho(x,x'',\\beta_1+\\beta_2)$ $\\implies \\boxed{ \\int \\rho(x,x',\\beta) \\rho(x',x'',\\beta) \\text{d}x' = \\rho(x,x'',2\\beta)}$ (note that in the discrete case, this is just matrix squaring). **So, if we have the density matrix at temperature $T=k_B/\\beta$ this equation allows us to compute the density matrix at temperature $T/2$**.\n", "\n", "* *The free density matrix* for a system of infinte size is $\\rho^\\text{free}(x,x',\\beta)=\\frac{1}{\\sqrt{2\\pi\\beta}}\\exp{\\left[-\\frac{(x-x')^2}{2\\beta}\\right]}$. Notice that in the high temperature limit ($\\beta\\rightarrow 0$) the density matrix becomes classical: $\\rho^\\text{free}\\rightarrow \\delta(x-x')$. The quantum system exihibits its peculiar properties more visibly at low temperatures.\n", "\n", "* *High temperature limit and the Trotter decomposition*. In general any Hamiltonian can be written as $\\mathcal{H}=\\mathcal{H}^\\text{free}+V(x)$. At high temperatures ($\\beta\\rightarrow 0$) we can approximate the density matrix as $\\rho(x,x',\\beta)=e^{-\\beta V(x)/2}\\rho^\\text{free}e^{-\\beta V(x')/2}$ (Trotter expansion). Hence an explicit expression for the density matrix is available without solving the Schrödinger (or more preciesly Liouville) equation for any potential." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Getting the density matrix for the harmonic oscillator at high temperatures by the Trotter decomposition." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "data": { "image/png": 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aSs8JTnihpQRkR3zKvRXwYmBrRNwWEXuAS4BTZ78csLL99Srgrryd+ojQ0pB4TtADIwtXMD6zWtKWjvsbI2Jjx/01wLaO+9uBo2ft40+Ar0l6K7AMOCHvRV0IrVp1yQl6YGTBCr5l90XE+h7Pz1VNZ+/5dODiiPiIpN8EPivpyIjuv71cCK16dcgJemBkQQIxXc6o8Xbg0I77a9m/63smcCJARHxf0hJgNbCj2059jtCqM++cYJSYE4xCOcGsALo7vBBR4FbANcDhkg6TNAGcBmyatc2dwPEAkp4LLAHu7bXT5I4IJR0IXAgcSfbevDkivl9tq6xUzgk2T5QzahwReyWdBVwBtICLIuImSecBWyJiE/BO4K8kvSN7Zd4Y0fsvL7lCCHwc+GpEvK5d8ZdW3SAbgNTmE/QECoNX0u+RiNhMFonpfOzcjq9vBo7pZ59JFUJJK4GXA28EaA+P76myTVYi5wQbLeXZZ1I7R/hrZH35v2mnwi+UtKxzA0kbJG2RtGWSx6tppc2fc4KNFMD0tHJvVUmtEC4CXghcEBFHAY8AT7iEJiI2RsT6iFg/zuIq2mjzMe+c4P4DI/PPCXbvDjsnOGABhPJvFUmqa0w2NL49Iq5u37+UWYXQasY5QWtL+S1N6ogwIu4Btkl6Tvuh44Gbe3yL1UHpOcH9u8POCdZASfmZQUjtiBDgrcDn2yPGtwFvqrg9Nl81mk/QOcFBK3wtcSWSK4QR8UOg1yU2ljrnBG0uCb+9yRVCGxHOCVqngKhwVDiPC6GVxzlB68mF0Joi0XWHnRNMQMJvtQuhlcPzCVoeF0IbWc4JWhH7AtWJciG0hfN8glZAym+7C6HNn3OC1g+PGttIcU7Q5kEJv/0uhDY/zglaPyq+hC6PC6EV55ygzVu1s8vkcSG0/jgnaPOV8F+FC6EV45ygLVTCfyU9C6Gk7wG3Ap+KiKuG0yRLinOCVobEc4R58xGeC+wELpT0z5Le0l5XxJrE8wlaCRT5t6r0LIQR8Y2IODsijgReBdwPvGsoLbPqed1hK9OITMy6NiIuGVhLLB3OCVrD9DNV/5WSjhtYSywt88oJdu8OOydoKXeN+zki/Ftgs6QzIuJLnU9IehnwwYh4Wamts+FyTtAGJUj6ErvCR4QR8QfAB4BLJP0XAEm/IekfgO8ATxpME22ovO6wDUpJ5wglnSjpVklbJc25yqWk/yTpZkk3SfrbvH32lSOMiPMk/Ry4QNLpwDHANuDNwGf62ZclxjlBG7Ayur6SWsD5ZIO324FrJG2KiJs7tjkceDdwTEQ8KOngvP32VQglHQQ8G5gC/i3wPeDYiNjbz34sIc4J2rCU81f2YmBrRNwGIOkS4FSeuOzv7wPnR8SDABGxI2+nhbvGkt5HtrzmW4CPkB0Frgc+WnQflijnBG0YinWNV0va0nHbMGsva8h6oftsbz/W6dnAsyX9k6SrJJ2Y17R+jgj/GLgQeH9E/AJA0p3A30l6KnBGREz2sT+rmucTtCHpY1T4vojotZzvXCMus/e8CDgcOBZYC/yjpCMj4pfddtpPIXxuRPz0Ca8e8a12pGYz8FXg+D72Z1VxTtCqUM6o8Xbg0I77a4G75tjmqvaB2e2SbiUrjNd022k/o8Y/7fL4dcDLgHVF92UJcE7QhqykHOE1wOGSDpM0AZwGbJq1zZeB4wAkrSbrKt/Wa6elzD4TEVslvbSMfdkAOSdoVSrhrzEi9ko6C7gCaAEXRcRNks4DtkTEpvZzvyXpZrKB3f8WEff32m9p03DtO29oifN8glaFEq8ciYjNZKfjOh87t+PrAP6wfSvE8xE2hXOCVrWEf6e5EI465wQtEUr4d1s/ky5YXTknaNaTjwhHmXOClpKEf7+5EI4i5wQtNRVPs5XHhXBUed1hS40LoQ2Fc4KWsoT/ml0IR41zgpYg4VHjvklqSbpe0leqbkttzDsnuP9CS/PPCXbvDjsn2HAFLq+ry1T9w/Q24BbAS4fmcU7Q6iLhv/LkjgglrQVeQzbllxXhnKDVwYgs5zksHyNbO3nFXE+2J2rcALCEpUNsVoKcE7QacXymIEmvBXZExLWSjp1rm4jYCGwEWKmDEn5rB8g5QaujhP/6kyqEZItBnSLpZGAJsFLS5yLijIrblR7nBK1OIu1R46QKYUS8m2z1KdpHhH/kItjBOUGrs4Q/BkkVQivAOUGrKZ8jnIeI+Dbw7YqbkQ7PJ2h150Jo8+acoI2CiuMxeVwI66D0nOD+3WHnBG2QhLvGNl/OCdoIcSG0/jgnaKMo4Y+HC2GqnBO0UeNCaIU4J2ijyjNUW1+cE7RRlfBHxYUwFc4J2ojzJXbWnXOC1hApd42Tm4+wkTyfoI26InMRFvxYSTpR0q2Stko6p8d2r5MUktbn7dOFsErzzgnuP73+/HOC4ZygDUcJhVBSCzgfOAk4Ajhd0hFzbLcCOBu4ukjT3DWuiuScoDVGiVeWvBjYGhG3AUi6BDgVuHnWdv8T+BDwR0V26iPCKuQNjHTNCXbvDjsnaKnTdOTegNWStnTcNszazRpgW8f97e3HfvU60lHAoRFRePE3HxEOU8GBEecEbeQUPwd4X0T0OqenLnvPnpTGgD8H3thH63xEOHQFBkb6ywnuPzDinKClqKTlPLcDh3bcXwvc1XF/BXAk8G1JdwAvATblDZi4EA5LHwMjXnfYRlI5o8bXAIdLOkzSBHAasGnmJSIeiojVEbEuItYBVwGnRMSWXjt113jQ5jGBgnOCNorKGCyJiL2SzgKuAFrARRFxk6TzgC0Rsan3HubmQjgMfQ6MeD5BG0klfawiYjOwedZj53bZ9tgi+3QhHKQu3WHGF3k+QWsWr2LXUD1ygoyPM71quXOC1hieobqJFjiBgnOCNpIS/kXrQlimkiZQcE7QRpGPCJukhAkUPJ+gjRyvYtcQJS605PkEbRR5sGSUDWChJecEbRS5EI66khdack7QRk6Q9OfOhXAh5pkTnFxZ5nyCzglaPXiwZBQtICfIqkl+/dAdzglasyT88XMhnI8BL7TknKCNGgeqR8mQFlpyTtBGTsxMvJokF8J+lb7QknOC1hAJfxRdCIsqMSeYNzDinKCNIneN62wAOcG8gRHnBG3kBFl6IVEuhEWUnBPMGxhxTtBGUsIfy6QKoaRDgc8AhwDTwMaI+HhFjcn+aLVAY0NdaGnizomsK9xlYCR27866wh4YsRpx17i4vcA7I+K69gLN10r6ekTMXrN0ODQ2UwTLWWip2MDIviLYbWBkpgh6YMRqJOVR46QWb4qIuyPiuvbXO4FbmLVm6VDMOydYzkJLzgnayCmycFOFdTK1I8IZktYBRwFXz3p8A7ABYAlLy37R9p+DzQnmDYw4J2ijJgtUp/s5TeqIcB9Jy4EvAW+PiIc7n4uIjRGxPiLWj7N4AC9edk5w/3WH8wZGnBO0kTRd4FaR5I4IJY2TFcHPR8RlQ3zhoeUE8yZQcE7QRlHKR4RJFUJJAv4auCUiPjqkF23/ObycYN4ECs4J2shJfIbq1LrGxwCvB14p6Yft28kDf9V55QS7d4cXPIGCc4I2crJrjfNuVUnqiDAivkt2XnXwKswJ5g2MOCdoIynhz25qR4TDVXpOcP+BkflMoOCcoI2c9gLvebciJJ0o6VZJWyWdM8fzfyjpZkk3SPqmpGfm7bOZhbDinGA2MOKcoDVMRP4th6QWcD5wEnAEcLqkI2Ztdj2wPiKeB1wKfChvv0l1jQcukZxg7sCIu8M2isr5GL8Y2BoRtwFIugQ4FZi5+iwiruzY/irgjLydNqsQwlDmE1zwBAougjaCNF2oZ7Na0paO+xsjYmPH/TXAto7724Gje+zvTODyvBdtTiFMKCeYt9CSu8M2coKigen7ImJ9j+fnGkyd82hB0hnAeuAVeS86+oUwwZygF1qyphFRVqB6O3Box/21wF37vZ50AvDHwCsi4vG8nTZjsCS1nGDewIiLoI2iEgZLgGuAwyUdJmkCOA3Y1LmBpKOATwGnRMSOIjsd3SPChHOCHhixRirhsx0ReyWdBVwBtICLIuImSecBWyJiE/BnwHLg/2YXq3FnRJzSa7+jWwihsvkEPYGC2SzFzxHm7ypiM7B51mPndnx9Qr/7HM1COOB1h73Qkln/Co4aV2K0CmFdcoIeGLHGKXwOsBKjVQihHjlBD4xY0wRJf9ZHpxDWKCeYFcB0uwlmA5HwR77+hdA5QbNa8MSsgzbkdYe90JLZPLgQDo5zgmY1EAFT6R4E1L4QOidoVhMJf/7rXQiFc4JmdeFCOCjOCZrVQpAlJhJV60IoyTlBs1pIu2dU60KIcE7QrA4CD5YMzNiYc4JmdZHwv4l6F0LJOUGzunAhHJBWyzlBs1rwpAsDE2NyTtCsDgLwNFwDMibnBM3qIuEDhVoXwqlxOSdoVgu+xG5gYgznBM3qICAS7jnVuxC2mCmCzgmaJc5XlgzG9ATOCZrVRcL/ZmpdCGmFc4JmdRDhUeNBWTwx6ZygWV0k/G+n1oVwYmzKOUGzWojs31Oial0Il4xNOidoVgeehmtwVrQec07QrC4SPqAYq7oBs0k6UdKtkrZKOqfXtuNMc4AmnBM0S1wA0f531etWRF6NkLRY0v9pP3+1pHV5+0yqEEpqAecDJwFHAKdLOqLb9i2pz5xgOCdoVoXo+HfV65ajYI04E3gwIp4F/Dnwv/P2m1rX+MXA1oi4DUDSJcCpwM1zbdzCOUGzuihpsKRIjTgV+JP215cCn5SkiO7/qFMrhGuAbR33twNHd24gaQOwoX338VVrtt/4q2d/NuDmLdhq4L6qG1FQndoK9WpvndoK8JyF7mAnD17xjbh0dYFNl0ja0nF/Y0Rs7LifWyM6t4mIvZIeAp5Mj/c8tUKoOR57QhVvvykbASRtiYj1w2hYGerU3jq1FerV3jq1FbL2LnQfEXFiGW2hQI0ouM0TJHWOkKy6H9pxfy1wV0VtMbP0FKkRM9tIWgSsAh7otdPUCuE1wOGSDpM0AZwGbKq4TWaWjiI1YhPwhvbXrwO+1ev8ICTWNW73588CrgBawEURcVOPb9nY47kU1am9dWor1Ku9dWorJNTebjVC0nnAlojYBPw18FlJW8mOBE/L269yCqWZ2chLrWtsZjZ0LoRm1ni1LYT9XIpXJUmHSrpS0i2SbpL0tqrbVISklqTrJX2l6rb0IulASZdK+lH7Pf7NqtvUi6R3tD8HN0r6gqQlVbepk6SLJO2QdGPHYwdJ+rqkn7T/fFKVbRyEWhbCfi/Fq9he4J0R8VzgJcBbEm5rp7cBt1TdiAI+Dnw1Iv4V8HwSbrOkNcDZwPqIOJLsZH/uifwhuxiYnfk7B/hmRBwOfLN9f6TUshDScZlNROwB9l1mk5yIuDsirmt/vZPsH+qaalvVm6S1wGuAC6tuSy+SVgIvJxslJCL2RMQvq21VrkXAAe1821ISy8lGxHfYP3N3KvDp9tefBv79UBs1BHUthHNdZpN0cQFoz4JxFHB1tS3J9THgXUDqM0/8GnAv8DftbvyFkpZV3ahuIuLnwIeBO4G7gYci4mvVtqqQp0bE3ZD9YgcOrrg9patrIez7EpqqSVoOfAl4e0Q8XHV7upH0WmBHRFxbdVsKWAS8ELggIo4CHiHhblv73NqpwGHA04Flks6otlUG9S2EtboUT9I4WRH8fERcVnV7chwDnCLpDrJTDq+U9Llqm9TVdmB7ROw7wr6UrDCm6gTg9oi4NyImgcuAl1bcpiJ+IelpAO0/d1TcntLVtRDW5lI8SSI7h3VLRHy06vbkiYh3R8TaiFhH9r5+KyKSPGqJiHuAbZL2zY5yPF2mbEvEncBLJC1tfy6OJ+HBnQ6dl6y9Afj7CtsyEEldYlfUPC7Fq9IxwOuBf5H0w/Zj74mIzRW2aZS8Ffh8+xfibcCbKm5PVxFxtaRLgevI0gTXk9DlawCSvgAcC6yWtB14H/BB4IuSziQr5r9dXQsHw5fYmVnj1bVrbGZWGhdCM2s8F0IzazwXQjNrPBdCM2s8F0IzazwXQjNrPBdCM2s8F0IbKEnPkjQp6f2zHr9A0k5JtVnf10aXC6ENVERsJZvX8B2SVgNIOhd4M/AfImLBi4ebLZQvsbPE7KmEAAAA00lEQVSBk3QI8FPgL4AfkV1fe3pEfLHShpm11XLSBauXiLhH0seAd5J95s52EbSUuGtsw/ITYDHw/Yg4v+rGmHVyIbSBk/RK4FPA94FjJD2/4iaZPYELoQ2UpBcCXyYbMDmWbD67P62yTWazuRDawEh6FnA58DXgre0VB98PnCzp5ZU2zqyDR41tINojxd8jOwJ8dUQ83n68BdwIPBgRdVivwxrAhdDMGs9dYzNrPBdCM2s8F0IzazwXQjNrPBdCM2s8F0IzazwXQjNrPBdCM2u8/w/OTQULktd7kQAAAABJRU5ErkJggg==\n", 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%pylab inline\n", "import math, pylab\n", "\n", "# density matrix for a free particle (exact)\n", "def funct_rho_free(x, xp, beta):\n", " return (math.exp(-(x - xp) ** 2 / (2.0 * beta)) /\n", " math.sqrt(2.0 * math.pi * beta))\n", "\n", "beta = 0.1\n", "nx = 300\n", "L = 10.0\n", "x = [-L / 2.0 + i * L / float(nx - 1) for i in range(nx)]\n", "rho_free, rho_harm = [], []\n", "for i in range(nx):\n", " rho_free.append([funct_rho_free(x[i], x[j], beta) for j in range(nx)])\n", " rho_harm.append([rho_free[i][j] * math.exp(- beta * x[i] ** 2 / 4.0 -\n", " beta * x[j] ** 2 / 4.0) for j in range(nx)])\n", "\n", "# graphics output (free particle)\n", "pylab.imshow(rho_free, extent=[0.0, L, 0.0, L], origin='lower')\n", "pylab.xlabel('$x$', fontsize=16)\n", "pylab.ylabel('$x\\'$', fontsize=16)\n", "pylab.colorbar()\n", "pylab.title('$\\\\beta$=%s (free)' % beta)\n", "pylab.savefig('plot-trotter-free.png')\n", "pylab.show()\n", "\n", "# graphics output (harmonic potential)\n", "pylab.imshow(rho_harm, extent=[0.0, L, 0.0, L], origin='lower')\n", "pylab.xlabel('$x$', fontsize=16)\n", "pylab.ylabel('$x\\'$', fontsize=16)\n", "pylab.colorbar()\n", "pylab.title('$\\\\beta$=%s (harmonic)' % beta)\n", "pylab.savefig('plot-trotter-harmonic.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, at high temperature, the density matrix is given by a simple correction to the free density matrix as seen above. Taking $\\rho^\\text{free}$ as a starting point, by the convolution property we can obtain the density matrix at low temperatures too, hence leading to a convenient numerical scheme through matrix squaring. The following section contains an implementation of this." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math, numpy, pylab\n", "\n", "#matrix squaring and convolution to calculate the density matrix at any temperature.\n", "\n", "# Free off-diagonal density matrix\n", "def rho_free(x, xp, beta):\n", " return (math.exp(-(x - xp) ** 2 / (2.0 * beta)) /\n", " math.sqrt(2.0 * math.pi * beta))\n", "\n", "# Harmonic density matrix in the Trotter approximation (returns the full matrix)\n", "def rho_harmonic_trotter(grid, beta):\n", " return numpy.array([[rho_free(x, xp, beta) * \\\n", " numpy.exp(-0.5 * beta * 0.5 * (x ** 2 + xp ** 2)) \\\n", " for x in grid] for xp in grid])\n", "\n", "#construct the position grid\n", "x_max = 5.0 #maximum position value on the grid\n", "nx = 100 #number of grid elements\n", "dx = 2.0 * x_max / (nx - 1) #the grid spacing\n", "x = [i * dx for i in range(-(nx - 1) / 2, nx / 2 + 1)] #the position grid\n", "\n", "beta_tmp = 2.0 ** (-8) # initial value of beta (power of 2)\n", "beta = 2.0 ** 0 # actual value of beta (power of 2)\n", "rho = rho_harmonic_trotter(x, beta_tmp) # density matrix at initial beta\n", "\n", "#reduce the temperature in log_2 steps by the convolution property (matrix squaring) \n", "#and get the updated density matrix rho\n", "while beta_tmp < beta:\n", " rho = numpy.dot(rho, rho) #matrix squaring is implemented by the dot product in numpy\n", " rho *= dx #multiply by the position differential since we are in the position representation\n", " beta_tmp *= 2.0 #reduce the temperute by a factor of 2\n", "\n", "# graphics output\n", "pylab.imshow(rho, extent=[-x_max, x_max, -x_max, x_max], origin='lower')\n", "pylab.colorbar()\n", "pylab.title('$\\\\beta = 2^{%i}$' % math.log(beta, 2))\n", "pylab.xlabel('$x$', fontsize=18)\n", "pylab.ylabel('$x\\'$', fontsize=18)\n", "pylab.savefig('plot-harmonic-rho.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $\\rho^\\text{free}$ with periodic boundary conditions\n", "\n", "Free density matrix in periodic boundary conditions (periodic box of size $L$) can be obtained by the *Poisson sum rule?* by $\\rho^\\text{per}(x,x',\\beta)=\\frac{1}{L}\\sum^\\infty_{n=-\\infty}e^{i\\frac{2\\pi n (x-x')}{L}}e^{-\\beta\\frac{2\\pi^2 n^2}{L^2}}=\\sum^\\infty_{w=-\\infty}\\rho^\\text{free}(x,x'+wL,\\beta)$, where $w$ is the *winding number* (that is the winding around the box of size L). The diagonal stripe is a manifestation of the fact that the system is translation invariant, i.e. $\\rho^\\text{free}(x,x',\\beta)$ is a function of $x-x'$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math, cmath, pylab\n", "\n", "ntot = 21 # odd number\n", "beta = 1.0 #inverse temperature\n", "nx = 100 #number of grid elements\n", "L = 10.0 #length of the system\n", "x = [i * L / float(nx - 1) for i in range(nx)] #position grid\n", "rho_complex = []\n", "for i in range(nx):\n", " rho_complex.append([sum(\n", " math.exp(- 2.0 * beta * (math.pi * n / L) ** 2) *\n", " cmath.exp(1j * 2.0 * n * math.pi * (x[i] - x[j]) / L) / L\n", " for n in range(-(ntot - 1) / 2, (ntot + 1) / 2))\n", " for j in range(nx)]) #append the i'th line to the density matrix\n", " #(j loop is for constructing the line)\n", " \n", "rho_real = [[rho_complex[i][j].real for i in range(nx)] for j in range(nx)]\n", "\n", "# graphics output\n", "pylab.imshow(rho_real, extent=[0.0, L, 0.0, L], origin='lower')\n", "pylab.colorbar()\n", "pylab.title('$\\\\beta$=%s (complex exp)' % beta)\n", "pylab.xlabel('$x$', fontsize=16)\n", "pylab.ylabel('$x\\'$', fontsize=16)\n", "pylab.savefig('plot-periodic-complex.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Path integrals - Quantum Monte Carlo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Path integral representation of the kernel\n", "\n", "The kernel $K$ is the matrix element of the unitary time evolution operator $U(t_i-t_f)=e^{-i/\\hbar(t_f-t_i)\\mathcal{H}}$ in the position representation: $K(x_i,x_f;t_f-t_i)=\\langle x_f \\left| U(t_f-t_i) \\right| x_i \\rangle$. We can write $K(x_i,x_f;t_f-t_i)=\\langle x_f \\left| U^N((t_f-t_i)/N) \\right| x_i \\rangle$, that is, divide the time interval $[t_i,t_f]$ into $N$ equal intervals $[t_k,t_{k+1}]$ of length $\\epsilon$, where $\\epsilon=t_{k+1}-t_k=(t_f-t_i)/N$.\n", "\n", "Then we can insert $N-1$ resolutions of identity ($\\int_{-\\infty}^\\infty \\text{d} x_k \\left|x_k\\rangle\\langle x_k\\right|$) to obtain\n", "\n", "$K(x_i,x_f;t_f-t_i)= \\left[\\Pi_{k=1}^{N-1}\\int_{-\\infty}^\\infty dx_k \\right] \\left[\\Pi_{k=0}^{N-1} K(x_i,x_f;\\epsilon = (t_f-t_i)/N)\\right]$,\n", "\n", "where $x_f=x_N$ and $x_i=x_0$. In the continuous limit, we would have \n", "\n", "$K(x_i,x_f;t_f-t_i)= \\lim_{N\\rightarrow\\infty} \\left[\\Pi_{k=1}^{N-1}\\int_{-\\infty}^\\infty dx_k \\right] \\left[\\Pi_{k=0}^{N-1} K(x_i,x_f;\\epsilon = (t_f-t_i)/N)\\right]$. (A)\n", "\n", "Let us now consider the limit $\\epsilon\\rightarrow 0$ ($N\\rightarrow \\infty$) to obtain the short time kernel $K(x_i,x_f;\\epsilon)$ and thereby switching from discrete to the continuous limit. It is known that for small $\\epsilon$ the Trotter formula implies that to a very good approximation \n", "\n", "$K(x_i,x_f;\\epsilon = (t_f-t_i)/N) \\simeq \\langle x_{k+1} \\left| e^{-i(\\hbar\\epsilon T} e^{-i/\\hbar \\epsilon V} \\right| x_k\\rangle$,\n", "\n", "which becomes exact as $\\epsilon\\rightarrow 0$. If we insert resolution of identity $\\int \\text{d}p_k \\left| p_k \\rangle\\langle p_k \\right|$, we get\n", "\n", "$K(x_i,x_f;\\epsilon) = \\int_{-\\infty}^\\infty \\text{d}p_k \\langle x_{k+1} \\left| e^{-i(\\hbar\\epsilon T} \\left| p_k \\rangle\\langle p_k \\right| e^{-i/\\hbar \\epsilon V} \\right| x_k\\rangle = \\int_{-\\infty}^\\infty \\text{d}p_k \\langle x_{k+1} \\left| p_k \\rangle\\langle p_k \\right| x_k\\rangle e^{-i/\\hbar \\epsilon \\left(\\frac{p_k}{2m} + V(x)\\right)}$\n", "\n", "$\\implies K(x_i,x_f;\\epsilon) = \\frac{1}{2\\pi \\hbar}\\int_{-\\infty}^\\infty \\text{d}p_k e^{i/\\hbar \\epsilon \\left[p_k\\frac{x_{k+1}-x_k}{\\epsilon}-\\mathcal{H}(p_k,x_k) \\right]}$. (B)\n", "\n", "Hence, inserting (B) into (A) we get\n", "\n", "$K(x_i,x_f;t_f-t_i) = \\lim_{N\\rightarrow \\infty}\\left[\\Pi_{k=1}^{N-1}\\int_{-\\infty}^\\infty dx_k \\right] \\left \\{ \\Pi_{k=0}^{N-1} \\int_{-\\infty}^\\infty \\text{d}p_k e^{i/\\hbar \\epsilon \\left[p_k\\frac{x_{k+1}-x_k}{\\epsilon}-\\mathcal{H}(p_k,x_k) \\right]} \\right\\}$. (C)\n", "\n", "We can simplify the exponent of the integrand in the limiting case $N\\rightarrow \\infty$, \n", "\n", "$\\lim_{N\\rightarrow \\infty} \\epsilon \\sum_{k=0}^{N-1}\\left[p_k\\frac{x_{k+1}-x_k}{\\epsilon}-\\mathcal{H}(p_k,x_k) \\right] =\\int_{t_1}^{t_2}\\text{d}t[p(t)\\dot{x}(t)-\\mathcal{H}[p(t),x(t)]]$\n", "\n", "$=\\int_{t_1}^{t_2}\\text{d}t \\mathcal{L}[x(t),\\dot{x}(t)] = \\mathcal{S}[x(t);t_f,t_i]$, (D)\n", "\n", "where $\\mathcal{L}[x(t),\\dot{x}(t)] = \\frac{m}{2}\\dot{x}(t)^2-V[x(t)]$ is the Lagrangian and $\\mathcal{S}[x(t);t_f,t_i]$ is the action between times $t_f$ and $t_i$.\n", "\n", "Furthermore we can introduce the following notation for the integrals over *paths*:\n", "\n", "$\\lim_{N\\rightarrow \\infty}\\left(\\Pi_{k=1}^{N-1} \\int_{-\\infty}^\\infty \\text{d}x_k\\right)=\\int_{x(t_i)=x_i}^{x(t_f)=x_f}\\mathcal{D}[x(t)]$, (E.1)\n", "\n", "$\\lim_{N\\rightarrow \\infty}\\left(\\Pi_{k=1}^{N-1}\\int_{-\\infty}^\\infty\\frac{\\text{d}p_k}{2\\pi\\hbar}\\right) =\\int \\mathcal{D}\\left[\\frac{p(t)}{2\\pi\\hbar}\\right]$. (E.2)\n", "\n", "Using (D) and (E) in (C), we get the path integral representation of the kernel\n", "\n", "$K(x_i,x_f;t_f-t_i)= \\int_{x(t_i)=x_i}^{x(t_f)=x_f}\\mathcal{D}[x(t)] \\int \\mathcal{D}\\left[\\frac{p(t)}{2\\pi\\hbar}\\right] e^{i/\\hbar \\mathcal{S}[x(t)]}$\n", "\n", "$\\implies \\boxed{K(x_i,x_f;t_f-t_i)= \\mathcal{N} \\int_{x(t_i)=x_i}^{x(t_f)=x_f}\\mathcal{D}[x(t)] e^{i/\\hbar \\mathcal{S}[x(t)]}}$, (F)\n", "\n", "where $\\mathcal{N}$ is the normalisation factor.\n", "\n", "Here we see that each path has a phase proportional to the action. The equation (F) implies that we sum over all paths, which in fact interfere with one another. The true quantum mechanical amplitude is determined by the constructive and destructive interferences between these paths. For example, actions that are very large compared to $\\hbar$, lead to very different phases even between nearby paths that differ only slightly, and that causes destructive interference between them. Only in the extremely close vicinity of the classical path $\\bar x(t)$, where the action changes little when the phase varies, will neighbouring paths contirbute to the interference constructively. This leads to a classical deterministic path $\\bar x(t)$, and this is why the classical approximation is valid when the action is very large compared to $\\hbar$. Hence we see how the classical laws of motion arise from quantum mechanics." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Path integral representation of the partition function\n", "**Heuristic derivation of the discrete case:** Recall the convolution property of the density matrix, we can apply it repeatedly:\n", "\n", "$\\rho(x_0,x_2,\\beta) = \\int \\rho(x_0,x_2,\\beta/2) \\rho(x_2,x_1,\\beta/2) \\text{d}x_2 = \\int \\int \\int \\rho(x_0,x_3,\\beta/4) \\rho(x_3, x_2,\\beta/4) \\rho(x_2,x_4,\\beta/4) \\rho(x_4,x_1 ,\\beta/4) \\text{d}x_2 \\text{d}x_3 \\text{d}x_4 = \\cdots $ \n", "\n", "In other words: $\\rho(x_0,x_N,\\beta) = \\int\\int \\cdots \\int \\text{d}x_1 \\text{d}x_2 \\cdots \\text{d}x_{N-1}\\rho(x_0,x_1,\\beta/N)\\rho(x_1,x_2,\\beta/N)\\cdots\\rho(x_{N-1},x_N,\\beta/N)$. The variables $x_k$ in this integral is called a *path*. We can imagine the variable $x_k$ to be at position $x_k$ at given slice $k\\beta/N$ of an imaginary time variable $\\tau$ that goes from $0$ to $\\beta$ in steps of $\\Delta\\tau=\\beta/N$. Density matrices and partition functions can thus be expressed as multiple integrals over path variables, which are none other than the path integrals that were introduced in the previous subsection.\n", "\n", "Given the unnormalised density matrix $\\rho_u$, the discrete partition $Z_d(\\beta)$ function can be written as a path integral for all ***closed*** paths (because of the trace property), i.e., paths with the same beginning and end points ($x_0=x_N$), over a “time” interval $−i\\hbar\\beta$.\n", "\n", "$Z_d(\\beta)= \\text{Tr}(e^{-\\beta \\mathcal{H}}) = \\text{Tr}(\\rho_u(x_0,x_N,\\beta) )=\\int \\text{d}x_0 \\rho_u (x_0,x_N=x_0,\\beta) $ $ = \\int \\int\\int \\cdots \\int \\text{d}x_0 \\text{d}x_1 \\text{d}x_2 \\cdots \\text{d}x_{N-1}\\rho_u(x_0,x_1,\\beta/N)\\rho_u(x_1,x_2,\\beta/N)\\cdots\\rho_u(x_{N-1},x_N,\\beta/N)\\rho_u(x_{N-1},x_0,\\beta/N)$. \n", "\n", "The integrand is the probabilistic weight $\\Phi\\left[\\{x_i\\}\\right]$ of the discrete path consisting of points $\\{x_i\\}$. The continuous case can be obtained by taking the limit $N\\rightarrow \\infty$. By defining\n", "\n", "$\\Phi[x(\\tau)] = \\lim_{N\\rightarrow \\infty} \\rho_u(x_0,x_1,\\beta/N)\\cdots \\rho_u(x_{N-1},x_N,\\beta/N)$, (G)\n", "\n", "(note that this is the probability weight of a particular continuous path), and by using (E.1), we can express the continuous partition function $Z(\\beta)$ as\n", "\n", "$Z(\\beta) = \\int_{x(0)}^{x(\\hbar \\beta)=x(0)}\\mathcal{D}[x(\\tau)] \\Phi[x(\\tau)]$. (H)\n", "\n", "But what is $\\Phi[x(\\tau)]$?\n", "\n", "**Derivation of the continuous case:** Again we start from $Z(\\beta)= \\text{Tr}(e^{-\\beta \\mathcal{H}})$. The main point of the argument that follows is the operational resemblance between the unitary time evolution operator $U(t)=e^{-(i/\\hbar) t\\mathcal{H}}$ and the unnormalised density matrix $e^{-\\beta \\mathcal{H}}$: the former is used to define the kernel which reads $K(x,x';t)=\\langle x \\left| e^{-(i/\\hbar) t\\mathcal{H}} \\right| x' \\rangle$; and the latter is used in defining the density matrix which reads $\\rho(x,x';\\beta)=\\langle x \\left| e^{-\\beta \\mathcal{H}} \\right| x' \\rangle$. If we regard $\\beta$ as the analytic continuation of the real time $t$ to the imaginary values: $t\\rightarrow i \\tau \\rightarrow i \\hbar \\beta$, and $t=t_i-t_f$, we get the cousin of the partition function that lives in the imaginary spacetime (i.e. Euclidian rather than Minkowskian)\n", "\n", "$Z\\left[\\beta\\rightarrow -\\frac{i}{\\hbar}(t_f-t_i)\\right]=\\text{Tr}\\left[U(t_f-t_i)\\right]=\\int_{-\\infty}^\\infty \\text{d}x \\langle x \\left| U(t_f-t_i) \\right| x \\rangle$\n", "\n", "$=\\int_{-\\infty}^\\infty \\text{d}x K(x,x;t_f-t_i)$\n", "\n", "$=\\int_{-\\infty}^\\infty \\text{d}x \\mathcal{N} \\int_{x(t_i)=x}^{x(t_f)=x}\\mathcal{D}[x(t)] e^{i/\\hbar \\int_{t_i}^{t_f}\\text{d}t \\mathcal{L}[x(t),\\dot{x}(t)]} $ (using (F)) \n", "\n", "$=\\mathcal{N} \\int_{x(t_f)=x(t_i)}\\mathcal{D}[x(t)] e^{i/\\hbar \\int_{t_i}^{t_f}\\text{d}t \\mathcal{L}[x(t),\\dot{x}(t)]} = \\mathcal{N} \\int_{x(t_f)=x(t_i)}\\mathcal{D}[x(t)] e^{i/\\hbar \\int_{t_i}^{t_f}\\text{d}t \\left[\\frac{m}{2}\\dot{x}(t)^2-V[x(t)]\\right]}$,\n", "\n", "which means that one is integrating not over all paths but over all *closed* paths (loops) at $x$. We are now ready to get the path integral representation of the real partition function by making the transformations $t\\rightarrow i\\tau$ so that $t_i\\rightarrow 0$ and $t_f\\rightarrow -i\\hbar \\beta$ (also note that $\\dot{x(t)}=\\frac{\\partial x(t)}{\\partial t}\\rightarrow -i \\frac{\\partial x(\\tau)} {\\partial \\tau} = -i x'(\\tau) \\implies \\dot{x}(t)^2 \\rightarrow -x'(\\tau)^2$):\n", "\n", "$\\implies Z(\\beta)=\\mathcal{N} \\int_{x(\\hbar \\beta)=x(0)}\\mathcal{D}[x(\\tau)] e^{-\\frac{1}{\\hbar} \\int_{0}^{\\beta \\hbar}\\text{d}\\tau\\left( \\frac{m}{2}x'(\\tau)^2+V[x(\\tau)]\\right)}$\n", "\n", "$\\implies \\boxed{ Z(\\beta)=\\mathcal{N} \\int_{x(\\hbar \\beta)=x(0)}\\mathcal{D}[x(\\tau)] e^{-\\frac{1}{\\hbar} \\int_{0}^{\\beta \\hbar}\\text{d}\\tau \\mathcal{H}[p(\\tau),x(\\tau)]} }$. (I)\n", "\n", "Notice that by comparing (H) and (I) we get an expression for the probabilistic weight $\\Phi[x(\\tau)]$ of a particular path $x(\\tau)$, that is \n", "\n", "$\\Phi[x(\\tau)] = \\lim_{N\\rightarrow \\infty} \\rho_u(x_0,x_1;\\beta/N)\\cdots \\rho_u(x_{N-1},x_N;\\beta/N) = \\exp{\\left\\{ e^{-\\frac{1}{\\hbar} \\int_{0}^{\\beta \\hbar}\\text{d}\\tau \\mathcal{H}[p(\\tau),x(\\tau)]}\\right\\}}$ (J), which is very intuitive, considering the definition of the unnormalised density matrix $\\rho_u$. This is an intriguing result, since we were able to obtain the complete statistical description of a quantum mechanical system without the appearance of complex numbers. \n", "\n", "Because of this reason, using (J) it is easy to see why some paths contribute very little to the path integral: those are paths for which the exponent is very large due to high energy, and thus the integrand is negligibly small. *Furthermore, it is unnecessary to consider whether or not nearby paths cancel each other's contributions, for in the present case they do not interfere (since no complex numbers involved) i.e. all contributions add together with some being large and others small.*\n", "\n", "#### Path integral Monte Carlo\n", "\n", "In the algorithm, so called the *naïve path integral (Markov-chain) Monte Carlo*, we move from one path configuration consisting of $\\{x_i\\}$ to another one consisting of $\\{x'_i\\}$ by choosing a single position $x_k$ and by making a little displacement $\\Delta x$ that can be positive or negative. We compute the weight before ($\\Phi[\\{x_i\\}]$) this move and after ($\\Phi[\\{x'_i\\}]$) the move and accept the move with the Metropolis acceptance rate (reject with certainty if the new weight is greater than the old one, smaller the new weight is, the higher the acceptance rate). Defining $\\epsilon \\equiv \\beta/N$, we can approximate $\\Phi[\\{x_i\\}]$ by making a Trotter decomposition *only around the point $x_k$*:\n", "\n", "$\\Phi\\left[\\{x_i\\}\\right]\\approx \\cdots \\rho^\\text{free}(x_{k-1},x_k;\\epsilon) e^{-\\frac{1}{2}\\epsilon V(x_k)} e^{-\\frac{1}{2}\\epsilon V(x_k)} \\rho^\\text{free}(x_{k},x_{k+1};\\epsilon)\\cdots$.\n", "\n", "Therefore, the acceptance ratio $\\frac{\\Phi\\left[\\{x'_i\\}\\right]}{\\Phi\\left[\\{x_i\\}\\right]}$ can be approximated as\n", "\n", "\n", "$\\frac{\\Phi\\left[\\{x'_i\\}\\right]}{\\Phi\\left[\\{x_i\\}\\right]}\\approx\\frac{\\rho^\\text{free}(x_{k-1},x'_k;\\epsilon) e^{-\\epsilon V(x'_k)}\\rho^\\text{free}(x'_k,x_{k+1};\\epsilon)}{\\rho^\\text{free}(x_{k-1},x_k;\\epsilon) e^{-\\epsilon V(x_k)} \\rho^\\text{free}(x_k,x_{k+1};\\epsilon)}$.\n", "\n", "This is implemented in the following program." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab qt\n", "import math, random, pylab, os\n", "\n", "# Exact quantum position distribution:\n", "def p_quant(x, beta):\n", " p_q = sqrt(tanh(beta / 2.0) / pi) * exp(- x**2.0 * tanh(beta / 2.0))\n", " return p_q\n", "\n", "def rho_free(x, y, beta): # free off-diagonal density matrix\n", " return math.exp(-(x - y) ** 2 / (2.0 * beta))\n", "\n", "output_dir = 'snapshots_naive_harmonic_path'\n", "if not os.path.exists(output_dir): os.makedirs(output_dir)\n", "\n", "fig = pylab.figure(figsize=(6, 10))\n", "def show_path(x, k, x_old, Accepted, hist_data, step, fig):\n", " pylab.clf()\n", " path = x + [x[0]] #Final position is the same as the initial position. \n", " #Note that this notation appends the first element of x as a new element to x \n", " y_axis = range(len(x) + 1) #construct the imaginary time axis\n", " \n", " ax = fig.add_subplot(2, 1, 1)\n", " #Plot the paths\n", " if Accepted:\n", " old_path = x[:] #save the updated path as the old path\n", " old_path[k] = x_old #revert the update to get the actual old path\n", " old_path = old_path + [old_path[0]] #final position is the initial position\n", " ax.plot(old_path, y_axis, 'ko--', label='old path')\n", " if not Accepted and step !=0:\n", " old_path = x[:]\n", " old_path[k] = x_old \n", " old_path = old_path + [old_path[0]]\n", " ax.plot(old_path, y_axis, 'ro-', label='rejection', linewidth=3)\n", " ax.plot(path, y_axis, 'bo-', label='new path') #plot the new path\n", " ax.legend()\n", " ax.set_xlim(-2.5, 2.5)\n", " ax.set_ylabel('$\\\\tau$', fontsize=14)\n", " ax.set_title('Naive path integral Monte Carlo, step %i' % step)\n", " ax.grid()\n", " \n", " #Plot the histogram\n", " ax = fig.add_subplot(2, 1, 2)\n", " x = [a / 10.0 for a in range(-100, 100)]\n", " y = [p_quant(a, beta) for a in x]\n", " ax.plot(x, y, c='gray', linewidth=1.0, label='Exact quantum distribution')\n", " ax.hist(hist_data, 10, histtype='step', normed = 'True', label='Path integral Monte Carlo') #histogram of the sample\n", " ax.set_title('Position distribution at $T=%.2f$' % T)\n", " ax.set_xlim(-2.5, 2.5) #restrict the range over which the histogram is shown\n", " ax.set_xlabel('$x$', fontsize = 14)\n", " ax.set_ylabel('$\\pi(x)=e^{-\\\\beta E_n}|\\psi_n(x)|^2$', fontsize = 14)\n", " ax.legend(fontsize = 6)\n", " ax.grid()\n", " \n", " pylab.pause(0.2)\n", " pylab.savefig(output_dir + '/snapshot_%05i.png' % step)\n", "\n", "beta = 4.0 # inverse temperature\n", "T = 1 / beta\n", "N = 8 # number of (imagimary time) slices\n", "dtau = beta / N\n", "delta = 1.0 # maximum displacement on one slice\n", "n_steps = 4 # number of Monte Carlo steps\n", "hist_data = []\n", "x = [random.uniform(-1.0, 1.0) for k in range(N)] # initial path (a position for each time)\n", "show_path(x, 0, 0.0, False, hist_data, 0, fig) #show the initial path\n", "\n", "for step in range(n_steps):\n", " #print 'step',step\n", " k = random.randint(0, N - 1) # randomly choose slice\n", " knext, kprev = (k + 1) % N, (k - 1) % N # next/previous slices\n", " x_old = x[k]\n", " x_new = x[k] + random.uniform(-delta, delta) # new position at slice k\n", " #calculate the weight before and after the move\n", " old_weight = (rho_free(x[knext], x_old, dtau) *\n", " rho_free(x_old, x[kprev], dtau) *\n", " math.exp(-0.5 * dtau * x_old ** 2))\n", " new_weight = (rho_free(x[knext], x_new, dtau) *\n", " rho_free(x_new, x[kprev], dtau) *\n", " math.exp(-0.5 * dtau * x_new ** 2))\n", " if random.uniform(0.0, 1.0) < new_weight / old_weight: #accept with metropolis acceptance rate\n", " x[k] = x_new\n", " Accepted = True\n", " else:\n", " Accepted = False\n", " show_path(x, k, x_old, Accepted, hist_data, step + 1, fig) \n", " hist_data.append(x[k]) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![caption](path_integral.gif)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the above program is very slow, as it takes very long to explore all of the available phase space." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Unitary time evolution\n", "\n", "Taking advantage of the Fourier transforms, the Trotter decomposition can also be used to efficiently simulate the unitary time evolution of a wavefunction as demonstrated by the following algorithm." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab qt\n", "import numpy, pylab, os\n", "\n", "#Define the direct and inverse Fourier transformations:\n", "def fourier_x_to_p(phi_x, dx):\n", " phi_p = [(phi_x * numpy.exp(-1j * p * grid_x)).sum() * dx for p in grid_p]\n", " return numpy.array(phi_p)\n", "\n", "def fourier_p_to_x(phi_p, dp):\n", " phi_x = [(phi_p * numpy.exp(1j * x * grid_p)).sum() * dp for x in grid_x]\n", " return numpy.array(phi_x) / (2.0 * numpy.pi)\n", "\n", "#The time evolution algorithm (using the Trotter decomposition)\n", "def time_step_evolution(psi0, potential, grid_x, grid_p, dx, dp, delta_t):\n", " psi0 = numpy.exp(-1j * potential * delta_t / 2.0) * psi0 #potential part of U (multiplicative)\n", " psi0 = fourier_x_to_p(psi0, dx) #pass to the momentum space to apply the kinetic energy part\n", " psi0 = numpy.exp(-1j * grid_p ** 2 * delta_t / 2.0) * psi0 #kinetic part of U (multiplicative)\n", " psi0 = fourier_p_to_x(psi0, dp) #return to the position space\n", " psi0 = numpy.exp(-1j * potential * delta_t / 2.0) * psi0 #potential part of U (multiplicative)\n", " return psi0\n", "\n", "#Potential function (barrier potential to demonstrate tunneling):\n", "def funct_potential(x):\n", " if x < -8.0: return (x + 8.0) ** 2 #barrier on the left hand side\n", " elif x <= -1.0: return 0.0 #0 potential in between the left wall and the bump barrier\n", " elif x < 1.0: return numpy.exp(-1.0 / (1.0 - x ** 2)) / numpy.exp(-1.0) #gaussian bump barrier\n", " else: return 0.0 #0 potential elsewhere\n", " \n", "#movie output of the time evolution\n", "output_dir = 'snapshots_time_evolution'\n", "if not os.path.exists(output_dir): os.makedirs(output_dir)\n", "def show(x, psi, pot, time, timestep):\n", " pylab.clf()\n", " pylab.plot(x, psi, 'g', linewidth = 2.0, label = '$|\\psi(x)|^2$') #plot wf in green colour\n", " pylab.xlim(-10, 15)\n", " pylab.ylim(-0.1, 1.15)\n", " pylab.plot(x, pot, 'k', linewidth = 2.0, label = '$V(x)$') #plot potential in black colour\n", " pylab.xlabel('$x$', fontsize = 20)\n", " pylab.title('time = %s' % time)\n", " pylab.legend(loc=1)\n", " pylab.savefig(output_dir + '/snapshot_%05i.png' % timestep)\n", " timestep += 1 #updtate the current time step\n", " pylab.pause(0.1)\n", " pylab.show()\n", "\n", "steps = 800 #total number of position (momentum) steps\n", "x_min = -12.0 #minimum position (momentum)\n", "x_max = 40.0 #maximum position (momentum)\n", "grid_x = numpy.linspace(x_min, x_max, steps) #position grid\n", "grid_p = numpy.linspace(x_min, x_max, steps) #momentum grid\n", "dx = grid_x[1] - grid_x[0] #position step\n", "dp = grid_p[1] - grid_p[0] #momentum step\n", "delta_t = 0.05 #time step width\n", "t_max = 16.0 #maximum time\n", "\n", "potential = [funct_potential(x) for x in grid_x] #save the potential on the position grid\n", "potential = numpy.array(potential) \n", "# initial state:\n", "x0 = -8.0 #centre location\n", "sigma = .5 #width of the gaussian\n", "psi = numpy.exp(-(grid_x - x0) ** 2 / (2.0 * sigma ** 2) ) #initial state is a gaussian\n", "psi /= numpy.sqrt( sigma * numpy.sqrt( numpy.pi ) ) #normalisation\n", "# time evolution\n", "time = 0.0 #initialise the time\n", "timestep = 0 #initialise the current timestep\n", "while time < t_max:\n", " if timestep % 1 == 0: \n", " show(grid_x, numpy.absolute(psi) ** 2.0, potential, time, timestep) #plot the wavefunction\n", " #print time\n", " time += delta_t #update the current time\n", " timestep += 1 #update the current timestep\n", " psi = time_step_evolution(psi, potential, grid_x, grid_p, dx, dp, delta_t) #update the wf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![caption](tunneling.gif)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Harmonic and anharmonic oscillators" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Harmonic oscillator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Markov-chain sampling by Metropolis acceptance using exact stationary states (Hermite polynomials)\n", "\n", "Probability distribution at $T=0$ is $|\\psi_0(x)|^2$. We can easily develop a Monte Carlo scheme for this system, because the stationary states of the harmonic oscillator are known, i.e. Hermite polynomials. In the following section, we obtain this distribution for $0$ temperature and finite temperatures by using the Markov-chain Monte Carlo algorithms implementing the Metropolis acceptance rate." ] }, { "cell_type": "code", "execution_count": 139, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import random, math, pylab\n", "from math import *\n", "\n", "def psi_0_sq(x):\n", " psi = exp(- x ** 2.0 / 2.0) / pi ** (1.0 / 4.0)\n", " return abs(psi) ** 2.0\n", "\n", "xx = 0.0\n", "delta = 0.1\n", "hist_data = []\n", "for k in range(1000000):\n", " x_new = xx + random.uniform(-delta, delta)\n", " if random.uniform(0.0, 1.0) < psi_0_sq(x_new) / psi_0_sq(xx): \n", " xx = x_new \n", " hist_data.append(xx)\n", " #print x\n", " \n", "pylab.hist(hist_data, 500, normed = 'True', label='Markov-chain sampling') #histogram of the sample\n", "x = [a / 10.0 for a in range(-30, 30)]\n", "y = [psi_0_sq(a) for a in x]\n", "pylab.plot(x, y, c='red', linewidth=2.0, label='Exact quantum')\n", "pylab.title('Position distribution at $T=0$', fontsize = 13)\n", "pylab.xlabel('$x$', fontsize = 15)\n", "pylab.ylabel('$\\pi(x)=|\\psi_0(x)|^2$', fontsize = 15)\n", "pylab.legend()\n", "pylab.savefig('plot_T0_prob.png')\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Probability distribution at a finite temperature is given by $e^{-\\beta E_n}|\\psi_n(x)|^2$, where $\\beta=1/T$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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+SHJyMmXKlGHJkiXce++9dOnShblz5/Lxxx/TokUL+7lHjhxJ9+7dqVevHq1atbK3ZBQsWJARI0bQuHFjKleuTM2aNe3HjBkzhsaNG1OpUiVCQkLSTWwpQkNDKVCgAGFhYURERPDMM89QuXJlQkJCqFOnDvXq1cuBT/X6IelVIT1BRAoAu4G2wGFgLfCIqm5PY9+pwAJVnZ1q/SrgZVVd6rCuvKrGiFXvHQtcVtVretI5atCggZrJ5Ax3Cn5uNhtXvct9Vdfy260QcAF+/RYKJVQiouvrHC1a2qlyrrrvk4GdmzdTCzjjncC+ElYtKOACVPQqgVSpkmlPtetJyuSQpUs79xkbmdu5cye1atW6ap2IrFfVBs4cn6ea3VQ1ERiI1WS2E/hBVbeLyGgRuQ9ARBqKSDTQFfhcROyJSUSCsGpOf6UqerqIbAW2AqWBN3L6WgzjKpcv89mcMTwW+L/Es2wKJHvV4qFH33E68WSJjw/UrElx9aVaLIjCicJwJPE0HDyYYZOZYeS0vNbshqouAhalWjfC4f1arOa4tI6Nwuq0kHp9G/dGaRhZoIr26c3M2luYVRuKXobF38CZm+oQ0XUUlwv65dy5fX2hZk2K7tpF1dOX2VvCaoIrcPYkZWN84Oabc+7ceciN2qMsL8tTNR/DuC698w6f7Z3BZw3BLwEWfAdeVOOJziNyNvGkKFgQqlWjeLIPlc9Yqw4VhbOxR8B2I94wcptJPoaRk+bPJ/LzlxliPeLBV/Pg5rhAIrqOIs63kEtFptntOjO+vlC9OqUSClD+PCCwvwRc/m8/XDSPwxm5zyQfw8gp+/ZxqH93ujwEid7WcDj37PGnT5cRnC5ULPfj8fODqlW5Oc56mDXJC/aWUJL27YUb9FkTw3NM8jGMnBAfT2L3h3nkrgvEFoL2e2D0n8KA+4dxsET277O4VPsBKFIEqViJymfgpgS4XAD+uynedEAwcp1JPoaRE15+mdH+61leCW4+B1/PgXdaP8GK7D7H4w4BAXiXDqDKafBSiC0EsZdPw8mTno4sSyIjI1mxYkWWjgkKCuKkm65z3rx5vP322y4d68448iuTfAzD3X79lcifPuSNllb35uk/wfrApkxucJ+nI/ufChW4yacQFc5aiweLweUj/1kT1+UTriQfd7rvvvsYNizDxwWNDJjkYxjudOYM5/v3JqKT9VDna8ugdXJFXrp7SN56qNPLC6pUofRlL0pcgmQviCqmaNQBtza/eWpKhbi4OHr37k1ISAihoaH8+OOP18SW1rmSkpKIiIigTp06hISEMHbsWMAa8DQ4OJjQ0FC6desGcNUUCseOHeOBBx4gLCyMsLAwe1JM73qMPPicj2Hka88+y4shRzlYHOodgeF/C0R+x7n5ZzwalryeM4lPR6afqHbu3MnMmTP5559/KFiwIAMGDGD69On07NmToUOH0r9/fxo3bkxwcDDt2rUDYPLkyZQsWZJLly7RsGFDOnfuTHJyMn379mXZsmVUrlyZU6dOUbJkSfr374+/vz8vvHDtaFljxoyhWLFibN26FcA+tpujtM4VFRXF4cOH2bZtGwBnzlj/3d5++20OHDiAr6+vfZ2jwYMH06pVK+bMmUNSUhJxcXHpnqNUqVJZ/JSvTyb5GIa7LFzI78um8nlPaxK4qT9DwReHEeThxOMpnpxS4ffff2fGjBn25bSmVEjrXDVq1GD//v0MGjSIDh062JNiaGgojz76KJ06daJTp07XlPXnn3/y9ddfA+Dt7U2xYsXSPYdJPhaTfAzDHc6f58LTfXniAWtxZCSEBNS2pjsY+btHQ4OMaygkJMD27RzwTyS2EPjHQ41LhZGaNbPVVOjJKRUyOya9c5UoUYLNmzezePFiJkyYwA8//MDkyZNZuHAhy5YtY968eYwZM4bt268ZbtLpcxgWc8/HMNxhxAhGV4vhYHGoGwNDV3rBtGnWw515XcGCULEiFc5ZNbY4H4jVC3DiRLaK9eSUCu3ateOTTz6xL6dudkvvXCn3oTp37syYMWPYsGGDfYqE22+/nXfffdc+2Vzqa/3ss88A677RuXPn0j2HYTHJxzCya+NGtn0/jg+bWr3bJi6AAi+8BPXru/48jhPcWnaJEhQoWpzAc9ZidFFIjIm2akUucpxSITQ0lDvvvJOYmBj++usv1q5da09APj4+TJkyhfbt25OYmEhoaCjDhw9Pc0qFsLAwHn7Ymn3v3nvvZc6cOWl2OHjttdc4ffo0derUISwsjKVLl161Pb1zHT58mNatWxMeHk5ERARvvfUWSUlJ9OjRg5CQEOrWrcuzzz5L8eLFrypv3LhxLF26lJCQEOrXr8/27dvTPYdhyVNTKuQlZkoFwylJSSQ3bUKrOutYXgmeWgufbg+i5oPv8+8HnXM0+UDG0yukNeR9huLj0W3b2F0imfO+UPoiBHmVhCpV3BCpcb25rqZUMIx8Z/Jkvo23Ek+ZOPi/P4AJE3JnwFB38/FBbrmFSmetGtzJQhAXdwoymVTNMFxhko9huOrsWeJGvcKwO6zF95bAiorN4J57PBtXdpQpg59PIcrZbmkcKgp66D8z9I7hdib5GIarxozhrZoniSkCjaKh83YfxrTta9+c001uOUIEKlakXJzV+eCCD8TqpXw39I6R95nkYxiu2LWLA9M+4oNm1uK4X+HzJl2JKRqQq0knR87l7493iZLcYut8cLgoJB05bEa+NtzKJB/DcMXQoQy9PYkrBeDRLRB4LoBJjR7wSCgpCcitiSgwkFJXhMLxkOANR/0S4ehR95Vv3PBM8jGMrFq5knVr5zKrtjUz6du/w9ute+fPTgbp8fFBypWngq32c8wfEk4eg/h4z8ZlXDfMCAeGkRWqMGwYr7S1FgetgeP+NVhQs4VHw3Km1uOemtH/aj8ZdfNOISL06NGDb775BoDExETKly9P48aNWbBggdNnjYyM5P3338/SMa4aNWpUumPGpeeee+7hu+++u+b5n7zA8bObN28eO3bsyBOjcTtV8xGRB0RksIjUSLV+oLsDEpH2IrJLRPaKyDWfkIi0FJENIpIoIl1SbUsSkU221zyH9ZVFZLWI7BGRmSLi4+64jRvE4sUs/W8ZS6pC0cswdDm826pX3hqxOg8pXLgw27Zt45JtqoYlS5Zwyy23ZKmMxHxwr2nRokV5MvGklpemgcg0+YjI28AQ4FZgiYg847C5jzuDERFvYAJwNxAMdBeR4FS7/QdEAN+lUcQlVQ23vRwnT3kHGKuq1YDTwOPujNu4QSQno6+8zMu2rtUvroBt5eqxqmKoZ+NykBd72N19990sXGjF9f3339O9e3f7tjVr1tCsWTPq1q1Ls2bN2LVrF2BNV9C1a1fuvfde++CeKdauXUvdunXZv38/p06dolOnToSGhtKkSRO2bNlCcnIyQUFBV40+feutt3Ls2LFrYks9VUOKHTt20Lp1a6pUqcL48ePt69ObIiFlcrioqChq1apF3759qV27Nu3atbMnXkezZs2yj77QsmVLAKKiomjRogX16tWjXr169mkZIiMjadWqFQ899BDVq1dn2LBhTJ8+nUaNGhESEsK+ffsAiIiIoH///rRo0YLq1aunWUt0nAYiIiKCwYMH06xZM6pUqcLs2bMBSE5OZsCAAdSuXZuOHTtyzz332Le5kzM1nw7AHao6GKgL3Cci79m2ufvnXiNgr6ruV9V4YAZwv+MOqhqlqluAZGcKFGt0wTZAyqc3Dbh2WFrDIJMv71mzmHdxE6sDrQdKn1kF77bsmXvBZcOWaM+NrN2tWzdmzJjB5cuX2bJlC40bN7Zvq1mzJsuWLWPjxo2MHj2aV155xb5t5cqVTJs2jT///NO+bsWKFfTv35+5c+dSpUoVRo4cSd26ddmyZQv/93//R8+ePfHy8uL++++3jya9evVqgoKCKFu27FVxnThxgr59+/Ljjz+yefNmZs2aZd/277//snjxYtasWcPrr79Ogm2YocmTJ7N+/XrWrVvH+PHjiY2NveZ69+zZw9NPP8327dspXrx4mnMJjR49msWLF7N582bmzbMaacqUKcOSJUvYsGEDM2fOZPDgwfb9N2/ezLhx49i6dSvffPMNu3fvZs2aNTzxxBN8/PHH9v2ioqL466+/WLhwIf379890INOYmBiWL1/OggUL7DWin376iaioKLZu3cqXX37JypUrMyzDVc4kHy9VTQRQ1VigPRAkIl85eXxW3AIccliOtq1zlp+IrBORVSKSkmBKAWdSriGjMkWkn+34dSeyOaiicZ1JSCBp+Kv2ez2vLYPIKi3YXu5Wz8aVD4SGhhIVFcX333/PPakewD179ixdu3alTp06PPvss1eNFn3nnXdeNX3Czp076devH/Pnz6dixYoALF++nMceewyANm3aEBsby9mzZ3n44YeZOXMmADNmzLCPB+do1apV6U7V0KFDB3x9fSldujRlypSx15rGjx9PWFgYTZo0sU+RkFrlypUJD7emS69fvz5RUVHX7NO8eXMiIiL44osvSEpKAiAhIYG+ffsSEhJC165d2bFjh33/hg0bUr58eXx9falataq9NhgSEnJV+Q899BBeXl5Uq1aNKlWq8O+//15zbkedOnXCy8uL4OBg+zUuX76crl274uXlRbly5bj99tszLMNVziSPGBGpl7Jgq5E8DChQx83xpFWTysqj1RVt4wo9AnwkIlWzUqaqTlLVBqraICAgIAunNa57U6YwvdA+dpSBSmegzwbhgxY9PB1VmlLX3nKs1pOFYXfuu+8+Xnjhhaua3ACGDx/O7bffzrZt25g/f/5Vv9QLFy581b7ly5fHz8+PjRs32telNTaliNC0aVP27t3LiRMn+Pnnn3nwwQdJSkoiPDyc8PBwRowYkeG0C74Oo5F7e3uTmJh41RQJmzdvpm7dumnWLNI6NrWJEyfyxhtvcOjQIcLDw4mNjWXs2LGULVuWzZs3s27dOuIdehY6lunl5WVf9vLyuqr81NeT2VQUjuWmfJa5Nd6nM8knAjjiuEJVk1X1CcDdXXyigQoOy4Gpz50RVT1i+3c/EInVTHgSKC4iKT37slSmYXDxIvFjRjGytbX4+lKYW7sdB0pm7cb5dSc62ulhd/r06cOIESMICQm5av3Zs2ftHRCmTp2aYRnFixdn4cKFvPLKK0RGRgLQsmVLpk+fDlj3RkqXLk3RokURER544AGee+45atWqRalSpfD29mbTpk1s2rSJ0aNHpztVQ3rcOUXCvn37aNy4MaNHj6Z06dIcOnSIs2fPUr58eby8vPjmm2/sNaKsmDVrFsnJyezbt4/9+/dTo0aNzA9K5bbbbuPHH38kOTmZY8eO2T9rd8u0q7WqRmewbYV7w2EtUE1EKgOHgW5YtZhMiUgJ4KKqXhGR0kBz4F1VVRFZCnTBuofUC5jr5riN60C693s++4wvyscQVQKCj0OP3b40j+ie9r552LyBze3vQwOLsyX6DKGBWeihFRdH4q5/2VoWkrzgXOwFip49C0708goMDGTIkCHXrH/ppZfo1asXH374IW3atMm0nLJlyzJ//nzuvvtuJk+ezKhRo+jduzehoaEUKlSIadOm2fd9+OGHadiwYbpJzXGqhuTkZPs9l/S0b9+eiRMnEhoaSo0aNbI1RcKLL77Inj17UFXatm1LWFgYAwYMoHPnzsyaNYvbb7/9mpqfM2rUqEGrVq04duwYEydOxM8v68+ede7cmT/++IM6depQvXp1GjdubJ+Z1Z2cnlJBRCpm50Sq+p+T57kH+AjwBiar6psiMhpYp6rzRKQhMAcoAVwGjqpqbRFpBnyO1RHBC/hIVb+ylVkFK/GUBDYCPVT1SkZxmCkVbiyOieeq51cuXSK+ahBVux0nuhjMngknizzIW7e7taOn20W93cE+5H1azW5pJR+nktGePcQkneVwUShyBWpcLgzZnPHUcI+IiAg6duxIly5dMt85E3Fxcfj7+xMbG0ujRo34559/KFeu3FX7ZHdKhaw8ZBpF1u6/2OOxHeftzM6qughYlGrdCIf3a7GazlIftwIISb3etm0/Vk86w8hU0LCF/0tAX33F1+WtxFP7ODzwXyHq9+ns2QCzwO33e265hTI7z3KnQKkCAAAgAElEQVTUH877wvnzFyhy/jwULere8xge1bFjR86cOUN8fDzDhw+/JvG4Q1aST2W3n90w8oD0mtuqvfgzO2e+zVu2IdteXQZf1G7P6ULub4LICdGnL1G2SNrbHJNSlprfChXCu2gxylw4S0wRiPGHIjExJvnkAZndM8uKnLrP48jp5KOqB3MyEMPIazpv/YOZxQ+zvyRUi4X7/y1Aqyc9M3ioKxTNsEcXXFszcioRlS9P2d1nOVYYzvnBhfPnKXz+PBRJJ9MZ1x139IgzA4saRloSE+m/6gfetB4+Z9hy+CG0PSf8S3g2LicFDVvIwTMJJF48l+Uvikyb6vz9KeBflDIXrcWYIkBMjGuBGvmOqhIbG+tSZwZHLg8sKiIhWPdRygF+wClgN7BCVU9nKyrD8LDnOr1E85uPszMAKp6BHjsK0Cof3esB+Hj1aQYBlYqfRDIZjGRJqu5AO8/fRPTpSwSWuCntAy5fJun4SWKLWs8yXDh/Ep+LF8HhuRHj+uXn50dg4DW33rMkS8nH1mvsKeBRoCxWz7IzwBWgOFAISBaRv4AvgZmq6tQwOIaRV3glJzFg5Q881NVaHvoPzK7Zlpii+evB43NXknlz2bXDv2RFhiNXt2rFpMLL+LgxdNsK38ffC/Pmpb+/YThwutlNRL4EtgPhwGisBzj9VDVAVQNV1R8oA9wLbAXeBXaKyG3uD9swcs7du1awu9RhNpaHcueh50bhsyZdPR2WR2Q41t3w4bz4jzXd9sw6sGvFfNi0KfeCM/K1rNzzuQzUVNU7VXWiqm5R1asewVXVk6r6i6o+A1QCRpC1sdkMI1el/nIVTebplTMYY7vX8+IKWFzzdg4Vd39X03yvbVsq1GpMxCZQgbdvA95809NRGfmE08lHVQdmpcebbQiemao607XQDCP3tdm3lmOFD7KqApS6CH3Xwac3aK0nUyLw2msMXQ5eyfBNGET9Phts0yIYRkZc6u0mIh9JZiPWGUY+1G/1T7xnG4VmyCr4q2oL9pWqkPFBN7IOHagaVJdu26whd8Y1Bj74wNNRGfmAq12tuwM/i0ihtDaKyN2uh2QYnhF+ZBeF47fzSzUoFA8D1sJnTbI/VMl1TQReeokXbaM8flEfTv8wDdKYuM0wHLmafJpgzWz6t4iUT1kpIneJyGog5ydaNww367f6Rz5oar3vsxF2lglje9mqng0qP+jShXC/IO7YBxd84POQeHCY4Mww0uJS8lHVA0AzrC7+a0Skj4isAH4BzgKt3RahYeSCSqePEBKzgumh1v2LZ1fBpEYPejqs/KFAAXj2WV6w1X7GNYYrn0+AuDjPxmXkaS6PcKCqZ4H3sUaX/gLrQdOmqtpOVf92U3yGkSseXzuXCY0hwRs674QrBYJYVrle5gcalj59aHeqOKFH4WgR+C7wDEye7OmojDzM1Q4Hd4nIcuBXYAXWVAbBWE1xhpGvlLh4lva7ljDRNhD8CytstR7TpwawuqOn9bzPVev8/ZEBT9trP+83Ax37IaQxi6dhgOs1n1+wRjVoZavpDAAGA5NF5HW3RWcYOSjly7PnhoV8GxbPWT9oGQWB50ozv1ZLzwaXHw0axMN7fLjlHOwoA78UPAizZ3s6KiOPcjX5tFbVtqq6PGWFqk4COgKDRWSGW6IzjBySknj8Ei7TfdN8PrJNSvnCCpjc4D4SvV0e9vCGkPL5XVX7KVsWnx69eMY2u/T7zYD33nN6qm3jxuJqh4Nl6axfAtyGmbjNyCe6bPuTP6qc51AxqHkCWkTdxIyw9p4OK8/KtPnt+efpu8Ga5XRpZVgfswGWLs3FCI38wu1TKqjqdqCxu8s1DHfzSk6iz9qfrF/owPMrYUbde4jzTfPxNcMZNWpQ7K77edI2A7299mMYqWRlYNHHRMTZqbBP2I65VURauBqcYeSkNvvW8V+xo2wqD2Xi4KGt3kyuf5+nw8rzMhxsFODFFxmyGgokwaza8N/KX2HnztwJzsg3slLzeR7YJyJjRCQsvZ1EpJSIPCoi84GNQPn09jUMT0j58uy9fq41HAzWaAZLarTieJFSHowsf7MnpebNCQxuQtcd1pA7nzYExo/3aGxG3pOVgUXDgaHA7cBGETknIqtFZKGI/CQif4rIAeA4MA7YhzUK9g9ZCUhE2ovILhHZKyLD0tjeUkQ2iEiiiHRxWB8uIitFZLuIbBGRhx22TRWRAyKyyfYKz0pMxvWn+okobj67hXk1rCkBnlyPqfW40zPP2DseTKoPF76fBqdOeTYmI0/J0j0f2yjVtwHVgBeBTUAiUBg4BkwD2gPlVfUZVT2clfJtzXoTgLuxnhvqLiLBqXb7D4gAvku1/iLQU1Vr22L4SEQcJ6N/UVXDbS8z6cgNLmL9fCY0gmQv6LYN/isezPZy5jG1jGTa3Oa4z4MP0kgCaXIITt8E3956Cb78MocjNPITV3u77VPVz1X1SVW9X1XvUtXuqjpKVZeoaoKL8TQC9qrqflWNB2YA96c6d5SqbsGaRdVx/W5V3WN7fwSrBpa/pp403C6tLsHFL52j3e4/+dI2gMGg1TDF1Hqy5ZrEVLAgDBzIkNXW4rgmoB+PhwRXvxqM643be7tl0y3AIYflaFyYjE5EGgE+WE1/Kd60NceNFZE0J5oXkX4isk5E1p04cSKrpzXykIx+pXffvJjZtRM46wdND0H5uAB+q940F6O7QfTtS+cDftxyDnYGwBLfwzBnjqejMvIItyYfEXlFRI7YvuS/FpHnRKRNVopIY12WnlCzjbL9DdBbVVNqRy8DNYGGQEmse1fXnkh1kqo2UNUGAQGm0nS9cExEt744lx4bFjDe1tFgyCr4pl4Hkryc6shpOME+HE/JkhTs0Yun11jrxzUGxo3zaGxG3uHums8gIBy4C/gea7DR/lk4PhpwnLkrEDji7MEiUhRYCLymqqtS1qtqjFquAFMwD8HekIKGLaTdnlXsCIhlZwDcfA7u3uPDjNC7PB3a9WvwYPqtB78EWFQddu1aAWvWeDoqIw9wd/LZpqrHbV/2v6jq/6nqQ1k4fi1QTUQqi4gP0A2Y58yBtv3nAF+r6qxU28rb/hWgE7AtCzEZ+VRaTW+9182z13oGrIUFtdpw9qYiuRzZDSQ4mFIt2tFji7X4san9GDbuTj4bReRDEbnJlYNVNREYCCwGdgI/qOp2ERktIvcBiEhDEYkGugKfi8h22+EPAS2BiDS6VE8Xka3AVqA08IbLV2jkW3WO7qXEpR0srA6+idBvPUypf6+nw7r+PfOMvePB1HA4M3cmHM5SR1jjOuTu0RNLAGFAtIjsxnrIdJNt0FGnqOoiYFGqdSMc3q/Fao5Lfdy3wLfplJmV+07Gdar3url80ghU4JGt8G9AOHsCKnk6rOvfXXdRp0QN2u7fxR9V4KvQJJ7/9FN4801PR2Z4kKvz+filtV5V+6pqI6wuzn2AZUBl18MzjKxLq7ktIO40rfYtY3Jda3nwapjSwHSvzhVeXjBkCENsd2E/aQRJkybCpUuejcvwKFeb3eJEZKeIzBCRl0XkHhEpnbJRVZNVdaeqzlDVl90Uq2G47JFNv/B9aBLnfa05e4pfLs/Sqg08HdaNo2dPOhwvRtVTEFUC5pU+BdOnezoqw4NcTT7dgB+werP1BRYAx0TkVxExj4kbeYpPYgKPbFpo3ezGqvVMq98Rlbz2mNt1rHBhvPr2Y7Dt3s9HTYCPPjJz/dzAXB3hYLaqjlTVTqpaBSgGPIg1zE6kiBR2Z5CG4ay0mtw6/Ps3628+y55SUPEMtNnvx6yQOz0Q3Y3lmum3Bw4kYosXRa7AsiDYGLsd/vjDY/EZnuXqPZ/PReQpEWkmIkVU9byqzgVaYT2XM8CtURqGq1Tpvf5/3aufXgs/17nTzNmTi+xJqGJFinbszOMbrPXjmmC6Xd/AXG13qAqMApYDZ2wjUP8IvAbsB0z/VSPXpVXrqXf4X3wS97L4VrgpAfpsgKmme7XnDBnCoDUgCt/XgWNLF8CePZ6OyvAAV5vd7lDVsljjrnUAJgGXsJ69eRBoLiJnRORvEfnEbdEaRhb1WT+Pj23jWTy2GTbf3JCDJW72bFA3smbNqFK1AffugvgC1nQLfGK+Im5Erja7hYhIAdtIBr+q6ruq2kNVQ4D3gV3AM8AGoLYb4zUMp5U/d4ImUcuZZnvUeNAaM3q1x4nAkCH2jgefNYT4aZPh3DnPxmXkOleb3TZjdbfeKCJTROQZEeksIoOwRiiYqapTVXWIqt7uvnANw3mPbVzI13WVCz7QZj/4JFVkeZCZR9DjunalzcUyBB+HmCLwY4U4mDrV01EZuczV5BMC9MYaBqcc8BIwC2sG03XAO26JzjBc5JtwhYc2/8ontia3IathaoN7rV/ehmf5+iL9n7LXfsY3Bj7+GJKTMzzMuL64es9nu6p+r6rDVPVuVb0ZKAqUUNU2qnrZvWEaRtZ02hHJiopxHCgBlU9D8/8KMyfYVMI9zd4ppH9/euwsQPFLsKoCrLm0F3791bPBGbnKbU/ZqWqcqp51V3mG4TJVeq+bZ80fgzVT6ayQu7jkk+aoUEYuCxq2EMqVo/CD3XjC1u3640aYbtc3GKeTj4hUzM4rJy/CMBw1/W8LiV4H+bMKFI6HnpuEb+p19HRYN7xrusIPHszTa8ErGWbWgaMrfoOdOz0TnJHrslLziQIOuPBKOc4wcozjF1vv9fPtD5X22gSrKzblcLEyHorMSFfDhgTVasp9uyDBGz433a5vKFlJPpWBKi68Uo4zjBxX4cxR6kav4ttQa3nQGjN6dZ42ePDV3a6/mQpnzng0JCN3OD2fj6oezMlADMMdeq2fz5R6cKkg3LUXEr2rsjbQPGqWZ3XuTOvny1PnWAzbysKsoIs8OnkyPPecpyMzcpjLHQ5EpFDK9NSGkRcUvnKRB7f+Zu9ePXi1bSgd07067ypYEBnw9NXdrj/5BJKSPBqWkfOy09ttNvCSiMwSkRnuCsgwssJx5OTO2/5gaZVLHCoG1WKhweGizK/V0sMRGmm5qvNBv348usuHEpdgTSCsjj8ACxZ4LjgjV2Qn+fyiqs+qaldV7ea2iAzDCal7Tokm02vDAntHg0Gr4fvwe7hSwMcD0RlZEhBAoa6P0He9tTi+MTB+vEdDMnJedpLPYyIySkQaioiv2yIyDBe02r+B8z6HWRYERa7AI1u8+bbuPZ4Oy3DW4MEMsHW7/qE2HFn7J2zb5umojByUneTTDvgLaAF85p5wQETai8gu2zQNw9LY3lJENohIooh0SbWtl4jssb16OayvLyJbbWWOFzE3AfIrxxrP1d2r/zdnT5+NsKxKC074l8zt8AxX1a1LpdAWdPoXElO6XX/8saejMnJQpslHRAamtV5Vz6jqUlX9UFX7uCMYEfEGJgB3A8FAdxEJTrXbf0AE8F2qY0sCI4HGQCNgpIiUsG3+DOgHVLO92rsjXiN3pSSb1E1uVWMPEXxsA9+FWPPEDFxj5uzJD9J66DSl48HEBnDlu6/h1KncD8zIFc7UfOyJRUS+ctwgIi3cHE8jYK+q7lfVeGAGcL/jDqoapapbgNSjEN4FLFHVU6p6GlgCtLf1yCuqqitVVYGvgU5ujtvwoIj185lUH64UgA674ZxfDTbfXMPTYRlZ1akTLZMDCT0Kx/3hhyqX4csvPR2VkUOcST6OTVR1U21z92BMtwCHHJajbeuyc+wttveZliki/URknYisO3HihNNBGzknrdlJHRW9HMe9O35ngkP3ajNnTz5VoADy9EB77WdcE9AJn0BiomfjMnKEM8lHM9jm7nsnaZWX0fmdOdbpMlV1kqo2UNUGAQEBTp7W8KRumxezqHo8MUUg+DjUPl6SX2o093RYhqueeIJH9vpR8iKsvxlWJR+CuXM9HZWRA5xJPhVFZKSI3AcUTLXN2cTgrGiggsNyIHAkm8dG2967UqaRh3knJ9Fz/Xw+amItD1kN39S/l0RvpwfuMPKAq2q3pUpxU7fH6Ge6XV/3nEk+T2DVHvoARUTkpIj8LSKTsCaSc6e1QDURqSwiPkA3YJ6Txy4G2olICVtHg3bAYlWNAc6LSBNbL7eegPkpdR24a/dKDhU7ydpboORF6Lzdh+/D7vJ0WEZ2DRrEU+vAOxlmB8Phjctg0yZPR2W4WabJR1V/VtVRqtpJVYOAW4HhwA6sL3y3UdVErGm4FwM7gR9UdbuIjLbVvLA9VxQNdAU+F5HttmNPAWOwEthaYLRtHcBTwJfAXmAf8Is74zbcL/W9nrTu/fRZN9de63lyPSyu0YYzNxXNjfCMnBQSQsV6t/PATqvb9cQGmNrPdSjL7ROqegaItL3cTlUXAYtSrRvh8H4tVzejOe43GZicxvp1QB33Rmp4UmjMbsqe38mPwdYv5AFrIaKr6Whw3RgyhMGDlzK7NnzeAF6dMB2/d94Bcy/2uuHMcz7TROS4iHwvIrVsTW7LRWRwbgRoGGnpvW4eExpBkhd03Q77S9Zlb2kzZ2F+4/js1lW1244duc2rEuExcKIwzKwWD1984aEojZzgzD2f+qpaBqumswb4CXgaqCUi7+VgbMYNLr2HSsucj6XN3mVMqm8tD1kNkxvcn/pwIz/z9kYGDrq62/WnEyAhwbNxGW7jTPJJto3dNglIUNWxqroZGADcnqPRGUYaHtu4iBkhyZy+CRpHQ8DFQP6qUs/TYRnu9vjjdN93E6UvwMbysMLrCPz0k6ejMtzEmeQzEVgJDAGeEZFCtvW+gJmb2HC7jB4s9U24QvdNixiX0r16FUypfy8q2Rmm0Mgrrmp+K14cvx4RV3e7Hufu59oNT3Gmt9unwONACayuz3tFZBuwDjgpIs0dEpJh5Kj7d/zFhpvPszMAbj4Hd+4rxE912ng6LMPN7Alo4EB7t+sfg+HQ9pWwerVngzPcwqmfi6q6UVVHquo9qnoz1sCcrwELgVeBPTkYo3EDyXA4HVX6rJvLONvo1U+vhdkh7bnoc1PuBGfkvuBgApu0o+t2q3PJJ42AsWM9HZXhBi61VahqtO35n+G2hOTs+GuG4bJmBzcjepBF1cEvAfqsF76u39HTYRk5KGjYQnjuOZ5dZS1/3gDi5s6Cgwc9G5iRbVlOPiJi+jsabnVNN9t09F4/j49ttZ4eW2B9hWYcKWpuO1732rWjUbFgmv8HZ/1gSmiyeej0OuBKzaet26MwbkjOJBz7vqcOUz96DVPDrWXTvfoGIgLPPcdzK63Fj5pA0peT4Nw5z8ZlZIvpImTkGRklo4j185lSFy74QNv9kORVjfW31MrF6IzcdtXfw6OPcv+pACqfhv0lYd7NcfDVV+kfbOR5JvkYHuVM7af4pXM8sP03e/fqZ1bBlAb3Wb+IjRuDnx/eAwYyxHbvZ2xTrG7XZq6ffMskHyPP67FxEQurx3OoGNQ8AXWPlGRhzds8HZaR2556ij47fCh6Gf6uBGsTDsKcOZ6OynCRST5GnuabGE/P9fN5v5m1/PxKmNqgEwneqaeWMq5X9g4pAQEU6dbL/tDp2KbABx+AuntaMSM3uJJ8Drs9CsNIR6ftS9lW9iwby0OZOLh/px8zws2cPTesZ55h0BrrodMfasOhnath5UpPR2W4IMvJR1Vb5EQghpGaaDJ918yx13oGrYE5de7mvG9hzwZmeE5wMBWb3U2XHdZDpx83xqr9GPmOy81uIhIgIk+JyFsi8rKIlHJnYIbRZt9arnhH80s1uCkBnljvZXU0MG5I9s4pzz9v73b9eX04t/An2L3bc4EZLnEp+YhIc6xZQYcDzYE3gEq2bY+JyK1ui9C4LjnTy63fmjl82NR633sjrAhqRUxRM5nYjS7ot0s0Kh1Gyyg454c1tYap/eQ7rtZ8PsKairoi0AZw7PNaGxiR1kGG4aywI7uoeHob34aCKDy7Cr5s+ICnwzI8LGjYQquL/Usv8dI/1rqxTeDKt1Ph6FGPxmZkjavJpzbwhaomAqm7mqwBmmUrKuO65kytp++aOXzSCOILwAM7IaZIODvKVsmF6Iz8oOomf+5JqESdY3CkKHxXPd5Mt5DPuJp8DgOV09l2AijvYrmGQYUzR2lx4B8+a2gtv7ACvmhkaj3G/yR5eSPPv8CLK6zld5tD8mefmiF38hFXk88kYJSIVE1jWxBw2tWARKS9iOwSkb0iMiyN7b4iMtO2fbWIBNnWPyoimxxeySISbtsWaSszZZsZjTIP67fmJ6bWVU7fBM3+g+JXglhW2cxUalyt5oHydI8pRYWz8G8ALCh3DiZN8nRYhpNcTT4fAv8CG7Du/yhQVETqYs3vs9SVQkXEG5gA3A0EA91FJDjVbo8Dp1X1VmAs8A6Aqk5X1XBVDQceA6JUdZPDcY+mbFfV467EZ2RfZk1uAXGn6LTtN3v36hdTaj1mKB0jlcsF/Sj49GB7z7d3mmPN9XPlikfjMpzj6nw+ScBdwP8BD2F1OPgDa3bTi8BQF+NpBOxV1f2qGg/MAFIPXXw/MM32fjbQVuSab6buwPcuxmDkEGfu9Ty+9mdm1UkkuhjUPg71jgQwr1arXIjOyI/CY6vxxM6bKHEJVlSEf7yPwPTpng7LcILLz/moapKqvgOUA8KBe4C6QENVPeJisbcAhxyWo23r0tzH1uHhLJD6GaOHuTb5TLE1uQ1PI1kBICL9RGSdiKw7ceKEi5dguKro5Ti6b15k/YIFhi2HSY27kOhdwLOBGXnWmZuK4t+rL0+vsZbfuQ147z1ITvZoXEbmsj22m1q2qOpi279J2SguraSQujddhvuISGPgoqpuc9j+qKqGAC1sr8fSOrmqTlLVBqraICDAPE+S23qtn89vVS+zuzQEnYa2+4sxK+QOT4dl5HHN48N5ao3glwDza8CO2H9h/nxPh2VkIq8NLBoNVHBYDgRS16Ls+4hIAaAYcMphezdS1XpU9bDt3/PAd1jNe0YeUij+Er3XzeX/bIM3vfQPTKv/AFcK+no2MCPPO1ysDKuCWtPbdof33ebAm2+aAUfzuLyWfNYC1USksoj4YCWSean2mQf0sr3vAvypav2ViYgX0BXrXhG2dQVEpLTtfUGgI7ANI1dldr+n++bFrAmMY1N5KBsHnXcU4tu69+RSdEZ+93njzrywwhpw9NtQ2L93Lfz2m6fDMjKQp5KP7R7OQGAxsBP4QVW3i8hoEUkZ1OsroJSI7AWeAxy7Y7cEolV1v8M6X2CxiGwBNmE9o/RFDl+K4SCzxOOTmEDfNT/Zaz3Pr4AZYfcS51soF6Izrge7AoLYW7oJj26xBhx9+zZg9GhT+8nD8tydXFVdBCxKtW6Ew/vLWLWbtI6NBJqkWncBqO/2QA23eXDbH+wteYq/K0HxS9Bzsw/t+5gBRI2sGd+sGx8sWMU3YTA1HF4bv4KKS5dCmzaeDs1IQ3ZGtfYWkSQRqevw3jwJaGSJd3IS/Vf/yFu2iUkHrYEFte7mdKFing3MyHe2lbuVw8Ua8PA2SPC23fsZM8bTYRnpyG6zm/C/3mfmKUDjGpk1ud2/I5LTfjEsqg6F4qH/Gm++MAOIGi76uFk3Xv3bev9lPYhZFwnLl3s0JiNteeqej3Fj8U5OYtCKGYxqbS33XwfLqrblaNHSHo3LyL823lKTOqF38OAOuFIA3jO1nzzLJB/DYx7YvpRTfjHMq2lNFvfsSi8+afawp8My8rvhw3ltmfV2YgM4/s9vsHq1Z2MyrmGSj+ERBZISr6r1PL0GllW5k+hiZT0al3EdaNmSutVb0nEXXCqINSGhqf3kOSb5GB7x4LY/OV7oKAtqWPd6hqz0ZkJTU+sx3OPR8u0Ybqv9TGgIsX8uhPXrPRuUcRWTfIxcVzApgUErZ9prPQPXwF+33snhYmamCyP7goYt5J9KYXhrTdrthThfW+1n+HBPh2Y4MMnHyHWdt/7BEf9jLKoOheNh8CpvJjR9yNNhGdcTEcY1787rkdbiuCZwbNkvpudbHmKSj5GrCiYlMDBVrefPandxpKip9RjutaxyPZpUbsG9u+CCD7zVAnjlFTPqQR6RrSkVgN7AAcf37grMuD49tGUJh4qe4Ndq4H8FBq3yZkITU+sxcoAIvPkmY/60Fj9rAIc2/23GfMsjslXzUdVpqno69XvDgGsfMPVNuMLTK3+w13oGrYEl1e82z/UYOadFC8LqtqfbVogvAGNaAa++amo/eYBpdjNyTcSG+ewudZLfboUiV2Dg6gJ82iTNYfoMw33eeIPXI60RryfXhT0H1sOcOZ6O6oZnko+RK4pdOs9TK3/gpTut5Zf+gYW1OnK8SOpJaA3DfYKGLSRo1lH2lG5OxCZrxOtRrYHXXoOk7Mx7aWSXST5GrhiwahZLql5k7S1Q7jw8vqGQ6eFm5JoPb+vBiGWCTyJ8HwJbY3fC9OmeDuuGZpKPkSMc7/fcfO44j26cxyttreVRkTCt/kOcuamoZ4Izbjj7Sleg4v096b8OVGB4G2DkSLhyxdOh3bCyM6VCiIg8LiKvisgYEXlWRDqISAl3Bmjkf8///S1fhyeytxRUPwl37ynJlPr3ejos4wZzm18LXllVgELxMLcmrEiKggkTPB3WDStLyUdEqojIeyJyBGtW0InAM1jdrMcA84ETIvKHiHS3TWtt3MBqHj/Anbv/5PVW1vJbf8DHzXtwpaCvZwMzbjjRxcvxa5W7eHaVtfzcXaCjX4eTJz0b2A3K6eQgIl8C24FwYDRQF/BT1QBVDVRVf6AMcC+wFXgX2Ckit7k/bCO/GPrXVD5qCsf9ockhCD5RgR/rtPV0WMYNalzzR3hqzU2UOw+rA2FmhXPWdNtGrstKzeQyUFNV71TViaq6xfZwqZ2qnlTVX1T1GaASMAK4xY3xGvlAyv2epge3UPvYet5rZq1/53d4t1Vvkr28PRidcSM7VagY0xp04w3bg6dD74BLkybAv//f3p3H6VT+fxx/fSGFXzYAAB1HSURBVGbGFsa+ZRsysmXJTmHILlKICpWStFMkLSr5ib4tvpRK+LbiK0qWRLZKlpHsS4PBWEf2ZJiZz++Pc6bmOw1mxrjPfY/P8/G4HzPn3Nc53qPJ5z7Xuc51bfU22FUozcVHVR9V1d3paJ+oqlNVdWrGoplAFpSYwPOLJvBKU2dixw7bIEdCVRZdV9fraOYqN7l2R5rvKkr1g7AnP7xTNxGeecbrWFedDN2TEZG3ReSKLJstIm1EZJuIRInIs6m8n0NEprrvrxSRMHd/mIj8KSK/uq/xyY6pLSIb3GPGXKns5u+rnh7r5pPITsbXgaBE517PyGb3OVOeGOOhcyHZGNX0fv7lzrIz4mY4tHg2LFzobbCrTEYHBPQAvhKRa1J7U0TaZuSkIhIMjAPaAlWAHiJSJUWzPsAxVa0AvAW8nuy9Hapa0331S7b/PaAvEO6+2mQkn7m4pMKT/8+TDFz2MY+3dR7q678adhRqytqSlTxOaIxj3vWNuaVEYzpsg1M54MUIYOBAe/DUhzJafBoAFYAfRKRE0k4RaS0iK4HZGTxvPSBKVXeq6jlgCtApRZtOwH/c76cDLS52JePmC1XVn1VVgY+B2zKYz6TBgB8+Y+F1p1lSDgqdgUE/5mBExH1exzLmbyJ0vO4ORi+AkASYcCNsOLgeJk3yOtlVI0PFR1V3AY2AI8AqEblfRJYD84ATQLMM5ikJ7E22HcM/Byz81UZV490/L2mOlnIislZElorIzcnax1zinACISF8RiRSRyNjY2Az+CFe3yod3ctumuTzdytke8T18UetODuW1yUONf1lfoiKbi0XwcCQkBsHA1qDPDYFjNj+yL1zOkgongDeAAsCHQE6goaq2UtUfMnja1K5gUk4/e6E2B4AyqloLGAB8LiKhaTyns1P1A1Wto6p1ihQpko7YV7ewZ+c4XW6qDFvwPqMbK3vzwY37ocXO4kyo29nriMakanSTXgz+MRv5/4QF18GMwkecNX/MFZfRAQetReRH4FtgOfA+zj2aCpeZJwYonWy7FLD/Qm1EJATIBxxV1ThV/R1AVdcAO4CKbvtSlzinyaDk0+h03LKMIn9sYnRjZ3vMPHiteV/OhWTzKJ0xF3cgtAhTa3RjxPfO9hNt4dSk8bBypbfBrgIZvfKZB8QBTd0rnf7A48BEEXn5MvKsBsJFpJyIZAe6A7NStJkF9Ha/7wIsUlUVkSLugAVEpDzOwIKdqnoAOCUiDdx7Q72Ary8jo0nFNef+5LnFHzGgNcSFwD3rIC5bHRZVqOd1NGMuanz9LtyyswT1YmBfKLzUDOjXD+LjvY6WpWW0+DRT1Raq+teC6Kr6AdABeFxEpmTkpO49nEeB+cAWYJqqbhKRV0Sko9vsI6CQiEThdK8lDcduAqwXkXU4AxH6qepR972HgQlAFM4V0byM5DP/K/lVz1M/fsa6Ykf5upKzQumr3wfzaosHPUxnTNqcC8nGsJaPMH6281jAO/Xh14O/wtixXkfL0kQzeUU/EakKfKOq5TP1xD5Wp04djYyM9DqGX0sqPtUPbOfTKQOp+bCyqwC8vgDyxnfh9Wb3ehvQmHSI3vMZTxz7gjENnKmgfpqam6Ct26CkTdKSViKyRlXrpKVteuZ265nUrXUxqroJqO8eUyHZqDOThSQVnmwJ53l93hiGRTiFp8ZB6LqpMP9udKfHCY1Jn7oF2/HqmlBKnIIVpWHC9X/Ak08C/1wS3ly+9HS7DQR2uMsn1LhQIxEpBLQSkW+AtUCJC7U1ga/fiumcyh7NO/WdLouPvoZhLR/jTPZcXkczJl1i8xRgVM27eftbZ3vwLXB43nTu7TrM01xZVXrmdqsJDAYigLUictKd3maOiMwQkUUisgs4DLyDc2+lkqpOuyLJjeeuO7KXviun0Kej+5zEzxBdMIKl5Wt7Hc2YDPm8Zhsq/l6B1lFwPJez7MKI+ePIG/eHXf1ksnQNOHAnCr0JZwjzMzhr+sQDuYFDODMPtAFKqOqTqrovk/MaPxD27ByCEhMYNe8d3m6YwMZicN1ReHRlqA0yMAEtMSiYoa0fZdw8Idd5+Kw6rCp5hBcXfuh1tCwnJIPHxanq+5maxASUnmvnkuv8Vl51F4n7cBaMatbPlsY2AW9T8QosqHA7Ixd+yRNt4aEOsOndhdzyW0OgvdfxsoyMDrWOFpE0jWgwWU/p4wcZuGwyD3SE88Hw4BqID6nH7Eo2tsRkDW/ddDctd5Sm2S5nIcSH28OI+WOo9fjnXkfLMjJafASY6d7ved0dCVfLXe4gh/usjcmKzp9nzKzRfFAnjp9LQ4lT8PySXLzQsr8tl2CyjLiQ7DzTfiAffi3kiYPpVWFRuRO8umD8pQ82aZLhud1wHgT9A2eW6UlAJHAa595P2GUnM/7plVdQtvGcuxL2B9/Ae436cDDUJg41WcvG4hWYXbU7b853tvu3h9oxP/Bop8HeBssiLqf4fKCq3VS1EpAHZzmEB4DRONPimCwiaZRPt7tf5+So1+hxh9Pd9uhKyJFYjy9qtPY4oTFXxtiGd9JgX3na/AbHcsGDHeGV796FAwe8jhbwLqf4/EVVz6rqGlX9j6q+pqo2fU0WU/3Jqbz1zb8Y2FrZXhiqHYKnl+dncNsnrLvNZFnxwSEMbD+AcXOCyf8nzKkIX1Y5DXfdZQvPXabLKT53i8it7iSeJgv667kGVUbMH8eKUrFMqA054uHzL2Fo64EcvSaftyGNucK2Fwljas2ejJvrbD/eFtZvWQLDhtmzP5fhcorPPTizQ/8mIqdEZJWITBKRgSJi/TBZSJeN31Nj/w886E7tOvo7+LlsZ34sV8vbYMb4yId1OxN2ojp9foGz2aBLNzg5ejhNd67xOlrAymjx+R5ojrOQXBPgaWAFUBYYBMzNlHTGc636jOOlhe/Sq7PT591uO0REl+ONJr28jmaMzyQGBfPErc/wwtL8VD8IvxWCvrfCm7PfgL17L30C8w8ZXUa7paquU9UTqvqTqr6vqo+ranNVLQYUz+ScxgN54/5g/MwRjLzpHEvKQbHT8O7s7DzRcZAtEGeuOrF5CjC43SCm/NcZfj21Gkytdgq6d4fz572OF3AyZcBBSqoaeyXOa668pCWxwwbP5o05b7Gh6H5GNHEmDf1iOoxr1I8dhUpf+kTGZEErylTnm6o9meAucflUa4iMXm5Lb2fAFSk+JvCkvHH62PIplP99Bb06O9sjF8Kh0FZMq9HKg3TG+I/3GnSh2JnaPLIKzoVA165wbOwbMHWq19ECihUf81fhSfraZttPPLD6Mzr2gJM54fbN0HpHeV5q2c/LmMb4BZUgnuowgIHLC1F7P0QXgDu7wumePcEWoEwzKz5XsdSGiVY9tIPRc/9F9y6wtYjzPM+b8/PS/7bniAvJ7kFKY/zPsWvyMbDDs0yZFkzR07DgOnjulvPQqRPs3+91vIBgxecqlLzoJP/+2pOH+Wj6y7wYcY5vw6HwH/Dl1CAGtXuOmPw2hsSY5H4pWZn3Gz7CzKmQPR7+XR/GX7sf2reHU6e8juf3rPhcRS5UdABCz55m8rRhTKt6lLcbQrYE+HIaTKzbn5VlbvB1VGMCwn+rt2JT8dt4f7az/Wg7mPPHr86NIBsBd1F+V3xEpI2IbBORKBF5NpX3c4jIVPf9lSIS5u5vKSJrRGSD+7V5smOWuOf81X0V9d1P5P9yxJ/jgxnD2Vh0D0+2cfZ99DX8VqQTU2q28TacMX7u/5rdR+lTdXl+KSQEQbeuELlhPvTtC4mJXsfzW35VfEQkGBgHtAWqAD1EpEqKZn2AY6paAXgLeN3dfwS4VVVvAHoDn6Q47m5Vrem+Dl+xH8LPpbziCUmIZ+zXIzkXtJG7bwcVGLEQCp1txGsR93uU0pjAkRgUzGMdB3HHlgr0+hXOZIf2d8H2bybDwIGg6nVEv+RXxQdnZuwoVd2pqueAKThLNiTXCWe5boDpQAsREVVdq6pJd/o2ATlFJIdPUgco0UTemPsWBc6sosNdzrQh/VZDi12VearDQBKDgr2OaExAOJM9Fw90eYkXlxalVZSzAF3LnrBn0tvw8stex/NL/lZ8SgLJ56qIcfel2kZV44ETQKEUbe4A1qpqXLJ9k9wutxdEUp+GWUT6ikikiETGxmbt52RFE3l93hjCY5fS+h44lQO6b4DHVpWm7x0vEJfN6rYx6XEkdwH6dHmV97/JR6M9sCe/U4AOvfEyjBjhdTy/42/FJ7WikPKa9aJtRKQqTlfcQ8nev9vtjrvZffVM7Q9X1Q9UtY6q1ilSpEi6gvurlM/wAAQlJjBq7hiqHlxI895w9BrosA1eXVyM3t1e43iuUK/iGhPQoguWpN/tw5kzJ5SaB2B7YWjeGw6NGAqvveZ1PL/ib8UnBkg+d0spIOWg+b/aiEgIkA846m6XAmYCvVR1R9IBqrrP/XoK+Byne++qkbzwhCTE88bct6l0eCER97rdAztgzLwC3Nv1NWLzFPQuqDFZwNai5bi/5QvMmJKDaodgc1GIuBcOjnweXnqJsMGzvY7oF/yt+KwGwkWknIhkx1kRdVaKNrNwBhQAdAEWqaqKSH5gDjBEVX9KaiwiISJS2P0+G9AB2HiFfw6/lON8HO99NYIyxxYTcS/E5obWUTD+m4Lc13WkPctjTCb5pWRlBrV/mW8+z8ENh2BLEWh6L+x+5xWGLXzfRsHhZ8XHvYfzKDAf2AJMU9VNIvKKiLiryfARUEhEooABQNJw7EeBCsALKYZU5wDmi8h64FdgH/Ch734qbyRNEJok9OxpPp72IiHxq4joDb9f4yyP8O7sQtzXbSTRBVPeWjPGXI7VpavxdIdXmPV5TmocdLrgbrof6u+ZDffcA3Fxlz5JFiZqwwBTVadOHY0MoHmawp6dQ/TI9qlOmVP6+EEm/3cYa4vHcM/tEBcCd62Hl5cU4/4uw9lToIQHiY25OtTat5W3Z73IPXec4ceyUOgMzPoCGpVrAjNnQsGs09UtImtUtU5a2vrVlY+5PKkVntoxm5nxyQC+rBxD125O4XlkFTz3Q1l69BhthceYK2xtyUr07TKKj2cWoP12p9eheW+Y+vsyaNQItm3zOqInrPgEuAuuIa/K3WvnMnnaEIbccpLBLZ3do76Dnusr0+Ou121wgTE+sq1IGL3uHM2b35bgoUjnQ2D3rjC82DYS69Tm4duGeB3R56zb7QICpdstteKT69xZXl44npuiF3JHN1hRGnKeh09mQjZtyqB2T9gM1cZ4IP+fJxk/Yzg/ltnMoJbOjCK3b4bJX0He/k/CqFGQLXBXCbZut6tYeOxuvv54AIVPL6R2X6fwlDkOP06E/fnu5MlbB1rhMcYjx3OF0uvO1yh3IoJvPod8Z2FGFaj3IPw65W0iy9WAmBivY/qEFZ8Ac6FutqDEBB5YNYOZnzzJJ9X3cEsvOJgXmu2CpZNy8GH9IbzZpCcq9p/cGC+dC8nGwPYD+Llcf376KJiqh521s+o/AEvLbCGxZg344ossPyec/UsUIFIWneTbFY7s4ctPB9F540Ra9D7P8KbO/heXwPjZ1/LgHW/y7fWNfZjWGHNRInxaqx1D2o5m5pTCPLzaWZL76dbQqv1R9j10F3TunKUXprPiE0BSFqAKz3xN/5+n8dXHjzE7fBu1+sGqUlDyJHz/H6geG0HnXu/wW5GyHiU2xlzM+hIV6XrPGLptrs2sz50FHL8vD9UfhqlRX6NVq8DkyVnyKsgGHFyAPw04SK2r7aZdaxm6+CP+DInm/k6wzp2coG8kDF12DW/d3I+Z1Zr/4zhjjP8RTeShlTPosfYT+t2awLfhzv5WUfDveVCxegT8619Qq5a3QS8hPQMOrPhcgL8Un5SFp2JsNM8tnkSVw2t4uSm8X8dZwKrcMZgwC+JDGjC0VX8bRm1MALruyF5GzXuLyBLbGXILHMvlrCr8zE/w3I+Qu3svGD4cSpe+9Mk8YKPdsqDiJ4/wf/PG8OUnj7G81BoqPA7v1nOm835iBSyZlJcZNwyib+ehVniMCVA7Cpem692jOZzvAX59Lzt9foHzwTCiCVR+BD5f+zEJ14fD0KFw7JjXcS+LXflcgL9c+dzywHs8tHIG7bYu5r/VEnghAmLyOe+12w6jFsC2ohEMb/4AR6/J521YY0ymKXtsP69+9x7Z4tfySHtY605GUjkWXloCXXfnJqjvQ/DUU1CqlKdZk1i3WybwtPiowvLlLLh3AI12r2LCjfBmQ2dxKoBaB+CN7yB3fDWGR/RhQ4lwb3IaY64sVZru+oXBSyawotReXm0C0QWct6oedorQ7VEhBN91Dzz9NFSt6mlcKz6ZwJPic+QIfPopTJzI4Z0bGFsPxtV1FnsDuP4IDF0GDWJK8nqz+1lYoR6kviirMSYLCU5MoMuGhby6fhr/KX6I4U3+/jBa7hj0Xw33r4WCNzaGPn2ga1fIk8fnOa34ZAKfFZ+4OFi4ECZPJn7WV3xXNp6JtWDW9U5fL0DDvTD4R6h2uDgf1uvC9BtuIT445MpnM8b4lejnm8LYscSNeYtJJQ8zqjHscq+Ecp6HuzY4hejGU7mRO7tDr17QuDEEB/sknxWfTHBFi8+pUzB3Lsycic6dw+acp/msOvynBux3V7AOSoQO2+GZ5ZDnfDjj63fhu/AGJAb55pfIGOO/csSfY1vFWKKGvMTWwgcZWw/mV/j7/Uqx0GMj9NgA4cFFoFMn56HVFi0gR44rlsuKTybI1OITHw9r1sCiRbB4MYlLl7Ci2Hm+qgQzK0FUob+bhv/uXD7ftU7YVqwuE+vcxs9lbrDuNWPMPwQlJrCz/nkYM4btm5bxXh34tDocyf13mxv3Q7dN0DYKbjiTB2neApo3h4gI5x5RUOYNerbikwkuq/gcOwaRkbB6NSxfDsuWsSv4FIvLwaJysLA8HErWHVv4D+i0De79FYqfvpbpN7Tiy2rNbci0MSbNwo7uY0nhaM5/PInvcx3ki2owszKcSnahc+1JaBPlFKLmu6BgniLQrBk0aAB168KNN0Lu3Bf8My7Fik8mSFPxSUiAHTtg82bYtAk2boTISM7timJ9MVh9LawqCYvLwe78/3to2DHovBVu2wrhv+dnUYUGzKwaQWTJKnaVY4zJsODEBJruXMOtW5bR5uAvzCt2km8qwrcVnMmGk6sUC433QuM90GgvhB8TgqpUhdq1nauiqlWhShUoUyZNV0hWfDJBnTp1NHL1am584gt+6RkO0dGwe7fz1X1p1G8czHaOzUVgcxHYVBR+KQHrijmTBCZX4E9oGu182oiIhtznivNdxUbMD2/I2pLX22zTxphMly3hPA32bOCTgvvRr2ayjkN8W8EpRCtLwtkUSwfliYPqh6DGIahx0Pl6/REoEJwbwsMhLMx5lS379/dhYZDf+XRtxScTVA/OpquCgjgfdI7d+WF3PojO77x2u19/KwjHc6V+/PVHoO4+qLsfbt4N154KZXXpGiwvW52fy1RnV4Fr7QrHGOMT0SPbQ2IibNjAqwPG8sI1Bzn3wxLW5jnNT2Xgp9Lwc2k4kDf14wudgYq/O/ekrzsGpU7+7ys0JDcULYrs2hW4xUdE2gDvAMHABFUdmeL9HMDHQG3gd+BOVY123xsC9AESgMdVdX5azpmanMVEc94PJ3JevF3+P6FqLFRxX9UPQc0DwqG8ZVlfPJx111ZkTcnKbC9cxq5ujDF+IzgxgRsORlFr/1ZeKn4GVq3i8P7fWFfMmah4XTHYWBR+KwR/XGL9ybxxThHaMo7ALD4iEgxsB1oCMcBqoIeqbk7Wpj9QXVX7iUh3oLOq3ikiVYAvgHrAtcBCoKJ72EXPmWqWa0V5yBk7X/YElD0OYced78OOO9vlj0Gw5iOqUFm2Fy5DVOEybC1Slk1Fr+PP7JeoWsYY42dCz57mhoNRfNYwj3Mfe/NmdNNGDiScYHshp7dnZwHYFwoxobAvL+zNB38mdd8NC9zi0xAYpqqt3e0hAKr6f8nazHfb/CwiIcBBoAjwbPK2Se3cwy56ztRUyya6LBtkS8jJvtBixOQrSky+v7/uCy3K3vzFOJ4rNPP+Aowxxt+oUuSP45Q6cch5nTzM4Eo5WfrdakqdOEz5M7EcJ46YUKh+OO3Fx98eky8J7E22HQPUv1AbVY0XkRNAIXf/ihTHlnS/v9Q5ARCRvkBfd/N0oXi2wVk4stt5ZZ7CwJHMPKGPWX5vWX5vBXL+DGXfDSQf+/vs0lQanQUgzStX+lvxSe0OfMpLswu1udD+1G60pHq5p6ofAB9cLGBmEJHItH468EeW31uW31uBnN+fsvvbHfAYIPkqSaWAlIuY/9XG7XbLBxy9yLFpOacxxhgf8rfisxoIF5FyIpId6A7MStFmFtDb/b4LsEidG1ezgO4ikkNEygHhwKo0ntMYY4wP+VW3m3sP51FgPs6w6ImquklEXgEiVXUW8BHwiYhE4VzxdHeP3SQi04DNQDzwiKomAKR2Tl//bClc8a69K8zye8vyeyuQ8/tNdr8a7WaMMebq4G/dbsYYY64CVnyMMcb4nBUfD4nIYyKyTUQ2icgor/NkhIg8LSIqIoW9zpIeIjJaRLaKyHoRmSki+S99lLdEpI37+xIlIs96nSc9RKS0iCwWkS3u7/sTXmfKCBEJFpG1IjLb6yzpJSL5RWS6+3u/xX2o3zNWfDwiIhFAJ5ypgqoCb3gcKd1EpDTOtEV7vM6SAQuAaqpaHWf6pSEe57kod+qpcUBboArQw51SKlDEAwNVtTLQAHgkwPIneQLY4nWIDHoH+FZVKwE18PjnsOLjnYeBkaoaB6Cqhz3OkxFvAYO4wEO7/kxVv1PVeHdzBc7zX/6sHhClqjtV9RwwBefDS0BQ1QOq+ov7/Smcf/hKXvwo/yIipYD2wASvs6SXiIQCTXBGC6Oq51T1uJeZrPh4pyJws4isFJGlIlLX60DpISIdgX2qus7rLJngfmCe1yEuIbWppwLqH+8kIhIG1AJWepsk3d7G+bCV6HWQDCgPxAKT3G7DCSKS8SVLM4FfPeeT1YjIQqB4Km8Nxfm7L4DTBVEXmCYi5dWPxr5fIv9zQCvfJkqfi+VX1a/dNkNxuoQ+82W2DEjL1FN+T0TyAF8CT6rqSa/zpJWIdAAOq+oaEWnmdZ4MCAFuBB5T1ZUi8g7OZMwveBnIXCGqesuF3hORh4EZbrFZJSKJOJP+xfoq36VcKL+I3ACUA9aJsyBeKeAXEamnqgd9GPGiLvb3DyAivYEOQAt/KvoXEPDTRIlINpzC85mqzvA6Tzo1BjqKSDsgJxAqIp+q6j0e50qrGCBGVZOuNqfjrgTgFet2885XQHMAEakIZCdAZspV1Q2qWlRVw1Q1DOcX+0Z/KjyX4i4wOBjoqKpnvM6TBgE9TZQ4n1I+Arao6pte50kvVR2iqqXc3/fuONN6BUrhwf1/c6+IXO/uaoEzG4xn7MrHOxOBiSKyETgH9A6AT99ZyVggB7DAvXpboar9vI10YReaesrjWOnRGOgJbBCRX919z6nqXA8zXW0eAz5zP7zsBO7zMoxNr2OMMcbnrNvNGGOMz1nxMcYY43NWfIwxxvicFR9jjDE+Z8XHGGOMz1nxMcYY43NWfIwxxvicFR9jjDE+Z8XHGD8nIk3dBfvaJttXTkQOi8gYL7MZk1E2w4ExAUBEFgE5VbWRiOQDlgO7gE6qmuBtOmPSz4qPMQFARG4GlgGtgYFAMeAmVT3taTBjMsiKjzEBQkQWAI2A40B9VY3xOJIxGWb3fIwJHFHANcBLVnhMoLMrH2MCgIj0Bf4NbAHOqmoDjyMZc1ms+Bjj50SkJTAHeADYDvwMtFPVeZ4GM+YyWPExxo+JSFXgJ2Csqj7v7lsA5FPVep6GM+YyWPExxk+JSFFgJRAJdEta6VZEmgBLgQ6qOsfDiMZkmBUfY4wxPmej3YwxxvicFR9jjDE+Z8XHGGOMz1nxMcYY43NWfIwxxvicFR9jjDE+Z8XHGGOMz1nxMcYY43P/D5aoE/7iv4J2AAAAAElFTkSuQmCC\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import random, math, pylab\n", "from math import *\n", "\n", "# Energy eigenstates of the harmonic oscillator\n", "def psi_n_sq(x, n):\n", " if n == -1:\n", " return 0.0\n", " else:\n", " psi = [math.exp(-x ** 2 / 2.0) / math.pi ** 0.25]\n", " psi.append(math.sqrt(2.0) * x * psi[0]) #save the wf's in a vector \"psi\"\n", " for k in range(2, n + 1):\n", " psi.append(math.sqrt(2.0 / k) * x * psi[k - 1] -\n", " math.sqrt((k - 1.0) / k) * psi[k - 2]) #Hermite polynomial recursion relations\n", " return psi[n] ** 2\n", " \n", "# Energy eigenvalues of the harmonic oscillator\n", "def E(n):\n", " E = n + 1.0 / 2.0 \n", " return E\n", "\n", "\n", "# Markov-chain Monte Carlo algorithm:\n", "def markov_prob(beta, n_trials):\n", " # Energy move:\n", " xx = 0.0\n", " delta = 0.1\n", " n = 0\n", " hist_data_n = []\n", " hist_data_x = []\n", " for l in range(1000000):\n", " if xx == 0.0:\n", " xx += 0.00001 #avoid division by 0\n", " m = n + random.choice([1,-1]) #take a random energy step\n", " if m >= 0 and random.uniform(0.0, 1.0) \\\n", " < psi_n_sq(xx, m) / psi_n_sq(xx, n) * exp(-beta * (E(m) - E(n))): \n", " n = m\n", " hist_data_n.append(n) \n", " # Position move:\n", " x_new = xx + random.uniform(-delta, delta) #take a random position step\n", " if random.uniform(0.0, 1.0) < psi_n_sq(x_new, n) / psi_n_sq(xx, n): \n", " xx = x_new \n", " hist_data_x.append(xx) \n", " return hist_data_x, hist_data_n\n", " \n", "#Exact quantum position distribution\n", "def p_quant(x, beta):\n", " p_q = sqrt(tanh(beta / 2.0) / pi) * exp(- x**2.0 * tanh(beta / 2.0))\n", " return p_q \n", " \n", "#Exact classical position distribution\n", "def p_class(x, beta):\n", " p_c = sqrt(beta / (2.0 * pi)) * exp(- beta * x**2.0 / 2.0)\n", " return p_c\n", "\n", "#Run the algorithm for different values of temperature:\n", "n_trials = 10000\n", "for beta in [0.2, 1.0, 5.0]:\n", " B = beta\n", " T = 1 / beta\n", " hist_data_x, hist_data_n = markov_prob(beta, n_trials)\n", " pylab.hist(hist_data_x, 500, normed = 'True', label='Markov-chain sampling') #position histogram of the sample\n", " x = [a / 10.0 for a in range(-100, 100)]\n", " y1 = [p_quant(a, beta) for a in x]\n", " y2 = [p_class(a, beta) for a in x]\n", " pylab.plot(x, y1, c='red', linewidth=4.0, label='exact quantum')\n", " pylab.plot(x, y2, c='green', linewidth=2.0, label='exact classical')\n", " pylab.title('Position distribution at $T=$%.2f' % T, fontsize = 13)\n", " pylab.xlabel('$x$', fontsize = 15)\n", " pylab.ylabel('$\\pi(x)=e^{-\\\\beta E_n}|\\psi_n(x)|^2$', fontsize = 15)\n", " pylab.xlim([-7,7])\n", " pylab.legend()\n", " pylab.savefig('plot_T_%.2f_prob.png' % T)\n", " pylab.show()\n", "\n", " pylab.hist(hist_data_n, 100, normed = 'True') #energy histogram of the sample\n", " pylab.title('Energy distribution at $T=$%.2f' % T, fontsize = 13)\n", " pylab.xlabel('$n$', fontsize = 15)\n", " pylab.ylabel('$\\pi(n)$', fontsize = 15)\n", " pylab.legend()\n", " pylab.grid()\n", " pylab.savefig('plot_T_%.2f_energy.png' % T)\n", " pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One can see that at high temperatures e.g $T=5$, the position distributions are almost the same. Hence the classical harmonic oscillator is a very good approximation for the quantum harmonic oscillator at high temperatures. The quantum behaviour becomes more prominent at low temperatures (eventually only the ground state is available for a sufficiently low thermal energy), especially below $T=0.2$, as one can see from the above figures.\n", "\n", "Here we also got an histogram for the energy ($n$) distribution. The result indicates that the values of $n$ are distributed according to a Poisson distribution?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Trotter decomposition (convolution) and path integral monte carlo simulation\n", "\n", "On the other hand, we can still obtain the position distributions even if we do not a priori have the analytic stationary states at our disposal. That is, we can approximate the density matrix at high temperatures by the Trotter decomposition and then take advantage of the convolution property to obtain the density matrix at successively reduced temperatures. This is implemented in the following algorithm." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%pylab inline\n", "import math, numpy, pylab\n", "from numpy import *\n", "\n", "# Free off-diagonal density matrix:\n", "def rho_free(x, xp, beta):\n", " return (math.exp(-(x - xp) ** 2 / (2.0 * beta)) /\n", " math.sqrt(2.0 * math.pi * beta))\n", "\n", "# Harmonic density matrix in the Trotter approximation (returns the full matrix):\n", "def rho_harmonic_trotter(grid, beta):\n", " return numpy.array([[rho_free(x, xp, beta) * \\\n", " numpy.exp(-0.5 * beta * 0.5 * (x ** 2 + xp ** 2)) \\\n", " for x in grid] for xp in grid])\n", "\n", "# Exact quantum position distribution:\n", "def p_quant(x, beta):\n", " p_q = sqrt(tanh(beta / 2.0) / pi) * exp(- x**2.0 * tanh(beta / 2.0))\n", " return p_q\n", "\n", "# Construct the position grid:\n", "x_max = 5 #maximum position value\n", "nx = 100 #number of elements on the x grid\n", "dx = 2.0 * x_max / (nx - 1) #position differential\n", "x = [i * dx for i in range(-(nx - 1) / 2, nx / 2 + 1)] #position grid\n", "\n", "beta_tmp = 2.0 ** (-5) # initial (low) value of beta (power of 2) (high temperature)\n", "beta = 2.0 ** 2 # actual value of beta (power of 2)\n", "\n", "rho = rho_harmonic_trotter(x, beta_tmp) # density matrix at initial (low) beta (Trotter decomp.)\n", "\n", "# Reduce the temperature by the convolution property (matrix squaring):\n", "while beta_tmp < beta:\n", " rho = numpy.dot(rho, rho) #matrix squaring (convolution)\n", " rho *= dx #also multiply by the differential since we are in position representation\n", " beta_tmp *= 2.0 #reduce the temperature by a factor of 2\n", " #print 'beta: %s -> %s' % (beta_tmp / 2.0, beta_tmp)\n", " \n", "# Output position distribution pi(x) at the final beta onto a file:\n", "Z = sum(rho[j, j] for j in range(nx + 1)) * dx #partition function (to normalise)\n", "pi_of_x = [rho[j, j] / Z for j in range(nx + 1)] #the diagonal element of the density matrix\n", "f = open('data_harm_matrixsquaring_beta' + str(beta) + '.dat', 'w')\n", "for j in range(nx + 1):\n", " f.write(str(x[j]) + ' ' + str(rho[j, j] / Z) + '\\n')\n", "f.close()\n", "\n", "# Plot the obtained final position distribution:\n", "T = 1 / beta\n", "x = linspace(-x_max, x_max, nx+1)\n", "y1 = [p_quant(a, beta) for a in x]\n", "pylab.plot(x, pi_of_x, c='red', linewidth=4.0, label='matrix squaring')\n", "pylab.plot(x, y1, c='green', linewidth=2.0, label='exact quantum')\n", "pylab.title('Position distribution at $T=$%.2f' % T, fontsize = 13)\n", "pylab.xlabel('$x$', fontsize = 15)\n", "pylab.xlim([-2,2])\n", "pylab.ylabel('$\\pi(x)=e^{-\\\\beta E_n}|\\psi_n(x)|^2$', fontsize = 15)\n", "pylab.legend()\n", "pylab.grid()\n", "pylab.savefig('plot_T_%.2f_prob_matrix_squaring.png' % T)\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Path integral Monte Carlo method is implemented in the following program." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%pylab inline\n", "import math, random, pylab\n", "\n", "def rho_free(x, y, beta): # free off-diagonal density matrix\n", " return math.exp(-(x - y) ** 2 / (2.0 * beta)) \n", "\n", "def read_file(filename):\n", " list_x = []\n", " list_y = []\n", " with open(filename) as f:\n", " for line in f:\n", " x, y = line.split()\n", " list_x.append(float(x))\n", " list_y.append(float(y))\n", " f.close()\n", " return list_x, list_y\n", "\n", "beta = 4.0\n", "T = 1 / beta\n", "N = 10 # number of slices\n", "dtau = beta / N\n", "delta = 1.0 # maximum displacement on one slice\n", "n_steps = 1000000 # number of Monte Carlo steps\n", "x = [0.0] * N # initial path\n", "hist_data = []\n", "for step in range(n_steps):\n", " k = random.randint(0, N - 1) # random slice\n", " knext, kprev = (k + 1) % N, (k - 1) % N # next/previous slices\n", " x_new = x[k] + random.uniform(-delta, delta) # new position at slice k\n", " old_weight = (rho_free(x[knext], x[k], dtau) *\n", " rho_free(x[k], x[kprev], dtau) *\n", " math.exp(-0.5 * dtau * x[k] ** 2))\n", " new_weight = (rho_free(x[knext], x_new, dtau) *\n", " rho_free(x_new, x[kprev], dtau) *\n", " math.exp(-0.5 * dtau * x_new ** 2))\n", " if random.uniform(0.0, 1.0) < new_weight / old_weight:\n", " x[k] = x_new\n", " if step % 10 == 0:\n", " hist_data.append(x[0])\n", " \n", "# Figure output:\n", "list_x, list_y = read_file('data_harm_matrixsquaring_beta' + str(beta) + '.dat')\n", "pylab.plot(list_x, list_y, c='red', linewidth=4.0, label='path integral Monte Carlo')\n", "pylab.hist(hist_data, 100, normed = 'True', label='matrix squaring') #histogram of the sample\n", "pylab.title('Position distribution at $T=%.2f$' % T, fontsize = 13)\n", "pylab.xlim(-2.0, 2.0) #restrict the range over which the histogram is shown\n", "pylab.xlabel('$x$', fontsize = 15)\n", "pylab.ylabel('$\\pi(x)=e^{-\\\\beta E_n}|\\psi_n(x)|^2$', fontsize = 15)\n", "pylab.legend()\n", "pylab.savefig('plot_T_%.2f_prob_path_int.png' % T)\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Anharmonic oscillator\n", "\n", "Our anharmonic oscillator is described by the potential $V_a(x)=\\frac{x^2}{2}+\\gamma_{cubic}x^3 + \\gamma_{quartic}x^4$, where the coefficients $\\gamma_{cubic}, \\gamma_{quartic}$ are small. We consider the case $-\\gamma_{cubic}=\\gamma_{quartic}>0$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Trotter decomposition\n", "\n", "When the cubic and quartic parameters are rather small, the anharmonic potential is similar to the harmonic one. In this case, there exists a perturbative expression for the energy levels $E_n(\\gamma_{cubic}, \\gamma_{quartic})$ of the anharmonic oscillator. This expression (that is too complicated for us to derive, see e.g. Landau Lifshitz: \"Quantum Mechanics (vol 3)\", exercise 3 of chap 38) allows us to compute the partition function $\\sum_n \\exp(-\\beta E_n)$ for small $\\gamma_{cubic}$ and $\\gamma_{quartic}$ (this is the meaning of the word \"perturbative\"), but it becomes totally wrong at larger values of the parameters." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "image/png": 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X3717d9LT0y2GZNy4cQD06tWLr776CoDc3FzuueceDh06hBCC0tJSSz3XXnstYWFhlve9e/e2hLiIiYlh+PDhAHTt2pVVq1YBmvExl33XXXfx1FNPWc4fO3YsXl5edOnShTNnzlS4rpUrV/Lggw9a3CDWdVszYYK2Rvfqq6/m0qVL5OTksG7dOosBvOaaa8jOziY3N7fCuStXrmTv3r2W95cuXSIvLw+AUaNG4efnh5+fHy1atHCo0ZrS0lIeeOABduzYgcFg4ODBg1Xmb0xkZmZSXFxMeHg4oaGhestxG5QhcXM6depkMST1FUHUuudQX4vTsrOz+fXXX9m9ezdCCIxGI0II3njjDQD8/PwseQ0Gg834hvmYdfrzzz/PkCFDWLp0Kenp6TZtFxgYaFO3ddleXl6W915eXpWOo1hPM7U+39rlZp1WnWmp9nmEEA7Lc1SWyWRiw4YNDkOZV9V2jnjvvfdo2bIlv//+OyaTyS22M3AX1LRfx6gxEjfHHMfn5MmTFBYW6i3HZXz55ZfcfffdZGRkkJ6eTmZmJlFRUaxbt65W5eXm5tK2bVtAGxepK/3797eM2yxevNjSG6oOw4cP58MPP7T8gFfm2vr8888BWLduHSEhIYSEhHD11VezePFiQBsrat68OU2bNiU4ONjS4zDX8e6771rem11WlWF/vjWXLl2idevWeHl5sWjRIoxGY7WvtaGjpv06RhkSN8fX19cSIsUckqEhsmTJEm666SabtJtvvplPP/20VuU99dRTPPPMMwwYMMApP4SzZ89m/vz5JCcns2jRIt55551qn3v//ffTvn17+vXrR7du3Sq9ptDQUPr378+DDz7IvHnzAG2wfOvWrSQnJzNt2jQWLlwIwOjRo1m6dKllsH327NmWfF26dOHDDz+sUlN4eDgDBgwgKSmJJ598soLehQsX0rdvXw4ePFihB9dYycvL4/Tp03h7e9dL2CJPQjjqOnsynr6xlSPWr1/PihUr6NatG2PHjnWJnn379tG5c+cK6Z4ad8kdqUpjamoqs2bN4qqrrqpnVRXxhLaEynVWdi/XlR07dvDNN98QGxvLHXfcUe3zPGhjqzQpZa1uQNUj8QDM/tjDhw879JkrFArXo8ZHKkcNtnsAERERFp/2mTNnaNWqld6SFE5m9erVektQVIGa9ls1qkfiAQghLDfvoUOHdFajUDQ+zHv1hIWFVTp9uzGjDImH0BjDpSgU7oJya1WNMiQeQnR0NEIIMjMz62W/BYVC8QfKkFSNMiQegr+/P+3atcNkMnHs2DG95SgUjYb8/HyysrJsInIrbFGGxIOo710T65ugoCCb9wsWLGDKlCk6qbFl69atTJ06VW8ZgBYXq7bra5zFK6+8omv99YnZndyxY8d62QveE1GGxIOwHidR04Ar4sqw8FdddZUlcq7eKENSv5gf3MwPcoqKKEPiQbRu3ZrAwEByc3PdcjMnV/Ldd9/Rp08fevTowbBhwyyBB2fOnMnkyZO58cYbufvuu1mwYAFjx45l9OjRREVF8e677/KPf/yDHj160LdvX0t4kh07dljCut90001cvHgR0BYGPv3006SkpBAXF8fatWsBbXruDTfcAGiujj/96U907dqV5ORkS1BFa9LS0hg8eDC9evXiuuuuIysri7KyMnr37m2Z6vvMM8/w3HPPAfC3v/2N3r17k5SUxOTJky0PCocPH2bYsGF069aNnj17cuTIEaZNm8batWvp3r07b731lk29UkqmTJlCly5dGDVqFCNHjrSEtrfeBGzr1q2WRXL2IffNMwMXLFjAuHHjGDFiBLGxsZZAldOmTePy5ct0796diRMnVtjwatasWcycOdPSno8//jhXX301nTt3ZsuWLYwbN47Y2FimT59em1uhXrGe9qvColSOWkfiQZijAe/cuZPDhw8TERHhmnpedM2+1/KFqntR5h8nMxcuXGDMmDEADBw4kI0bNyKE4KOPPuKNN97g73//O6D9aP/444+0aNGCBQsWsHv3brZv305RURGdOnXi9ddfZ/v27Tz++ON8/PHHPPbYY9x9993MmTOHwYMHM2PGDF588UXefvttQOvZbN68mWXLlvHiiy+ycuVKG50vvfQSISEh7Nq1C8BihMyUlpbyyCOP8M033xAREcHnn3/Oc889xzvvvMOCBQsYP348s2fPZvny5WzatAmAKVOmMGPGDECLLvz9998zevRoJk6cyLRp07jpppsoKirCZDLx2muvMWvWLL7//vsKbbh06VIOHDjArl27OHPmDF26dGHSpElVtrt9yP0XX3yRb775BtAM7vbt2/Hz8yM+Pp5HHnmE1157jXfffddhCHpH+Pr6smbNGt555x1uvPFG0tLSCAsLIyYmhscff5zw8PAqz9eTU6dOcfnyZUJDQ9W03ypQhsTD6NSpk8WQ9OvXT285TqVJkyY2wQYXLFhg2QfjxIkT3HbbbWRlZVFSUkJUVJQl35gxY2yi3g4ZMoTg4GCCg4MJCQlh9OjRgBYWfufOneTm5pKTk8PgwYMBuOeee7jlllss51uHpXf0I7ly5Uqbjbfsw4kfOHCA3bt3c+211wLaxlbmMPWJiYncddddjB49mg0bNuDr6wvAqlWreOONNygsLOTChQskJiaSmprKyZMnLTHIqhOFd82aNUyYMAGDwUCbNm245pprrniOfcj94uJiy7GhQ4cSEhICQJcuXcjIyKBdu3ZXLNMa88NA165dSUxMtLRFdHQ0mZmZbm1IzL2zTp06VSuCc2NFGRIPIzo6GtB2sSspKbH8EDkT656Du8RdeuSRR/jLX/7CmDFjWL16tcV1As4JC+/o/MpCrl8pLLyUksTERDZs2GCTbo62u2vXLpo1a2ZxzxUVFfHwww+zdetW2rVrx8yZMykqKqr1OFhl2ry9vS07bVpPIbcPuW82sFC9EPTW5dqXbV2G9Wdhfu/KcS1noKb9Vg81RuJhBAYG0qZNG4xGIxkZGXrLqTesw8KbI+DWlpCQEEJDQy3jH4sWLbL58bwS9iHb7V1b8fHxnDt3zmJISktL2bNnDwBfffUV2dnZrFmzhqlTp5KTk2P54W3evDn5+fmWMY2mTZsSGRlp2YmxuLiYwsLCKkPAX3311Xz22WcYjUaysrIsG3OBNkaSlpYGYDOuU5uQ+z4+PpbNwlq2bMnZs2fJzs6muLjYocvNEykoKODUqVMYDAY17fcKKEPigTTGcCkzZ87klltuYdCgQTRv3rzO5S1cuJAnn3yS5ORkduzYYRmfqA7Tp0/n4sWLJCUl0a1bN5sfa9DGBL788kuefvppunXrRvfu3Vm/fj3Z2dlMmzaNefPmERcXx5QpU3j00Udp1qwZDzzwAF27dmXs2LH07t3bUtaiRYuYPXs2ycnJ9O/fn9OnT5OcnIy3tzfdunWrMNh+0003ERsbS9euXXnooYdsDOQLL7zAo48+yqBBgzAYDJb02oTcnzx5MsnJyUycOBEfHx9mzJhBnz59uOGGG0hISKh2W7oz5kH2Dh06uKTn35BQYeR1oi6hpU+cOMG8efNo1qwZU6dOdYrvVoWRdz16aLz33nu54YYbKuwjXxWe0Jbg+jDyX331Fbt27WL48OF1Go9UYeQVbknbtm0JDAwkJyeHs2fP6i1HoWhwGI1GS49fTfu9Mmqw3QMRQhAXF8f27ds5cOAALVu21FuSwk1xxjbDjRFzTLvw8HCnuFIbOqpH4qHEx8cDcPDgQZ2VKBQNj/379wN/fM8UVaMMiYcSHR2Nt7c3J0+erHQGj0KhqDlSSszjrMqQVA9lSDwUHx8fS+wf1StRKJzHuXPnyMnJISAggMjISL3leATKkHgwcXFxAHjCLDWFwlMwu7Xi4uLw8lI/kdVBtZIHYzYkR48epaSkRGc1zmHp0qUIISxf5ithHYjQnTh16lSNptzWlStF4x05ciQ5OTn1pKbm3H///ezdu1dvGQDKrVULdDUkQogRQogDQojDQohpDo63F0KsEkJsF0LsFEKM1EOnuxIUFERkZCRGo5GjR4/qLccpLFmyhIEDB9rEsnIVrgzP0aZNG8sK9fqgMkMipcRkMrFs2TKaNWtWb3pqgtFo5KOPPqJLly56SyEvL49Tp07h7e2twsbXAN0MiRDCALwHXA90ASYIIezvpOnAF1LKHsDtwPv1q9L9cbp7SwibV3DTphXS6vSqgvz8fH777TfmzZtnY0jMC7rGjx9PQkICEydOtIlDNWfOHAYNGkTXrl0tPRn70Ojm9lmwYAG33HILo0ePZvjw4axevZrBgwdz6623EhcXx7Rp01i8eDEpKSl07drVsro5IyODoUOHkpyczNChQzl+/DigLfibOnUq/fv3Jzo62mI8rEOrG41GnnjiCUvY+jlz5lS49uqGWx87diy9evUiMTGRuXPnAo7Dunfu3JmHH36Ynj17kpmZaem5bdmyheTkZIqKiigoKCAxMZHdu3fbaCkoKGDUqFF069aNpKQkPv/8cwCWL19OQkICAwcOZOrUqZaw+jNnzmTWrFmW85OSkizBLh3pBe0hyLwafsOGDaSmploCdAYFBfHcc8/RrVs3+vbta4lJduTIEfr27Uvv3r2ZMWOGJfijMzHfJzExMWoTq5ogpdTlBfQDfrJ6/wzwjF2efwJPW+Vff6Vy4+LipCewatUqp5Rz5swZOXPmTPnGG29Io9FY63L27t2r/QOufVXBokWL5KRJk6SUUvbr10+mpaVJKbW2atq0qczMzJRGo1H27dtXrl27VkopZYcOHeTs2bPlpUuX5HvvvSfvu+8+KaWUubm5srS0VEop5YoVK+S4ceOklFLOnz9ftm3bVmZnZ1vKDgkJkadOnZJFRUWyTZs2csaMGVJKKd9++2356KOPSimlvOGGG+SCBQuklFLOmzdP3njjjVJKKe+55x45fvx4aTQa5Z49e2RMTIyUUspjx47JxMREKaWU77//vhw3bpy8cOGClFJa6rZm8ODB8qmnnrLU27p1a4umtm3byvPnz9ucW1hYKBMTEy3pgYGBlrKOHTsmhRByw4YNlrQOHTrIc+fOSSmlfO655+Rf//pX+fDDD8tXXnnF4edw//33W97n5OTIy5cvy8jISHnw4EFpMpnkLbfcIkeNGiWllPKFF16Qb775piV/YmKiPHbsWJV6Afn555/bXP+WLVssx7799lsppZRPPvmkfOmll6SUUo4aNUp++umnUkopP/jgA5trtsZyL9eCxYsXy5kzZ1ruPWfgrO+6qwG2ylr+nuu5ILEtkGn1/gTQxy7PTOBnIcQjQCAwzFFBQojJwGSAiIgIy8ZB7kx+fr5TdEop8ff3p7CwkO+++84S8rumhISEaCEn6qyoaqqaqrxo0SIefvhh8vLyGDt2LAsXLiQ2NpbCwkJ69epFSEiI5Sl63759dOvWDSklw4cPx2g0kpCQwH/+8x/y8vI4efIkTz31FEeOHEEIQWlpKXl5eRQVFZGamoqPjw95eXkUFhbSs2dPgoKCKCkpoWPHjgwcOJC8vDxiYmJYsWIFeXl5rF+/noULF1q0Pfnkk+Tl5VFaWsp1111HQUEB7dq148yZM+Tl5ZGfn4/JZCIvL4/ly5czadIkhBDk5eVZ6rbGaDQybNgwS70JCQkWTR06dGD//v0kJyfz5ptvWoIiZmZmsmPHDlJSUmzaNj8/n/bt25OYmGhJk1KSn5+Pn58fjz/+OKmpqfj5+fHyyy9X0JKQkMD06dN5/PHHGTFiBP379yctLY327dvTqlUr8vPzufnmm5k/fz55eXkUFxfbXJPJZCI/P5+8vLxK9RoMBoYPH245x2g0UlBQQF5eHr6+vgwePJi8vDy6dOnCqlWrLJ/BokWLyMvLY/To0TzxxBMO76eioqJafbeMRqMl2u/58+ed9jvirO+6O6OnIXHk57AP/DUBWCCl/LsQoh+wSAiRJKU02Zwk5VxgLmixtjwhro0z4+8UFxezadMmAgMDa13mvn376iW+UmV1mCPi7t+/HyEERqMRIQRvv/02AQEBBAQEWM719/fHx8eH4OBghBCEh4djMBho2rQpUkqCg4N5/fXXufbaa/nuu+9IT08nNTWV4OBg/P39adasmaUs+7J9fHyRXduYAAAgAElEQVQIDQ0lODjYsoe8uZ7g4GBL1FsvLy/Le+vyzPUHBQVZ8hgMBgIDAzEYDJVev8FgsKnXXpOfnx9paWmsXbuWTZs2ERAQQGpqqk2Z5r9BQUEEBQXZ1CWEsKSdPn2awsJCjEYjPj4+FcLwx8fHs23bNpYtW8ZLL73E8OHDGTNmDN7e3pYymzRpYnkfGBho+TwASkpKCAoKqlKv+XOwvv7AwEBLmzZt2tRyLea2N//19va2uDYdtae/vz89evRw2M5VsXfvXqSUREZGMnz48BqfXxmeEmurLug52H4CsN4hJxI4ZZfnPuALACnlBsAfUPEK7DDPLnHKOImdMyrv0iXnOrcq4csvv+Tuu+8mIyOD9PR0MjMziYqKYt26dbW6jNqERq+K/v37W8ZtFi9ezMCBA6t97vDhw/nwww8tg/vm7X5rSm5uLqGhoQQEBLB//342btxoOWYd1v1KTJ48mZdeeomJEyfy9NNPVzielZVFQEAAd955J0888QTbtm0jISGBY8eOWcaMlixZYsnfsWNHtm3bBsC2bds4duzYFfXWhr59+1rC37tiMoZ5PZaarVVz9DQkW4BYIUSUEMIXbTD9W7s8x4GhAEKIzmiG5Fy9qvQA2rdvj7+/P+fPnyc7O1tvObViyZIllp0Azdx88818+umntSqvNqHRq2L27NnMnz+f5ORkFi1axDvvvFPtc++//37at29Pv3796NatW62vacSIEZSVlZGcnMzzzz9P3759Lcesw7pXxccff4y3tzd33HEH06ZNY8uWLfz66682efbs2UNKSgrdu3fn5ZdfZvr06fj7+zN37lxGjRrFwIED6dChgyX/zTffzIULF+jevTsffPCBZQJIVXprw9tvv80//vEPUlJSyMrKsvRanIHJZLIYkoYSBr9eqe3gijNewEjgIHAEeK487W/AmPL/uwC/Ab8DO4DhVyqzsQ22m/nvf/8rZ86cKdevX1+r8ysboLx06VJdZNUbnqDTEzRKWT2dq1atsgy21xcFBQXSZDJJKaVcsmSJHDlypMN8tRlsP3bsmJw5c6acPXu2pQ5noQbbXYyUchmwzC5thtX/e4EB9a3LE4mLi2PXrl0cOHCgwe3lrlAApKWlMWXKFKSUNGvWjNmzZzutbOtFiGpv9pqjwsg3EDp16oSXlxfHjx+nsLCQgIAAvSUpGjCpqan1PoA8aNAgfv/9d8t7ZwUrlVIFaawrKkRKA8Hf35+OHTsipbRMYawpsorBcIXCE6jNPXzu3DkuXrxIQEAA7dq1u/IJigooQ9KAqMsqd39/f7Kzs5UxUXgsUkqys7Px9/ev0Xnm74sK0lh7lGurAREfH8/y5cs5fPgwZWVleHtX/+ONjIzkxIkTnDtnOymuqKioxl9MPfAEnZ6gETxbp7+/f41Dv1sbEkXtUIakAdGsWTNatmzJmTNnyMjIqFHQOR8fH6Kioiqkr169ulaLu+obT9DpCRqhcenMz8/n5MmTKkhjHVH9uAaG2qNEoag+5u9JdHQ0vr6+OqvxXJQhaWBYr3JX4x0KRdUot5ZzUIakgdGmTRuCgoK4dOkSp0+f1luOQuG2lJSUWPbxUdN+64YyJA0MIYRybykU1eDIkSMYjUbatm1rCdCpqB3KkDRAzE9X5thBCoWiImoRovNQhqQBEhUVhY+PD1lZWW69T7dCoRcqSKNzUYakAeLj40NsbCyg7bGgUChsycjI4PLly4SFhdG8udqZoq4oQ9JA6dKlC6AMiULhiD179gDa90QFaaw7ypA0UGJjY/H29ubkyZPk5ubqLUehcBtMJhP79+8HIDExUWc1DQNlSBoovr6+ltlbqleiUPxBRkYGBQUFhIWF0bJlS73lNAiUIWnAKPeWQlER5dZyPsqQNGDM7q0TJ04o95ZCgebW2rdvH6DcWs5EGZIGjK+vr5q9pVBYkZGRQWFhoXJrORllSBo4yr2lUPyBcmu5BmVIGjhxcXHKvaVQoNxarkQZkgaOtXvL/CVSKBoj6enpyq3lIpQhaQQo95ZC8cf9n5iYqNxaTkYZkkaA2b2VmZnJpUuX9JajUNQ71m4t84OVwnkoQ9II8PX1pVOnToBybykaJ2a3Vnh4uHJruQBlSBoJyr2laMyo2VquRRmSRkJcXBwGg4Hjx4+Tl5entxyFot5QsbVcjzIkjQQ/Pz+1OFHRKLF2a7Vo0UJvOQ0SZUgaEcq9pWiMKLeW61GGpBGh3FuKxoZya9UPypA0Ivz8/NTsLUWjQrm16gdlSBoZyr2laEyY3VpqEaJrUYakkWF2b2VkZCj3lqJBoxYh1h/KkDQy/P39iYmJAZR7S9GwOXbsGJcvX6Z58+bKreVilCFphCj3lqIxYL6/1Wwt16OrIRFCjBBCHBBCHBZCTKskz61CiL1CiD1CiE/rW2NDJD4+3uLeys/P11uOQuF0jEajChlfj+hmSIQQBuA94HqgCzBBCNHFLk8s8AwwQEqZCDxW70IbINbuLdUrUTRE0tPTLW6tiIgIveU0ePTskaQAh6WUR6WUJcBnwI12eR4A3pNSXgSQUp6tZ40NlqSkJAB27typsxKFwvns2rULUG6t+kJIKfWpWIjxwAgp5f3l7+8C+kgpp1jl+Ro4CAwADMBMKeVyB2VNBiYDRERE9Priiy/q4QrqRn5+PkFBQbrVbzQa2bBhA0ajkd69exMQEOAwn946q4sn6PQEjeD5Oqt7b9cXntKeQ4YMSZNSXlWbc72dLaYGOHpMsLdq3kAskApEAmuFEElSyhybk6ScC8wFiI+Pl6mpqU4X62xWr16N3jrz8/PZsWMH/v7+lWpxB53VwRN0eoJG8HydO3fuxGg0EhkZyciRI+tfmB2e0p51QU/X1gmgndX7SOCUgzzfSClLpZTHgANohkXhBJKTkwHNDaBXz1ShcDZmd223bt10VtJ40NOQbAFihRBRQghf4HbgW7s8XwNDAIQQzYE44Gi9qmzAdOzYkaZNm5KTk8Px48f1lqNQ1Jm8vDyOHj2KwWBQs7XqEd0MiZSyDJgC/ATsA76QUu4RQvxNCDGmPNtPQLYQYi+wCnhSSpmtj+KGhxCCrl27AmrQXdEwMPeu4+LiaNKkid5yGg26riORUi6TUsZJKWOklC+Xp82QUn5b/r+UUv5FStlFStlVSvmZnnobImb31p49eygrK9NZjUJRe6SU/P7778Af97WiflAr2xs5LVq0oFWrVhQXF3Pw4EG95SgUtebMmTOcPXuWJk2aWDZxU9QPypAoLE9vyr2l8GTMvZGkpCQMBoPOahoXypAo6Nq1K0IIDh06RGFhod5yFIoaYzKZLIsQ1Wyt+kcZEgVBQUHExMRgMpnYvXu33nIUihpz5MgRCgoKCA8Pp02bNnrLaXTUeEGiEKIrWniTVoA/cAFt9fl6cygTheeRnJzM4cOH2blzJykpKXrLUShqhNktm5ycrEKi6EC1DIkQIhp4CJgItARMQA5QDDQDAgCTEOJ/wEfA51JKk0sUK1xCQkICvr6+nDx5kvPnz9O8eXO9JSkU1aKoqMiyL7uaraUPV3RtCSE+AvYA3YG/AT0AfyllhJQyUkoZBLQARgO7gDeAfUKIga6TrXA2Pj4+ln1K1KC7wpPYt28fZWVldOzYkWbNmuktp1FSnTGSIiBBSnmtlPJDKeVOKaXROoOU8ryU8kcp5WNAB2AG0NYFehUuRIVMUXgiau2I/lzRtWUdjbc6lLu0Pq+1IoVu2IdM6dChg96SFIoqycnJISMjA29vb7Uvu47UaNaWEOJtoUayGiwqZIrC0zDfpwkJCfj5+emspvFS0+m/E4CvhRAOA/wLIa6vuySFnqiQKQpPQUqpIv26CTU1JH2BTmj7grQ2JwohrhNCbAK+d6Y4Rf3TokULWrdurUKmKNyevLw8srOzCQwMJDo6Wm85jZoaGZLyPUH6A+eBzUKISUKI9cCPQC7aBlQKD0eFTFF4AmfOnAG0yAxeXmpttZ7UuPWllLnALCAU+BfaosR+UsrhUsq1Ttan0IGkpCRLyJTS0lK95SgUFTAajZw9exZQbi13oKaD7dcJIdYBy4H1wD+BLmjuLkUDwTpkivnLqlC4E4cOHaKsrMwSvVqhLzUNkfIj2gZTg6WU6wCEEDuAfwsh4qSULzhboEIfzCFTTp8+rbcUz8RohLNn4dQp7ZWVRfutW+HgQWjd+o9Xy5bgXeNIRY0e89oR1RtxD2p6B6dKKddYJ0gp5wohjgFfCCHipZS3O0+eQi8SEhLw9/cnPz+frKwsWrdufeWTGiOlpbBuHfz4Ixw48IfhOH0aTLZRgqIB/vUv2/OFgIgIzai0aQOdO8OIEXD11aCmszokLy+PAwcOAFimqyv0pUaGxN6IWKWvKA+J8p1TVCl0x8fHh27durFp0ya2bt3K6NGj9ZbkPpw7pxmO77+Hn36CS5dqX5aUWs/l7Fn4/Xet3H/8AwID4dprYeRI7dVWBYows337dqSUNG/enODgYL3lKKherK27hBBX3CVGSrkH6FN+TichxCAn6FPoSK9evQDYvXs3xcXFOqvRESm1H/mXX4Z+/ZAtW8I998B//lM3I1IVBQXw9dcweTJERkKPHjB9OmzYoOlppJhMJrZt2wagesluRHV6JH8FXhJCLAK+lFL+7iiTECIcGC6EuB1tGvB9TlOp0IWIiAhCQkLIzc1l165dXHXVVXpLql9MJli6FF55Bcp/vACqG9rBGNoM0aYtXm3bQps2ZBYU0C4gALKyMJ06icw6hSG7mjsv7NihvV5+GZKS4Jln4NZbG934yuHDh8nNzSU0NJTQ0FC95SjKqU6sre5CiNuAR4DnhBD5wD60tSTmMPJRQHvgIvAJ8KCU8qTLVCvqjdatW5Obm0taWhq9evVqHHs9lJbC4sXw2mvauMcVMEU0x2vkKM0VFRWljXW0aoXB398m35HVq2mXmgpYuQJKSuDMGcjKgvR0+PlnjD98j+H0mcor3L0bJk6E55+HJ5+Ee+8Fu7oaKmlpaQD07NlTRV5wI6r1OCOl/Bz4XAjRCRgK9ETb2CoQOAOsAX4DVksp1cKDBkRERAQZGRmcPn2aU6dO0bYh++ovX4Z58+DNN+H48Sqzyh49EDfcAKNG4dW7N9R2QZyvL7Rrp71SUuDWWzFIqfU+fvgB+cP3sGkzwpE76+hReOghePFFePxxePBBaNq0djo8gNzcXA4dOoSXlxc9evRgy5YtektSlFPTfnGxlPKfLlGicEu8vLzo3r07GzZsIC0trWEaktxc+OAD5FtvIapaNzNyJIwdCyNHIlzZDkJoYyI9eiCmT9cG95cvh6VLkd98g7CbDcbp0/D008hXX0X83//Bo49qM8EaGNu2bUNKSWJiIoGBgXrLUVhR08eodCFEI3OUK6wH3YuKinRW40SkhIULkTEx8MwzDo2INBjgrrtgzx744Qd44IH6n0EVEaFp+OorxIED8MADSF/fCtlETg68/LJ2Pe+9V2H6sSdjNBotg+zm+1HhPtTUkAhgqRDiByHE6+UzunoIIfzKXw4H4hWeTXh4OB07dqS0tLThxN86ckQb07j3XkR2doXD0s8PHn4YcegQfPwxuMteF506wdy5iKNH4a9/RQZWDMQt8vJgyhQYOFAbT2kAHDx4kPz8fMLDw9U+OW5IbRy7PwEFwI3AfGArkI82VtLRacoUboX5KTAtLc2zd08sLYXXX0cmJcEvv1Q4LIOC4KmnEOnp2lN9VFT9a6wObdvCrFmIjOMwcyYyzMEMpg0bkOZpwx7ekzQPsl911VWNY8KHh1EbQzJXSnmrlDIBCAJSgPuBNwG1qr2B0rlzZwICAjh79iwnTpzQW07t2LIF2bs3TJuGsPthlf7+8MILiOPH4fXXwVPiN4WHa7ozjsObb2qG0ApRVqZNGU5OhlWrdBJZNy5evMiRI0cwGAwqJIqbUqfYy1LKIillmpRyoZTyZSnlj84SpnAvDAYD3bt3B/54OvQY8vPh8ceRffsifnfgfR06FLF7N8ycCZ66NiEoCJ54ArF3L4wZU/H4oUNwzTUwaRI4cOW5M+b7LSkpiSZNmuisRuGI2hiSiUKI0UIItZNMI8Ps3tqzZw+XL1/WWU01Wb0amZgIb79dYbaTDAuDBQtgxQqIidFHn7Np105bEf/f/yIdrfyePx/ZuTN8+239a6sFRqOR7du3A2qQ3Z2pjSG5E/gGOCSEyBNCbBZCzBdC/FUIcZ2T9SnciLCwMKKjoykrK3P/QXeTCV59FTl0qOausmfiRMS+fVqok4bmcxcCxo3Tru+hhyoePncObrwRnn4a3HxR3759+ygsLKRFixZERkbqLUdRCTU1JL8A16BtanU18ASwEegAPAUsc6o6hdvhEYPuFy9qP5TPPltxzUWHDlpgxE8+gRYt9NFXX4SEwPvva9GJHc06e+MNzd2VlVX/2qqJGmT3DGq61e61UsrfpZS5UsrfpJT/lFJOlVJeI6VsibbaXdGAiY+PJygoiHPnznH8Cqu/dWHrVkw9e2iRea2QQmirv/fs0cK0NyYGDIDt2+Fvf0Pax+Zau1ab2eWGA/Hnz58nPT0dHx8fy/bPCvfEqRsdSynPObM8hfvhtoPuUsI//4lpQH+80jNsD4WFIZYt+yM8e2PE1xeefx6xejWyTRubQ+LMGeSwYVpwSjdaxGg9yO6n9mZxa5xqSBSNA7N7a+/evRQWFuqsBigoIOHVV+HBB/EqsQv1lpKC2L698fVCKmPAAK09hg2zSRYmEzz3HIwejXdurk7i/qC0tNSyC2KjizrtgShDoqgxzZo1o1OnThiNRsuXXTcOHMCU0ptWK1ZUPDZlCqxdC+3b178ud6ZFCy1214wZmsvPmmXL6DV5MmzerI+2cvbu3cvly5dp06YNbex6UAr3Q1dDIoQYIYQ4IIQ4LISYVkW+8UIIqeJ8uQ9uMei+ciXG3lfhtXefTbIMDIQlS2DOHM2lo6iIwQAvvoj48UdkeLjNoSZnzyKvvlrbuEsnzG4tNeXXM9DNkJTvuvgecD3QBZgghKgwtUQIEQxMBTbVr0JFVcTFxREcHEx2djZHjx6tfwH//jem60dgyMu3Te/cGbFlC9yugixUi+uu01xdffvaJIviYm3jrDfeqPcdGU+fPk1mZiZ+fn4kJSXVa92K2qFnjyQFOCylPCqlLAE+Q4vfZc9LwBuAZwcLamB4eXnRu3dvADZs2FB/FUupbeh03314lRltj91xh+aS6dy5/vQ0BNq1g//9Tws/b8/TT2v7nNTjehPz/dS9e3d8VY/SIxB6uSWEEOOBEVLK+8vf3wX0kVJOscrTA5gupbxZCLEaeEJKudVBWZOByQARERG9vvjii/q4hDqRn59PkF1cJHekKp2lpaVs3LgRk8lEr169XH49oqSE+DffpNXKlRWO7f3Tnzh7111uvbjQEz7zVsuXEzdrFl5GWyOdnZLC3hdewBhQMdqwMykuLmbTpk1IKenTpw/+Vez86AntCZ6jc8iQIWlSyloNH+i54bOjb7zFqgkhvIC3gHuvVJCUci4wFyA+Pl6mlm9n6s6sXr2ahqCztLSULVu2YDQaXXs9Fy9ivGkshv+tsU3394dFizjbvLnbt6dHfOapqeyIiKDbSy8hrGZvhW/ezIBnn8Hr+x/AhSvMV6xYYdm8asQVZtp5RHviOTrrgp6urRNAO6v3kcApq/fBQBKwWgiRDvQFvlUD7u5F33Lf+s6dO8nLy3NNJceOUda3T0Uj0rw5/PorjB/vmnobKTm9eiHWr9eiAFjh9ftOTCkp2jbALqC4uNgyyN6/f3+X1KFwDXoaki1ArBAiSgjhixaC3hJJrnz1fHMpZUcpZUe0UCxjHLm2FPoRFhZG586dMZlMbHbFlNEtWyhLuQrvg4ds02NjYeNG6NfP+XUqtJAqGzeC3RoOr6wsTAMHamFmnMy2bdsoLi6mQ4cOasqvh6GbIZFSlgFT0DbK2gd8IaXcI4T4mxDCQRxshbvSr/zHfOvWrZSUlDiv4GXLMF49CO/zF2zTBwyADRsaTsRed6VVK1i9WotbZoVXQQFy9GiYP99pVRmNRjZt0iZmqt6I56HrOhIp5TIpZZyUMkZK+XJ52gwpZYUY11LKVNUbcU/atWtHZGQkRUVFlpDfdeazzzDdOAZDUbFt+m23wcqV2oZOCtcTGAj//S889phNsjAatb1N3nrLKdXs3buX3NxcwsPDiY2NdUqZivpDrWxXOAXzU+SmTZsw1TVe04cfIu+4o+L03mnT4NNPtQF2Rf1hMGgGY/ZspJfdT8Zf/gIzZtRprYmU0jLlt1+/firKrweiDInCKcTHxxMaGsrFixfZv39/rcuRr74KDz2EsP5hEkILh/7qq2D/Q6aoPx55BPHll0j7tR0vvQRTp9Y64GN6ejpZWVkEBgaqrXQ9FPWtVDgFLy8vywyuWi1QlBLTU08inn3WNt3bGxYvdrhBk0IHbroJ8cMPFaMov/su8p57oLTU8XlVYL5fevfujbd9mHuFR6AMicJpdO/eHX9/f06cOEFmZmb1TzQaMU5+AK83Z9mm+/tr28ZOmOBcoYq6MWwY/PJLhf3txSefYBo3DmqwDfO5c+c4dOgQ3t7elkgJCs9DGRKF0/D19bWE/K52r6SkhNIJt2L4aJ5tenAw/PQTjBrlZJUKp9CnD6xZA3b7wnt9/z3GEdfBpUvVKsY6HEqAi1fNK1yHMiQKp5KSkoLBYGDfvn1cuHCh6syFhZSMHonPf76yTW/eXNux7+qrXSdUUXeSkrRtfKOibJINa9ZSNiQVzp+v8vT8/Hx27twJ/DGFXOGZKEOicCrBwcF07doVgI0bN1aeMS+P4uHX4PvzL7bpkZHaHiIqfLhnEB2tGRO7KL3e27ZTNnBAlfvBb968GaPRSOfOnQkLC3O1UoULUYZE4XTMg+47duzgsiN/eU4ORUMG4feb3c4AsbHaj1JCQj2oVDiNNm206MF9+tgkex84SOnA/uBgvKykpIQtW7YAqjfSEFCGROF0WrZsSUxMDKWlpWzdareGNDuby4MH4J9mt7Nit25aT8QuvpPCQwgL0xaKDh1qk+xzNF0zJseO2aTv2LGDoqIiIiMjadeuHQrPRhkShUswP2Vu3ryZMvNeFmfOcHlgH5rs3GubuU8fbUykZct6VqlwKkFB8P33cMMNNsk+x09QOqAfHDwIgMlksgyyq3AoDQNlSBQuITo6mpYtW/4xoHryJIUDUmiy/4htxoED4eefK0wlVXgo/v5aSJWbb7ZJ9sk6o/VMdu9m//795OTkEBoaSnx8vE5CFc5EGRKFSxBCWJ42d3zzDYX9ehNw5LhtpqFDYflyaNpUB4UKl+HrC599BhMn2iT7nMum9OqB7PnkE0DrtXqpSAUNAvUpKlxGUlISUSYTo9+ZRUCm3eyd66+H776ruEJa0TDw9oaFC+G++2ySfS7mMvIfs4i7eJEePXroJE7hbJQhUbgMr4MHuem9t4nILbQ9cOONsHQpNGmijzBF/WAwwNy58H//Z5McWFzKzXM/xLs2oXQUbokyJArXsGsXlwf0ITjbboXzbbfBf/4Dfn766FLUL15eMGcOPPGETbLv5WLKhg/TZnopPB5lSBTOZ9s2igb2pckFWyOyp1cvShcsAB8ffXQp9EEIjK++yqbrrrNJ9i4qwTjqeli2TCdhCmehDInCuWzaRNHgAfhfsnVn7Rs4kC9HjSLNRft9K9yb33fuZHm/fmwYPdom3VBShvHGMZqrU+GxKEOicBpyzRqKh1yNf36R7YFHHsHrX/8CLy/WrVvn3O14FW5PWVkZa9asASDo5Zcr7KpoKDNiumU8LFmihzyFE1CGROEU5MqVlAwfit9lOyPx5JPwzjvExcfTtm1bCgoKLKExFI2Dbdu2kZubS4sWLUhKStK27f3gA5s8XkYTpol3IJ24D7yi/lCGRFFnjD98T9nIEfgVl9kemDEDXn8dhEAIQWpqKgC//fYbxcXFFQtSNDhKS0tZu3YtAKmpqX9so/vggzB/vs2Ol14SxKRJSDsjo3B/lCFR1Anj0q+QY2/Ep9Ruf/VXXoEXX9S2yS0nJiaGdu3acfnyZTZtsgvYqGiQbN26lfz8fFq1akWCfTDOe+/Vdr80GGySxcMPY7JzfyncG2VIFLWmdMli5C3j8S6z26v7rbfgmWcq5BdCMGTIEEDb0KioqKhCHkXDoaSkhHXr1gEwZMiQP3oj1tx+uzYd3G4mn9df/oLxlZfrQ6bCCShDoqgVxfPm4jXxTryN0vbA++9rPvBKiIqKomPHjhQVFdVub3eFx7Bp0yYKCwtp27YtsbGxlWe86SZtS2W7tUWG56ZT9uw0kLKSExXugjIkihpT+I/X8bv/zxisv99CwLx58NBDVzzf3CvZuHEjhYWFV8it8ESKiopYv349ANdcc43j3og1I0dqkYPtoh14v/o6Jf/3IJhMlZyocAeUIVFUHynJm/E0AX+dZptuMMAnn8CkSdUqpn379sTExFBSUmL5sVE0LDZu3EhRUREdOnQgym4r3koZNgx++kkLR2+F7wdzKb5zApSVVXKiQm+UIVFUDynJmfpngl96wzbdxwe++ALuuKNGxZlncG3evJmCggIniVS4A5cvX7Zss1zp2EhlDBoEv/xSYVsBvyVfcPmmG0DN9nNLlCFRXBmjkQt330qzd/9lm96kieaOGDeuxkVGRkYSGxtLaWkpv/32m5OEKtyB9evXU1xcTHR0NB1qs+NlSgqsWQOtWtkkN/n+Jwqvuwby852kVOEslCFRVIkoKyN73AjCPvnS9kDTprBiBQwfXuuyzWMlmzdv5sKFC3WRqXATcnNzbXojtSYpyeHWywH/W09B6gC4eLEuMhVORhkSReVcvkzktKmEf2sXoTUiAlavhgED6lR869atSU5Oxmg08tNPP9WpLIV78PPPP1NWVkaXLl2IjDinyo4AAB1hSURBVIysW2GdOsG6dWC3/iQwbScFA1LwUQ8fboMyJArHXLrEucG9iUnbZ5seGam5HZy0KdGwYcPw9fXl4MGDHDp0yCllKvTh6NGj7N27Fx8fH4bXoadqg/l+69nTJjlw32E6T/kzZGQ4px5FnVCGRFGRM2c417crEVv22KZX8oRYF4KDgxk8eDAAy5cvp0zNzPFIjEYjy5cvB2DQoEGEhIQ4r/CICPj1V20g3oqwrPMUpPSAXbucV5eiVihDorBBHjzIhR4JROyz21+9Ep+1M+jTpw/NmzfnwoULFv+6wrPYvHkz586dIzQ0lH79+jm/gpAQWL5c26LZisCzFynq1xv566/Or1NRbZQhUVgoXb+OvN7JhGXl2B7o0wf+978Ks2ichcFgYMSIEQCsWbOGS5cuXeEMhTuRn5/P//73PwBGjBiBt7e3ayoKCNBWwN96q02yf0ExZdddi/HTxa6pV3FFlCFRAFC49AuMQwbT9JLtPP0LvXtrs7PCwlxaf0xMDAkJCZSWlrJSbb/qUaxcuZLi4mLi4uKIi4tzbWW+vvDppzBlik2yT5kJw8Q7KX79VRVSRQd0NSRCiBFCiANCiMNCiGkOjv9FCLFXCLFTCPGLEML5fhUFF995Hb+bb8O/xC4MxT33sOuVVyA4uF50XHfddXh7e7Nr1y4y1CCqR5CZmcnvv/+OwWDgOrutdF2GwQCzZ3Nk8uQKh/ymPUvhlD+rkCr1jG6GRAhhAN4Drge6ABOEEF3ssm0HrpJSJgNfAnbLqhV1QkrO/vUhQh+bZhs3C2D6dJg/H+kqN4UDmjVrxoDyKcU//vgjJvVj4NaYTCZ+/PFHAPr370+Yi3utNghB5oQJWmgeu8jBAe//i7xxN4CKLl1v6NkjSQEOSymPSilLgM+AG60zSClXSSnNUf02AnWcmK6wUFpK1m0jafGPD23Tvbzgww/hpZds9hKpLwYMGEBISAhnzpxh69at9V6/ovps27aNrKwsmjZtysCBA/URMXEiLFtWodcc/M2PXErtrxYu1hNC6uRPFEKMB0ZIKe8vf38X0EdKOaWS/O8Cp6WU/8/BscnAZICIiIheX3zxheuEO4n8/HyC7ILT1ReGggJaTH+U+B1HbNKNfn7sff55sq0WGuqh89y5c+zduxdvb29SUlLwsXvidISe7VldPEEjVE9naWkpmzdvtiw+jIiIqCd1f2CtM+jwYbpOm4ZfdrZNnrORERx9/W2K2rSpd31mPOVzHzJkSJqU8qpanSyl1OUF3AJ8ZPX+LmBOJXnvROuR+F2p3Li4OOkJrFq1Spd6yw4ekFkdwqXUhiT/eIWHS7l+fYX8eug0mUzy448/ljNnzpTffvtttc7Rqz1rgidolLJ6Or///ns5c+ZMuXDhQmkymVwvygEVdKanS9m5c4V7u6BpE2n8ZaUuGqX0nM8d2Cpr+Xuup2vrBNDO6n0kcMo+kxBiGPAcMEZKqUJ/1oH8H7+hsEcSrTJsn9qIioL168EV8/9rgRCCESNG4OXlxbZt2zh1qsJtodCRrKwstm7davmcahTd15V06KAtmLVzswVcuoy89lqKZqvte12FnoZkCxArhIgSQvgCtwPfWmcQQvQA/olmRM7qoLFhICVnX5+B/w1jCS4otT3Wq5dmRFw9bbOGRERE0KdPH0AbeJdqSqdbIKW0DLD36dOHFi1a6KzIjrAwbbq63VoTg0ni/+hfuDTpTigp0Ulcw0U3QyKlLAOmAD8B+4AvpJR7hBB/E0KMKc/2JhAE/EcIsUMI8W0lxSkqo6SEzAkjaTHtJbztJ0HdfrvDcN3uwuDBgwkKCuLEiRNs2bJFbzkKIC0tjczMTAIDAy2hbdwOf3/47DP4fxWGU2k6fzE5V6fAuXM6CGu46LqOREq5TEoZJ6WMkVK+XJ42Q0r5bfn/w6SULaWU3ctfY6ouUWGNPHOGE70TaPf5ctsDQsArr2gLuwIC9BFXDfz8/Li+PCTGihUrOH/+vM6KGjfZ2dn8/PPPgLaC3d/fX2dFVSAEPPccLP3/7d15fJTltcDx38lCQoAkJJgQAoSlgJAABpQdCqRWBQyLVhAXClqLXtva2+Vqa3trW29re6+tdau24oKaaoFoKgpSUEBkTQJIWAMCCQSCISSGkP25f7wDhmQCCbO8M8n5fj7zyTDvO5OTJ2HOvM9ynnTo0OGiQ5Gbd1A6dCDs3GlTcK2PrmxvpSq3baYoqS/dd35+8YGOHa0yE488Ysv03pYaNGgQQ4cOpaamhvT0dGpra+0OqU2qra0lPT2d6upqBg8eTFJSkt0hNc+MGbBxI/TqddHD4QVFVIwcTvXSf9oTVyujiaQVKvz7U9SNHUOXLxpsYdunD2zaBKn+dWF34403EhERwfHjx1m3bp3d4bRJ69at49ixY4SHhzNlyhS7w2mZwYNh61Zo0BUXWlFD8K23Ufrj7+l+8C7SRNKalJdz6NZvEPOdh2jfsNzJpEmwZQskJtoTmwtCQ0OZOXMmAOvXrycvL8/miNqW/Px81q9fD8DMmTN9u0urKV26WIPw99/f6FD4/z3D6ZFDQf+urpgmklaickcWxwd2p8/S1Y0PPvggrFwJ0dHeD8xNEhISGDNmDMYY0tPTqdKZN15RVVXFsmXLMMYwZswYejXoIvIrwcHw3HPWrUHpn6is3ZxN7E/1O8tsCs6/aSLxd8Zw4s+PU3fdtXQ72qAcREgIvPgiPP10o3pE/mjSpEnExsZSXFysW/N6ycqVKykuLiY2Nta1Pdh9yf33w+rVEBd30cMdvqwgeOYtlNy/QKcIt5AmEn9WWsrnU8bQ9YeP0r66wTqL/v2t8ZDvfMee2DwgKCiIWbNmERgYSFZWFvv27bM7pFZt3759ZGVlERgYyKxZszy3z4gdJkyA7dvBsQ9OfRF/fZnTwwbBwYNOnqic0UTip8o3f8KJq7vTe4WTHQXvugsyM+Gaa7wfmIfFxMSQkpICQEZGBmfPnr3MM9SVKCsrIyPDWraVkpLiewsP3SEmBpYvhyeesErT1xOVc5BzQwZRlfa6TcH5F00k/qa2lqOP/SdB4ybQteDLi4+FhcErr8Brr1nTfFupUaNG0bt3b8rLy8nIyNBV725mjCEjI4Py8nJ69+7NqFGj7A7JcwIC4Kc/tbaR7tnzokPty6toN/cuTt8xC0pKbArQP2gi8SMVO7M5PCSBnr/6E+1qGrx5DhliXYXMm2dPcF4kIkyfPp2QkBD2799Pdna23SG1KgUFBRw4cIDQ0FBmzJjhO7W0PGn0aKuryzE7sL6oN9Mp/VoPqt9NtyEw/6CJxB9UV3Pkp98lYPhweu0+1vj4woXWeMjVV3s/NptEREQwdepUAFasWMG5c+dsjqh1KCoq4qBjbGDq1KmEh4fbHJEXde4MS5dak1PatbvoUPgXXxI8YxZFs24ErbDQiCYSH3duy6fkX92NhD++2PgqJCIC3n4bnn8e2re3J0AbnV9hXV1dTU5ODpWVWhzaFRUVFbz99tvU1dX51+p1dxKxpstv3AgDBjQ6HJ2+krJ+CdbYiXapXqCJxFdVVHD4P+4gePRYuh9y8gkoNRVycuBb3/J+bD5k6tSpREdHc/bsWZYsWaLb816h2tpalixZQmFhIWFhYf63et3dhg2zuroeeaTRQHzHM+W0m3sXRTdNhIICe+LzMZpIfFDZRx9S0C+OXs+92bhib5cukJZm1cuKj7clPl8SGhrK3LlzCQ4OJjc3lxUrVujgewudLw1/8OBBwsLCSEpK8s/V6+4WGmoVN92yBYYObXQ4euU6yvv3pvLF56GNf4DRROJDao8eYf+0MXScfANx+Wcan3D77bB7t1X+vS0MgDZTVFQUiYmJBAYGsnXrVjZv3mx3SH5l48aNZGZmEhgYyJw5c2jfBrtJL2nYMKtW129/22jsJKyskpDvPsAXg79G3bq1NgVoP00kvqCsjM+/fzdVX+tN/+UbGx/v1g0yMqyy7zbsje0PIiIimD59OmCtxtbFis2zd+9eVq1aBVh1tHr06HGZZ7RRwcFWWfrsbHBsuFZfl92fE/D1iRRNmQSHDtkQoL00kdiptpaTT/+e0z260PvpxY1XpwPce681FnLzzd6Pz88MHjyYiRMnArB06VIKtP/6ko4fP87SpUsBmDx5Mol+WNDT6wYNgg0b4MknnU5wif7gY6oH9KPke99tU2tPNJHYJGTrBo4NiCP2+48QdcbJbKOkJKse0N/+BpGR3g/QT02YMIEhQ4ZQXV1NWloapaWldofkk0pKSkhLS6OmpoZrrrmGcQ32OVeXEBgIP/yh9QHv1lsbHQ6uqSPimRc5m9CNir/8CWkDe+hoIvGyqqxtfP71IYz+6aPEH3Sy3WdMjFVoMTsbJk/2foB+TkS4+eab6dmzJ19++SVpaWlaKbiByspK3nzzTcrKyujVqxfTpk1rG4sO3a13b/jnP61V8dde2+hwh5JyQn/wnwyYN5uat9KgFScUTSReUrH+Iw6NS6Ld8Ovove6zxieEhFhTDQ8csAottqYCeV4WFBTE7Nmz6dy5MydOnGDZsmU6Ldihrq7uwjTf6OhobrvtNgIbTG9VLTRuHGzeDIsXQ/fujQ53PVZE0Jy5FPeNp/qlv0F1tQ1BepYmEk8yhvLl73JkWF9CJ0ymz4Yc5+fdfjvs22dNNWxLK4k9KCwsjLlz5xIaGsq+fftYuXJlm58WbIzh/fffJzc390L76AwtNwkIgDvvtP4f//rXVt27BjofOUnwvfdR2jOWqqeehFZUjUETiSfU1VH2j8UcG9idsGkzSMhuYhbH6NHWCto334SEBO/G2AZ06dKF2bNnExAQwJYtW3jvvffa7JVJXV0dGRkZF03zjYqKsjus1icsDH7xC6tnYf58p9P0w08U0+6hH3E2PoaKxx+DVjCOp4nEncrKOP3M/3Kydwwdb7+b+H3HnZ83YgSf/eY31uyP1lxZ1Qf06tWL2267jaCgILKysliyZAk1bWx/7urqat566y22b99+odtPp/l6WLdusGgR5ORw4oYbGq2OB+hQXEboo7/iXHwsZT980Eo+fkoTiauMoW7LZvLmTOHcVZFEfe8nxB4tcn5uSoo1E2vTJorGjdNFhV4yYMAA7rzzTkJCQtizZw9vvPEGFRUVdoflFefOnWPx4sXs37+f9u3bM2/ePPr162d3WG3HwIHsffhhyM2FBx6wxkIbaF9WQcc/Pwv9+3N6dDJ1aW+Cn9WN00Rypc6cofTJ33GyfzwBI0fR460PaF/RxKyMGTOswbh//9uaiaUJxOsSEhKYP38+HTt25PDhw7z66quUlZXZHZZHlZaW8vLLL5OXl0d4eDjz58+nu5PBYOUFvXrBs8/C4cPwk580uV9Q1KbtBMy9g/LYKM59/wHYu9erYV4pTSQtUVuLWbuWglu+SWVsF8J/9DNic5tY9BYYaA2+7doF6ekwYoR3Y1WNxMbGcs899xAVFcWJEydYtGgRp0+ftjssj/jiiy9YtGgRp06d4qqrrmLBggVcpVUR7Ne1K/zhD3DkCDz2GDQxThVWUk77p5+HgQMpGTkU8/LLUFzs5WCbTxPJ5VRXY1au5ORdMym9KhyZOJG4ZasIqWri6iMuDn72M+tSdvFi0NXCPiUyMpIFCxYQFxdHcXExixYtanUr4PPz81m0aBElJSV0796d+fPnExERYXdYqr6oKPjlL+HoUXj5ZRgzpslTI7bsRBYsoPaqLpRMHI154QUoLPRisJenicSZc+eoeyedwltvojyqE3LjjcS+/g7hxeXOzw8IgKlTrYq8R4/C449bl7LKJ3Xo0IF58+bRp08fzp49yyuvvMLhw4ftDsstcnNzee211zh37hz9+vXj7rvv1im+vqxDB/j2t62JN599Bj/4gbXBlhOBtXVErN2ELFxIXVxXSkcNwzz1FOTnezdmJzSRgLVBzYED1Pz1eU5NmUhl53ACZs4iZukKwsouMejVs6d1eXrkCLz3HkyfrgsJ/URISAhz584lMTGRqqoqXn/9dT799FO/nR5cW1vLJ598QlpaGtXV1QwdOpTZs2cTHBxsd2iquZKS4M9/hmPH4PXXYcKEJk8NqDOEb85GHnoIevTgy+RE6h79OXz0EdgwkaTtvusdOYJZs4aSD9IJXLueToVnCAIu24vcqZN19TFvHlx/vdNpfco/BAYGcsstt9ChQwe2bNnCqlWr2L17N6mpqcTExNgdXrMVFBSQkZHBiRMnABg7diwpKSla9sRftW8Pd9xh3fbts7rIly695MB7p+27YftuePx/qGkXROXIawn75lQkJcUq3+LhDxRtI5HU1Fj7eGRmcvbjVdSt+Ted8k8hQLPKIUZHWzOvZs2ypvA6mcKn/JOIcNNNN9G3b1+WL1/OsWPHeOGFFxg/fjzjx4/36fIhNTU1rF27lg0bNmCMITIykmnTptG3b1+7Q1PuMmCAtQ/Kb38Le/ZYCWXpUmv3xiYEVdUQtH4TrN8Ev/gF1WGh1I4bS+iESVZSGT7c2iDPjVpfIjEGduyAzEyqtmyiYvMG2u/eT3CVtQitQ3NfJz7eShyzZlm1dLTLqlXr378/CQkJrFq1iszMTNauXcuePXtITU0l3gd3ojx69CgZGRkUFVlrlkaOHMnkyZNp12DjJdWKDBwIjz5q3Q4dgmXLrKSyadMlnxZcXkHwh6vhw9UXHqvo3pWg60YRNGLkV8nFBa3u3bFj7gG45hoA2jluzRIaCmPHWus8vvENq3EDdAipLQkJCWHatGkkJSXxr3/9i8LCQl566SVGjRrFpEmTfGK8obKyktWrV7N161bAKgOTmpqqK9Xbmj594Mc/tm7Hj8OaNdZt9Wprws9lhOafgPx3IP0dt4TT6hKJNLcuX3CwVetq0iQreYwcqV1WCrDKqixcuJCPP/6YjRs3snHjRvbu3UtKSgpXX321Ld1dNTU17Nmzh9WrV1NSUkJAQADjxo1j/PjxBOnVctvWrZu1Zu3OO60emc8//yqxrFkDJ096PIS28xcYF2ddvg0fbnVVjRnjtEKnUgDBwcFcf/31JCYm8u6771JYWMiSJUsICwtj6NChJCcne2WB38mTJ8nKymLnzp0XyrrExcWRmppK165dPf79lZ8Rsa5W+vSxdlc1xhpb+eQTyMyEbdtg505r3NiNWmci6dr1q36/87du3eyOSvmhbt26cd9995GZmUlmZiaFhYUXrlJ69OhBcnIyiYmJbh2bqKysZNeuXWRnZ3Ps2LELj8fFxTF8+HCSk5MJ0G5X1Rwi1vbAgwZ99VhFhbVmZdu2r245OS5tvGVrIhGRG4GngEDg78aY3zc4HgK8BgwHioDZxpjDl3rNsj594OBBzwSs2qTAwEBGjBjBddddx/Hjx8nKymLXrl3k5eWRl5fHihUrSEpKIjExkejoaDp16tSiN/q6ujpKS0spKipi165d5OTkUO3Y/CgkJIQhQ4aQnJxMXFycp35E1ZaEhsJ111m38yoqnO5B31y2JRIRCQSeBa4H8oGtIpJhjNld77R7gGJjzNdEZA7wBDD7Uq9rtL9YeYiIEB8fT3x8PDfccAM5OTlkZ2eTl5dHVlYWWVlZAAQEBBAZGXnh1rlzZzp37syZM2fYtWsXxcXFnDlz5sLXkpKSRgshExISGDZsGAMHDvSJQX7VyoWGuvR0O991RwC5xphDACLyD2A6UD+RTAd+5bi/BHhGRMS09a3ulO3atWtHcnIyycnJnDp1iuzsbPLz8ykuLqasrIzTp087LQi5Y8cOp6/XqVMnIiMj6dmzJ8nJyURHR3v6R1DKbexMJPFAXr1/5wMjmzrHGFMjIiVANPBF/ZNE5D7gPsc/K0Vkl0cidq8uNPg5fJTG6T7+ECNonO7mL3EOuNIn2plInNVvaHil0ZxzMMa8CLwIICLbjDHXuh6eZ2mc7uUPcfpDjKBxups/xXmlz7Vz6kc+UH8VVXeg4d60F84RkSAgAmidG0gopZSfsjORbAX6iUhvEWkHzAEyGpyTAcxz3L8VWKPjI0op5Vts69pyjHk8CKzEmv67yBiTIyK/BrYZYzKAl4DFIpKLdSUypxkv/aLHgnYvjdO9/CFOf4gRNE53a/Vxin7AV0op5QpdHquUUsolmkiUUkq5xO8TiYj8UUT2ishOEUkXEad7VYnIjSKyT0RyReRhG+L8lojkiEidiDQ5FVBEDovIZyKy3ZXpeFeqBXHa3Z5RIrJKRA44vjrd6FpEah1tuV1EGk7m8FRsl2wbEQkRkbccxzeLSC9vxOUkjsvF+W0ROVWv/e61IcZFIlLY1NowsfzF8TPsFJFh3o7REcfl4pwoIiX12vKX3o7REUcPEflIRPY4/p//wMk5LW9TY4xf34BvAkGO+08ATzg5JxA4CPTB2qJkBzDIy3EOxFrw8zFw7SXOOwx0sbE9Lxunj7TnH4CHHfcfdvZ7dxwr83Jcl20b4AHgr477c4C3bPg9NyfObwPPeDu2BjFMAIYBu5o4PgX4AGvN2Shgs4/GORF4z862dMQRBwxz3O8E7Hfye29xm/r9FYkx5kNjzPmayJuw1qM0dKEcizGmCjhfjsVrjDF7jDH7vPk9r0Qz47S9PR3f71XH/VeBGV7+/k1pTtvUj30JkCLe32DdF36Hl2WMWcel145NB14zlk1ApIh4vbplM+L0CcaYAmNMluP+l8AerAoi9bW4Tf0+kTSwACuTNuSsHIvv7Z9qMcCHIpLpKP3ii3yhPWONMQVg/ecAYpo4L1REtonIJhHxRrJpTttcVPoHOF/6x5ua+zu8xdG9sUREfHEbRl/4W2yu0SKyQ0Q+EJFEu4NxdKkmA5sbHGpxm/pFqVwR+TfgbBefnxtj3nWc83OgBnjD2Us4eczt856bE2czjDXGHBeRGGCViOx1fNpxGzfEaXt7tuBlejrasw+wRkQ+M8Z4cp8Bt5X+8bDmxPAvIM0YUykiC7GuoiZ7PLKW8YW2bI4sIMEYUyYiU4B3gH52BSMiHYGlwEPGmNKGh5085ZJt6heJxBjzjUsdF5F5wDQgxTg6+RpoTjkWl10uzma+xnHH10IRScfqgnBrInFDnLa3p4icFJE4Y0yB47K7sInXON+eh0TkY6xPYJ5MJC0p/ZNvY+mfy8ZpjCmq98+/YY1B+hqv/C26qv6btTHmfRF5TkS6GGO8XsxRRIKxksgbxphlTk5pcZv6fdeWWJtj/ReQaowpb+K05pRjsZ2IdBCRTufvY00k8MVKxr7QnvXL58wDGl1JiUhnsTZHQ0S6AGO5eJsCT/CX0j+XjbNBv3gqVn+6r8kA7nbMNBoFlJzv8vQlItL1/DiYiIzAeu8tuvSzPBKHYFUM2WOMebKJ01repnbPInDDLIRcrP687Y7b+dkw3YD3G8xE2I/1afTnNsQ5EyvTVwIngZUN48SaQbPDccvx1Th9pD2jgdXAAcfXKMfj12LttgkwBvjM0Z6fAfd4KbZGbQP8GuvDDkAo8E/H3+4WoI+326+Zcf7O8Xe4A/gIuNqGGNOAAqDa8Xd5D7AQWOg4Llgb5B10/I6bnBFpc5wP1mvLTcAYm+Ich9VNtbPee+YUV9tUS6QopZRyid93bSmllLKXJhKllFIu0USilFLKJZpIlFJKuUQTiVJKKZdoIlFKKeUSTSRKKaVcoolEKaWUSzSRKOVBIvJ1ETEiclO9x3o7NkH6i52xKeUuurJdKQ8TkTVAqDFmjIhEAJ8CnwPTjTG19kanlOs0kSjlYSIyHquC8w3Aj4BYYJwxpszWwJRyE00kSnmBiKzCKiJ5BhhpjMm3OSSl3EbHSJTyjlwgDPhvTSKqtdErEqU8zLFl8tNY+3lUGGNG2RySUm6liUQpDxKR64HlwL1Ye39sBKYYYz6wNTCl3EgTiVIeIiKJwAbgGWPMo47HVgERxpgRtganlBtpIlHKA0QkBtgMbANuM+e3nhOZAKwFphljltsYolJuo4lEKaWUS3TWllJKKZdoIlFKKeUSTSRKKaVcoolEKaWUSzSRKKWUcokmEqWUUi7RRKKUUsolmkiUUkq55P8BYtavcTZNDTQAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "g = 0.001 Perturbative partition function: 0.424365129708 Monte Carlo partition function 0.4243933472931773\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "g = 0.01 Perturbative partition function: 0.415052418619 Monte Carlo partition function 0.49819385022243384\n" ] }, { "data": { "image/png": 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WDB48GID27duzY8cOQFM+hrYnTpzInDlzjNePGjUKJycn2rZtm+dChu3btzNt2jRcXLSPW35BM8eP1/bo9uvXj6SkJBISEti9e7dRAd5zzz3cunWLxMTEXNdu376d06dPG48NS1YBhg8fjru7O+7u7tSpU6fQxRaZmZk8/fTThIWF4ezszLlz5wqsX5FRjvaioRRJJaMoK7dMZw7ltTnt1q1b/PXXX5w8eRIhBNnZ2Qgh+OCDDwBwd3c31nV2djbzbxjOmZa/8cYbDBw4kI0bNxIREWEWfdXSRGHatpOTk/HYyckpXz+K6TJQ0+vz8j1JKYu0bNSyjhAiz/byakuv17Nv3z6qVKmS61xBY5cXn332GXXr1uX48ePo9Xo8PDwKlb2iojYiFg3lI6lk2OvKrR9//JFJkyYRGRlJREQEUVFRNG/enN27d5eovcTEROOvyNWrV5davl69ehn9NmvXrjXOhorC4MGDWbZsmfELPD/T1vr16wHYvXs3Pj4++Pj40K9fP9auXQtovqJatWpRrVo1vL29zfxcgwcP5tNPPzUeG0xW+WF5vSlJSUnUr18fJycnQkJCyM7OLvK9ViTS09OJi4vD2dmZevXq2Vocu0YpkkqGYUYSFxdnV18Q69atY/To0WZlY8eO5bvvvitRe3PmzOHVV1+ld+/eVrnPJUuWsGrVKoKCgggJCeGTTz4p8rVTpkyhSZMm9OzZkw4dOuR7T9WrV6dXr15MmzaNlStXApqz/PDhwwQFBTF37lzWrFkDwIgRI9i4caPR2b5kyRJjvbZt27Js2bICZapZsya9e/emXbt2zJ49O5e8a9asITg4mHPnzlVaJ7NhNlKvXj2jWVKRN8Jel4GWFJXYqnCWLFnC7du3mTZtmnGGcubMGdq0aZOrrqPGXbJHCpJxwIABLFq0iK5du5azVLlxhLGE/OXM71kuLrt27eKvv/6ie/fuDB06tMTtOFBiqyNSyhI9gGpGUglRSa4UisJRK7aKjpqvVULq1q1LeHi43flJKjOhoaG2FkFhgl6vN+4VKk5a3cqKmpFUQlTMLYWiYG7cuEFaWho+Pj74+vraWhy7RymSSogybSkUBWPYoNm0aVPbCuIgKEVSCalevTqurq7odDpSU1NtLY5CYXdERkYCSpEUFaVIKiFOTk7Url0bULMShcISKaVRkTRr1sy2wjgISpFUUgzmrdjYWBtLchcvLy+z49WrVzN9+nQbSWPO4cOHmTFjhq3FADSzS0n311iLd99916b9lyVxcXGkpqbi7e1N9erVbS2OQ6AUSSWlQYMGgJaHoqJQlmHhu3btaoyca2uUIilbTP0jKiNi0VCKpJLiaIrkt99+o0ePHnTq1In77rvPaJJbsGABU6dO5cEHH2TSpEmsXr2aUaNGMWLECJo3b86nn37KRx99RKdOnQgODjaGJwkLCzOGdR89ejS3b98GtI2Br7zyCt27d8ff359du3YB2vLcBx54ANDC3T/55JO0b9+eoKAgY1BFU44cOUL//v3p0qUL999/PzExMWRlZdGtWzfjUt9XX32V119/HYC3336bbt260a5dO6ZOnWqMsXXhwgXuu+8+OnToQOfOnbl48SJz585l165ddOzYkY8//tisXykl06dPp23btgwfPpxhw4YZQ9ubJgE7fPiwcZOcZcj98+fPA9qMcMyYMQwZMgQ/Pz9joMq5c+eSmppKx44dmTBhQq6EV4sWLWLBggXG8Zw1axb9+vWjTZs2HDp0iDFjxuDn58e8efNK8iiUOco/UnzUPpJKSt26dXF2dubWrVukpaWZnRNvlc2vMPlmwVEUDF9OBuLj4xk5ciQAffr0Yf/+/QghWLFiBR988AH/+c9/AO1Le+vWrdSpU4fVq1dz8uRJjh07RlpaGq1ateL999/n2LFjzJo1i2+++YYXXniBSZMmsXTpUvr378/8+fN56623WLx4MaDNbA4ePMiWLVt466232L59u5mcCxcuxMfHh7///hvAqIQMZGZm8vzzz/Prr79Su3Zt1q9fz+uvv84nn3zC6tWrGTduHEuWLOH333/nwIEDAEyfPp358+cDWnThzZs3M2LECCZMmMDcuXMZPXo0aWlp6PV63nvvPRYtWsTmzZtzjeHGjRs5e/Ysf//9N9evX6dt27ZMnjy5wHG3DLn/1ltv8euvvwKawj127Bju7u60bt2a559/nvfee49PP/00zxD0eeHm5sbOnTv55JNPePDBBzly5Ag1atSgZcuWzJo1i5o1axZ4fXmi/CMlQymSSoohEN3Vq1ftZlZSpUoVs2CDq1evNubBiI6O5pFHHiEmJoaMjAyaN29urDdy5EizqLcDBw7E29sbb29vfHx8GDFiBKCFhT9x4gSJiYkkJCTQv39/AJ544gkeeugh4/WmYenz+pLcvn27WeItSzv62bNnOXnyJIMGDQK0xFaGMPWBgYFMnDiRESNGsG/fPtzc3ADYsWMHH3zwAXfu3CE+Pp7AwEAGDBjA1atXjTHIihKFd+fOnYwfPx5nZ2caNGjAPffcU+g1liH309PTjefuvfdefHx8AGjbti2RkZE0bty40DZNMfwYaN++PYGBgcaxaNGiBVFRUXalSG7dukVKSgpVq1a1K7nsHaVIKjENGzbk6tWrXL16lVq1ahnLTWcO9hJ36fnnn+fFF19k5MiRhIaGGk0nYJ2w8Hldn1/I9cLCwkspCQwMZN++fWblhmi7f//9N76+vkbzXFpaGs8++yyHDx+mcePGLFiwgLS0tBKnQ85PNhcXF/R6vbFPA5Yh9w0KFooWgt60Xcu2TdswfS8Mx2Xp1yoJyj9SMpSPpBLjSH4S07Dwhgi4JcXHx4fq1asb/R8hISFmX56FYRmy3dK01bp1a+Li4oyKJDMzk1OnTgHw888/c+vWLXbu3MmMGTNISEgwfvHWqlWL5ORko0+jWrVqNGrUyJiJMT09nTt37hQYAr5fv358//33ZGdnExMTY0zMBZqp5siRIwBmfp2ShNx3dXU1JgurW7cuN27c4NatW6Snp+dpcnMUlH+kZChFUokxfHkYwmXbMwsWLOChhx6ib9++ZrOnkrJmzRpmz55NUFAQYWFhRv9EUZg3bx63b9+mXbt2dOjQwezLGjSfwI8//sgrr7xChw4d6NixI3v37uXWrVvMnTuXlStX4u/vz/Tp05k5cya+vr48/fTTtG/fnlGjRtGtWzdjWyEhISxZsoSgoCB69epFbGwsQUFBuLi40KFDh1zO9tGjR+Pn50f79u355z//aaYg33zzTWbOnEnfvn1xdnY2lpck5P7UqVMJCgpiwoQJuLq6Mn/+fHr06MEDDzxAQEBAkcfSnlD+kZKjwsjbCHsILS2l5P333yc9PZ1x48YRGBiYq469mLYKwxHktIWM//jHP3jggQdy5ZEvCEcYS7B+GPn4+HiWLl1KlSpVmD17ttVMW/bwWS8KKoy8okQIIYzmLXtKcqVQ2ALlHyk5ytleyWnQoAGXL19WiqSCYo00w5UF5R8pOWpGUskx+EnsbfWMQlHeKP9IyVGKpJJjUCTZ2dklXm6qUDg6CQkJJCYm4uHhYczXoyg6SpFUcry9vfHy8kJKqcxbikqLwT/SpEkTnJzU12JxUSNWyTF1uGdkZNhYGoXCNij/SOlQikRhNG8ZNpjZko0bNyKEIDw8vEj1TQMR2hPXrl0r1pLb0lJYNN5hw4aRkJBQTtIUnylTpnD69Gmb9a/8I6XDpopECDFECHFWCHFBCDE3j/NNhBA7hBDHhBAnhBDDbCFnRccwI7EHRbJu3Tr69OljFsuqrCjLBQYNGjQw7lAvD/JTJFJK9Ho9W7Zssdvc49nZ2axYsYK2bdvapP+kpCRu376Nm5sb9erVs4kMjo7NFIkQwhn4DBgKtAXGCyEsn6R5wAYpZSfgUeDz8pWycmA2IxHC7OVdrVquslK9CiA5OZk9e/awcuVKM0Vi2NA1btw4AgICmDBhgtnCgKVLl9K3b1/at29vnMlYhkY3bFJdvXo1Dz30ECNGjGDw4MGEhobSv39/Hn74Yfz9/Zk7dy5r166le/futG/fnosXLwLaL9Z7772XoKAg7r33Xq5cuQJoG/5mzJhBr169aNGihVF5mIZWz87O5uWXXzaGrV+6dGmuey9quPVRo0bRpUsXAgMDWb58OZB3WPc2bdrw7LPP0rlzZ6Kioowzt0OHDhEUFERaWhopKSkEBgZy8uRJM1lSUlIYPnw4HTp0oF27dqxfvx6A33//nYCAAPr06cOMGTOMYfUXLFjAokWLjNe3a9fO6HPIS17QkpgZdsPv27ePAQMGGAN0enl58frrr9OhQweCg4ONMckuXrxIcHAw3bp1Y/78+cbgj6VF+UesgJTSJi+gJ/CHyfGrwKsWdb4EXjGpv7ewdv39/aUjsGPHDluLYMb+/fvl1atXpYSyfRVASEiInDx5spRSyp49e8ojR45IKbWxqlatmoyKipLZ2dkyODhY7tq1S0opZdOmTeWSJUtkUlKS/Oyzz+RTTz0lpZQyMTFRZmZmSiml3LZtmxwzZoyUUspVq1bJhg0bylu3bhnb9vHxkdeuXZNpaWmyQYMGcv78+VJKKRcvXixnzpwppZTygQcekKtXr5ZSSrly5Ur54IMPSimlfOKJJ+S4ceNkdna2PHXqlGzZsqWUUsrLly/LwMBAKaWUn3/+uRwzZoyMj4+XUkpj36b0799fzpkzx9hv/fr1jTI1bNhQ3rx50+zaO3fuyMDAQGN51apVjW1dvnxZCiHkvn37jGVNmzaVcXFxUkopX3/9dfnSSy/JZ599Vr777rt5vg9TpkwxHickJMjU1FTZqFEjee7cOanX6+VDDz0khw8fLqWU8s0335QffvihsX5gYKC8fPlygfICcv369Wb3f+jQIeO5TZs2SSmlnD17tly4cKGUUsrhw4fL7777Tkop5RdffGF2z6acPn06z/L82LRpk1ywYIHxmbI29vZZzw/gsCzh97ktNyQ2BKJMjqOBHhZ1FgD/J4R4HqgK3JdXQ0KIqcBUgNq1axsTB9kzycnJdiWnp6dnufSTX7BB0OJKPfvss+h0OkaNGsWaNWvw8/Pjzp07dOnSBR8fH+Ov6DNnztChQweklAwePJjs7GwCAgL44Ycf0Ol0XL16lTlz5nDx4kWEEGRmZqLT6UhLS2PAgAG4urqi0+m4c+cOnTt3xsvLi4yMDJo1a0afPn3Q6XS0bNmSbdu2odPp2Lt3L2vWrDHKNnv2bHQ6HZmZmdx///2kpKTQuHFjrl+/jk6nIzk5Gb1ej06n4/fff2fy5MkIIdDpdMa+TcnOzua+++4z9hsQEGCUqWnTpoSHhxMUFMSHH35oDIoYFRVFWFgY3bt3Nxvb5ORkmjRpQmBgoLFMSklycjLu7u7MmjWLAQMG4O7uzjvvvJNLloCAAObNm8esWbMYMmQIvXr14siRIzRp0oR69eqRnJzM2LFjWbVqFTqdjvT0dLN70uv1JCcno9Pp8pXX2dmZwYMHG6/Jzs4mJSUFnU6Hm5sb/fv3R6fT0bZtW3bs2GF8D0JCQtDpdIwYMYKXX345z+cpLS2tWJ+tM2fOAFqIlLL4TNrbZ70ssKUiycvOYbmRYTywWkr5HyFETyBECNFOSqk3u0jK5cBy0GJtOUJcG3uLv2OaB6QsyS+GkyEibnh4OEIIsrOzEUKwePFiPD098fT0NF7r4eGBq6sr3t7eCCGoWbMmzs7OVKtWDSkl3t7evP/++wwaNIjffvuNiIgIBgwYgLe3Nx4eHvj6+hrbsmzb1dWV6tWrG5dFG2QWQuDt7W2Meuvk5GQ8Nm3P0L+Xl5exjrOzM1WrVsXZ2Tnf+3d2djbr11Imd3d3jhw5wq5duzhw4ACenp4MGDDArE3DXy8vL7y8vMz6EkIYy2JjY7lz5w7Z2dm4urrmCsPfunVrjh49ypYtW1i4cCGDBw9m5MiRuLi4GNusUqWK8bhq1arG9wO01X9eXl4Fymt4H0zvv2rVqsYxrVatmvFeDGNv+Ovi4mI0beY1nh4eHnTq1CnPcbZEp9Pxv//9D1dXV4YPH24WzNJa2NtnvSywpUEwGjDNkNMIsIxn/hSwAUBKuQ/wAEof+lUHTFo2AAAgAElEQVSRC8MH6Mb162bGKF1SknWNW/nw448/MmnSJCIjI4mIiCAqKormzZuze/fuEt1PSUKjF0SvXr2Mfpu1a9fSp0+fIl87ePBgli1bZnTuG9L9FpfExESqV6+Op6cn4eHh7N+/33jONKx7YUydOpWFCxcyYcIEXnnllVznY2Ji8PT05PHHH+fll1/m6NGjBAQEcPnyZaPPaN26dcb6zZo14+jRowAcPXqUy5cvFypvSQgODjaGv7fWYgzDaq3GjRuXiRKpLNhSkRwC/IQQzYUQbmjO9E0Wda4A9wIIIdqgKZK4cpWykmD4EGVlZZklKSov1q1bZ8wEaGDs2LF89913JWqvJKHRC2LJkiWsWrWKoKAgQkJC+OSTT4p87ZQpU2jSpAk9e/akQ4cOJb6nIUOGkJWVRVBQEG+88QbBwcHGc6Zh3Qvim2++wcXFhccee4y5c+dy6NAh/vrrL7M6p06donv37nTs2JF33nmHefPm4eHhwfLlyxk+fDh9+vQx228xduxY4uPj6dixI1988QX+/v6FylsSFi9ezEcffUT37t2JiYkxzlpKg9o/YiVK6lyxxgsYBpwDLgKv55S9DYzM+b8tsAc4DoQBgwtrUznbS8bp06fl9evX5dWrV2VaWpqxPCkpyYZSFR1HkNMRZJSyaHLu2LHD6GwvL1JSUqRer5dSSrlu3To5bNiwPOsVx9n+2WefyQULFsjIyEiryJgX9vZZzw8c1NmOlHILsMWibL7J/6eB3uUtV2XFzc2NrKwsMjMzzVKiKhT2wJEjR5g+fTpSSnx9fVmyZEmp2ktJSSEuLg4XFxfjXipFyVBh5BVGXF1dAfvYmKiwbwYMGFDuDuS+ffty/Phx43FBKwCLgsGs1ahRI1xc1FdhaVC7bxRGDIpExdxSOCqygAUdlij/iPVQikQBaEsmExMTAW1Nvy0c7gpFaZBScuvWLTw8PIpUX8XXsh5qPqcAtOl9dHQ0cXFxZGdnc/PmTVxdXUlLSyvyB9OWOIKcjiAjOLacHh4eNGrUqNBr79y5w/Xr13F2djYuE1eUHKVIFIBm1mrevDlnz57lwIEDDBw4kH79+hEaGlrkzV22xBHkdAQZoXLIeenSJUCLr2Uw6SpKjjJtKcwwrF65ds1yb6hCUXG4cOECAK1atbKxJBUDpUgUZhim+VevXrWxJApF2SClVIrEyihFojCjRo0aeHh4kJycTFJSkq3FUSisTmxsLCkpKVSrVo3atWvbWpwKgVIkCjNMU++qWYmiImKYjbRs2RJRSI4cRdFQikSRC+UnUVRklFnL+ihFosiF8pMoKippaWlERUUhhKBFixa2FqfCoBSJIhcGRXLt2rVi7RRWKOydy5cvI6WkcePGDrFXxlFQikSRC29vb7y9vUlPTyc1NdXW4igUVuP8+fOAMmtZG6VIFHlimJWUNjCeQmEvSCmNibmUIrEuSpEo8sTgcFeKRFFRiIuLIykpiapVq1KvXj1bi1OhUIpEkSeGGYnaS6KoKJiu1lLLfq2LUiSKPGnYsCFCCHQ6nQorr6gQmO4fUVgXpUgUeeLu7k79+vUBiIqKsrE0CkXpyMjI4MqVK4BSJGWBUiSKfDEk/ImIiLCtIApFKYmIiCA7O5uGDRvi6elpa3EqHEqRKPLFkPDHkABIoXBU1LLfskUpEkW+NGnSBNB2uKs87gpHRUX7LXuUIlHki4eHB15eXuj1eqKjo20tjkJRIuLj40lISKBKlSrGZe0K66IUiaJAfHx8AOUnUTgupqu1nJzUV15ZoEZVUSC+vr6A8pMoHBdl1ip7lCJRFIhhRhIdHU1WVpaNpVEoikdmZqZxNq2W/ZYdSpEoCsTV1ZU6deqQnZ2twsorHI7IyEiysrKoV68eXl5ethanwqIUiaJQ1H4ShaOizFrlg1IkikJR+0kUjoqK9ls+KEWiKBTDjCQqKors7GwbS6NQFI2EhARu3ryJu7s7jRo1srU4FRqlSBSFUrVqVWrVqkVWVpbK465wGAxmrRYtWuDs7GxjaSo2SpEoioTykygcDeUfKT+UIlEUCeUnUTgS2dnZXL58GVCKpDxQikRRJEz9JHq93sbSKBQFc+XKFTIyMqhTpw7VqlWztTgVHhdbC6BwDLy9valRowbx8fHExMQYMygqCiArCy5dgtOn4cwZWh06BAcOQOvWEBAALVuCq6utpayQnDt3DlCbEMsLmyoSIcQQ4BPAGVghpXwvjzoPAwsACRyXUj5WrkIqjDRt2pT4+HgiIyOVIrHk0iU4eBDOnDEqDs6fB5Psko0ANm68e42zs6ZMDIqldWvo0QPatSt38SsSUkrOnDkDQJs2bWwsTeXAZopECOEMfAYMAqKBQ0KITVLK0yZ1/IBXgd5SyttCiDq2kVYBmp/k2LFjREZG0qtXL1uLYx8cPAgLF8LmzcW/Njsbzp3TXr/9dre8Tx946SUYMUJTNopice3aNRITE/H29lbLfssJW/pIugMXpJSXpJQZwPfAgxZ1ngY+k1LeBpBS3ihnGRUmGPwkkZGRyk+yezfcf782gyiJEims7dGjtRnKp59CcrJ126/gGGYjAQEBCCFsLE3lQEgpbdOxEOOAIVLKKTnHE4EeUsrpJnV+Ac4BvdHMXwuklL/n0dZUYCpA7dq1u2zYsKEc7qB0JCcnO0TsH0s5Dxw4QFpaGp07d8bb29uGkplTLuMpJb7HjtE0JITqYWFFuiSjenVSmjXjTpMmJPn6Ui0hAc8rV/CMisL95s0itZHp7c21ESO4OmoUGbVrl+YOioSjPpugmbUOHjxIWloaHTp0MEavtiWOMp4DBw48IqXsWpJrbekjyeungqVWcwH8gAFoJuZdQoh2UsoEs4ukXA4sB2jdurUcMGCA1YW1NqGhoTiinImJiYSFhVG7dm2Cg4NtJ5gFZTqeUsIff2gmrL1786/XpQv07w9t20KbNtCmDW7Vq+MGVAfOh4bSxlRGnU4za4WHw9mz2kxkx45czbrqdDT97juabtgAjz4K8+eDn5+179KIoz6bALGxsezcuRNPT09GjhxpF/lHHGU8S4MtFUk00NjkuBFguW06GtgvpcwELgshzqIplkPlI6LCkqZNmxIWFkZkZKRdKZIyIz4eJkyA33NNhO/Sty+88Qbcdx8Ux5Ti7a0pny5d7padOAEffwxr14JleuOsLPj2W/jpJ/joI3jmmeL1VwkwNWvZgxKpLNhypA8BfkKI5kIIN+BRYJNFnV+AgQBCiFqAP3CpXKVUmGHqJ7GVWbTcOHUKunXLX4ncey+EhsLOnTBokHW+1IOCYNUqiIyE11+HGjVy10lNhX/+E0aOhBvKbWiKQZG0bdvWxpJULmymSKSUWcB04A/gDLBBSnlKCPG2EGJkTrU/gFtCiNPADmC2lPKWbSRWgJYxsVq1aqSmpnKjIn+J/forBAdry3otGTpUM3Ft366ZssqC+vXhX/+CqCj44gvw989dZ/NmaN8e/vvfspHBwYiLiyMuLg4PDw9jJAZF+WDTuZ+UcouU0l9K2VJK+U5O2Xwp5aac/6WU8kUpZVspZXsp5fe2lFcBQgizWUmFQ6/XfCGjRuVeLdWzJxw6BFu2aP+XB56eMG2ati/l66/B0ml74wY88AA8+yzcuVM+MtkppmYtFaSxfFFGREWxqbCKJDkZHn5Yc2ZbMmWK5gjvWqJFLaXHyQmefBKOH89biX3xheZrOXq0/GWzE9QmRNuhFImi2JgGcKwwfpLLl6FXL82RbYqLC3z2GSxfDu7utpHNlBYtNJ/M22/n3qwYHq6Z4z74QFtpVomIj48nNjYWNzc3WrRoYWtxKh1KkSiKTY0aNfDy8iIlJYWbRdwLYdf89ZfmVP/7b/PyWrVg2zbNbGRPq6NcXLRVYnv2aCFWTMnMhFde0WZQWVm2kc8GGGYjrVu3xsVFhRAsb5QiURSbCuUn+eUXGDwYblms4QgK0vwh9rz+v0cPCAuDp57Kfe7rr+GRRyA9vfzlsgHKrGVbiq1IhBDthRBPCSFeF0IsFELMEkIMF0JULwsBFfZJhVAku3fD+PFazCtTxo3TVmU5wsofLy9YsQJ+/jn3UuGff4bhw7WNjxWYxMRErl69iqurq8o9YiOKNAcUQrQA/glMAOoCeiABSAd8AU9AL4T4H7ACWC+lrOTBmCo2Bj9JREQEUkrHi2l0+rQWFDEtzbz8X/+C116zL1NWURg9GgIDtf0sV67cLf/zT22j5JYtULOm7eQrQwyzET8/P1xVWH6bUOiMRAixAjgFdATeBjoBHlLK2lLKRlJKL6AOMAL4G/gAOCOE6FN2YitsTa1atfD09CQ5OZlblmYheyc6GoYMgYQE8/KvvtI2ATqaEjHg76/NsgICzMsPHoR+/eDqVdvIVcYos5btKYppKw0IkFIOklIuk1KekFKa2QKklDellFullC8ATYH5gEpYUYERQhiTBp0/f97G0hSDhARtQ2FUlHn5229rDmpHp3Fj2LUr9zLl06e18PQ5ecwrCjqdjitXruDs7IxfGcYfUxRMoYpESjldSllkQ7iUUi+lXC+lXF860RT2juGD6zCKJC0NHnwQTp40L582DebNs41MZUGtWppJy3KhQESEpkyOH7eFVGVCeHg4oOVld7eH5dmVlGI524UQi4XDGcMVZUWrVq0QQhAZGUm6va8Oys6Gxx/X9mCYMmqUlvOjoj3W1arB1q1aPC5Trl/Xwrrs22cbuayMMmvZB8VdtTUe+EUI4ZnXSSHE0NKLpHAUqlSpQuPGjdHr9Vy8eNHW4uSPlDBzZu7Nhr17w3ffVdwshB4e2j0/8YR5eWIiDBumBaV0YDIyMoiIiMDJyQn/vGKRKcqN4iqSYKAVWl6Q+oZCIcT9QogDgJVTxSnsHYcwb733nrY73ZQ2bWDTJqhSxTYylRcuLtqekpkzzcsTErQFB5a+Igfi1q1bSClp0aIFVSr6+2jnFEuRSCkvA72Am8BBIcRkIcReYCuQiJaASlGJMFUkdhku5ZtvtOW8pjRsqIWGzytEe0XEyUnLcfLGG+bl0dFauuD4eNvIVUri4uIAZdayB4q9IVFKmQgsQkv69hXgAfSUUg6WUu6ysnwKO6dOnTpUq1aNlJQUYmJibC2OOadOacmfTPHx0ZRIkya2kclWCAFvvaWFezHlzBltP42DRQ5OTU0lISEBIQQBlsudFeVOcZ3t9wshdgO/A3uBL4G2aOYuRSVECGGclZw7d87G0piQmqqFCDHdcOjuruUZadfOdnLZEiFgyRIYO9a8fO9eLYWvA8XmOnfuHFJKmjVrhqdnni5bRTlS3BnJVrTd7P1zZiDPAjOAr4UQb1ldOoVDYHB02pWf5KWXcjuTly8vu0RUjoKzs5au13IcfvtNy7poj+bJPFCrteyL4obJHCClNFs/KaVcLoS4DGwQQrSWUj5qPfEUjkDz5s1xcXHh2rVrJCcn42WZfKm82bhRy89hysSJMGlSuYsipSQ+NZ6Y5BiOJxyn9o3a1PeuT3WP6rYLK+PhoQWr7NfPPOLxihVaZsZ77rGNXEUkJSXF+KNFKRL7oFiKxFKJmJRvywmJ8ptVpFI4FK6urjRr1owLFy5w4cIFOnbsaDthoqJyR8Nt1Sr3qi0rkpSexJ+X/uTvG38To4shJjnnpYshNjmWTH3m3co5ewHdnd2p51WP+t71tb9e9anvVZ8O9TpwT/N78HIrY2Xs66v5inr2NI/NtXAhDXQ6u456fPLkSfR6vTGdgcL2FKpIhBATge8sw6JYkpNvvUfONa2A+sr5Xnnw8/PjwoULnD9/3naKJCsLJkyA27fvlrm6wvffg7e31bqRUnIq7hRbz29ly4Ut7L6ymyx9/v4FH3cf6nvXxznDmSzXLGKSY0hKTyIyMZLIxNxBI9yc3ejXtB/DWg1jqN9QWtdsXTazlwYN4I8/tN3uJvHS/D75RCuz9KXYCWFhYQDUq1fPxpIoDBRlRvISsFAIEQL8KKXMM76CEKImMFgI8SjaMuA8kiQoKir+/v5s3bqVixcvkp2dbZuc2e+8o8WZMuXf/9ZS0JaS5Ixk/rz0J1vOb2Hrha1EJd3df+EknOjduDd9m/SlYbWG2uzCZKZRxVXb4xAaGsqAnF/6dzLvGGcvscmxxOhiiE6K5n+R/+Pg1YNsv7Sd7Ze28+L/vUhz3+YMbTWUoX5DGdhsIFXdqpb6fowEBMDmzZo5KzUVACGlppCbNNESftkRsbGxxMbG4uHhQc0KGs3YESlUkUgpOwohHgGeB14XQiQDZ9D2khjCyDcHmgC3gW+BaVLKihlqVJEnvr6+1K5dm7i4OK5cuULz5s3LtX+fEye0wIum3H8/zJpVqnYv3b7ER/s+4utjX5OalWosr1u1LkNaDWFoq6EMajmIGlWKtyfF09WTljVa0rJGy1znbt65yR8X/mDrha38cfEPLidc5vPDn/P54c+p6lqVqV2mMit4Fo19Gpfq3owEB8MPP2hxyAy5WdLTtdD0R45A3brW6ccKGGYj7du3x8lJ5eWzF4rkI8kJwLg+x2R1L9AZqAdUBa4DO4E9QKiUMjPfhhQVGj8/P+Li4jh//nz5KpL4eNq88w7oTVLg1K0La9Zom/FKwLGYY3yw9wM2nNqAPie1Ts9GPRnmN4yhrYbSqX4nnETZfJHV8qzFhKAJTAiaQLY+m8PXDrP1wla2nN/CoWuH+Hj/xyw9uJTH2j/GnF5zCKwTWPpOhw/XnO1PPnm37OpVLcnXn3+Cm1vp+ygl2dnZ/J2zOKBjx472tdy8klPcT0K6lPJLKeUzUsoHpZT3SynHSykXSCm3KSVSubFJuBQpYcoUPG7cMC//5pti/5KWUvLnpT8ZHDKYzss78/3J73ESTjzR4QlO/vMke5/ay7x+8+jSoEuZKRFLnJ2c6dGoBwsGLODg0wc5OvUo49uNRy/1fHP8G9p90Y4R60awK3JX6SML/OMf8OKL5mW7d5d6Vmctzp8/z507d6hTpw7169cv/AJFuVHcT0OEEKJr4dUUlZHGjRvj7u7OzZs3iS+vsBtffqkt9zVl9mwtD3sRydZns+HUBrp91Y37Qu5j26VteLl58WLwi1yacYnVo1Zb51e/FehUvxPfjf2OC89f4Lluz1HFpQqbz22m3+p+9P66N7+G/2qcQZWI99/ndufO5mWffw4rV5ZOcCtgMGt16NDB8TJyVnCKq0gEsFEI8V8hxPtCiIlCiE5CCPecV8VJdKAoNs7Ozsac2eUyKzl7Nvev5W7dtHS5ReTwtcP0WNGDR358hCMxR6jtWZt/DfwXV164wn/u/4/1/BBWpnn15nw67FMiX4hkfr/51KhSg33R+xi1fhR9vu7D39f/LryRvHBx4dT8+bnz1T/7LOzfX2q5S4ph74gQgqCgIJvJocibkszP/wBSgAeBVcBhIBnNV9LMapIpHJJyM2/p9fD00+YhULy9Yd26Itnzk9KTmLF1Bj1W9OBIzBEaV2vMF8O/IPKFSF7v9zrVq1QvQ+GtR+2qtXlr4FtEvhDJ4vsXU8+rHvui99Hpy07M2TaHlIyUYreZ5eOjbVg0jaibkaEtB7ZRPLUTJ06g1+vx8/NTe0fskJIokuVSyoellAGAF9AdmAJ8CKhd7ZUcw4wkIiKCjIyMsutoxYrcS30/+wxa5l4FZYqUkh9O/UDApwEsPbgUgeDlni9z+rnTTOs6zbhU19HwcvNiZvBMwp8L57luz6GXej7c+yGBnwey+VwJsjt06KCFnzfl2jXN+V6W72seSCmNZi2bbnZV5EupPIZSyjQp5REp5Rop5TtSyq3WEkzhmFStWpWGDRuSnZ3NpUuXyqaTa9c0P4gJt3r00DIgFsDl25cZ/t1wHv7xYWKSYwhuFMyRqUf4cPCHZb+TvJzw8fDh02Gfsn/KfjrW60hkYiQj1o1gzPoxRCdFF6+xRx+FOXPMy/buhRkzrCdwEYiNjeXGjRtUqVJFJbCyU0qiSCYIIUYIIVpYXRpFhaDMzVvPPw9JSXePq1bl3KxZ+abLzcjO4L3d7xH4eSBbL2zF18OXZcOXsWfyHjrU61A2MtqY7g27c+jpQ3x8/8d4uXmxMXwjbT5rw+L9iwvchZ+Ld9/NvXDhyy+1AJjlhOneEZtsdFUUSkkUyePAr8B5IYROCHFQCLFKCPGSEOJ+K8uncEBMowFbPdnVxo3w88/mZe+8Q3o+S33Db4bT7atuvPrnq6RmpfJY+8cIfy6cZ7o+U25LeG2Fi5MLLwS/wJnnzjCmzRiSM5KZ9ccseq3sxaXbRZwtOjtrfqcWFr8bp08vl7zvWVlZZntHFPZJcT9JfwL3oCW16ge8DOwHmgJzgC1WlU7hkNSrVw8vLy90Oh3Xr1+3XsOJifDcc+Zl3btrX2p58O2Jb+m6vCsnrp+gZfWWbJu4jbVj1lLXy352apcHjao14qeHf+K38b/RxKcJh64dotOXnfjp9E+FXwxaJslffoGqJqFZMjO1fC8mMbrKgvPnz5OamkrdunXV3hE7pripdgdJKY9LKROllHtyNifOkFLeI6Wsi7bbXVHJKbNkV3Pnmq8acnHRnO4W5o47mXeYsmkKEzdOJCUzhQntJ3DsmWPc1+I+68nigDzg/wDHpx1ndMBoktKTGPfDOGZunUl6VnrhF7dvD6tXm5dFRWmbGMswh4lysjsGVp3bSynjrNmewnGxup9k925Ytsy8bM4c7QvOhPCb4fRY0YOVx1bi4eLBihErCBkdgre79aL/OjK+Hr789PBPfDLkE1ydXFlycAm9v+5dNFPXuHFawjBTNm+Gjz4qE1mTk5M5f/48Tk5OtLd4nxX2RcU2EitsRosWLXByciI6Opo7pc0Hnp6u7Rkxxd8f3njDrMhgyjp54yT+Nf05MOUAT3V+Su2CtkAIwYweM9gzeQ/NfJtxJOZI0U1d//439OhhXjZ3bpn4S06cOIGUEn9/f6pWtWLEY4XVUYpEUSa4u7vTLGd39IULF0rX2LvvQni4edny5VqmPzRT1odnPzSash5r/xiHnz5MUF21A7ogujXsxrFnjuUydWXoC9gn4uoK69dribEMZGVpS4WtGBbHdO9Ihw4Vc2VdRcKmikQIMUQIcVYIcUEIMbeAeuOEEFLF+XIsDKu3Tp8+XfJGTp3SfgWb8vTTxpzjF+Mv0mNFD7bEbsHDxYOvRnzFt6O/VaasImIwdS2+f7HR1DUjbAZRiVH5X9S0qRZZ2ZQrV6zqL4mJiSEuLg5PT0+jmVRhv9hMkQghnIHPgKFAW2C8EKJtHvW8gRnAgfKVUFFa2rZtixDCuPKm2BjCoGSaBJWuVw8++ACAXZG76LGiBydvnKRxlcYcmHKAKZ2nKFNWMRFCMDN4ptHUdVZ3lu4runP42uH8Lxo5Mnecs99+g48/topMau+IY2HLGUl34IKU8pKUMgP4Hi1+lyULgQ+AtDzOKewYb29vmjdvjl6vL9msZNmy3Lb3pUvB15eQ4yHcF3Ift1JvMcxvGF90/kKZskpJt4bdODL1CJ18OxGbHEu/Vf34+czP+V/w3nva8mtTXnkFDpTuN5/p3pFOnTqVqi1F+SCsvmGsqB0LMQ4YIqWcknM8EeghpZxuUqcTME9KOVYIEQq8LKXM9TNJCDEVmApQu3btLhs2bCiPWygVycnJDhF8rrRyxsbGcvbsWXx8fIq1hNP19m16TJyIS8rdoIM3e/fmxNtvsTpyDSFXQgAY03AMz7Z8ltSUVLsfT0d5z28n3earmK/YGqtFPJrafCqPNn40z5meR2wsXZ5+GtfkZGNZWt26HF6+nKxq1UrUv+GZ8fLyoksBaZIdZTwdRc6BAwcekVKWzH0gpbTJC3gIWGFyPBFYanLsBIQCzXKOQ4GuhbXr7+8vHYEdO3bYWoQiUVo5U1NT5cKFC+WCBQtkQkJC0S+cPFlKzeKuvby85J1L5+QjPzwiWYB0estJLj2w1GpylgeOIKOUmpx6vV6+t+s9yQIkC5CTf5ks07PS875g40bz9wqkHDlSSr2+2H3r9Xq5bNkyuWDBAnn06NFC5XQEHEVO4LAs4fe5LU1b0YBpsodGwDWTY2+gHRAqhIgAgoFNyuHuWHh4eNC6dWsATp48WbSL9u/PFXlW9+pL3PPXJNafWo+3mzebx29meve8d7QrSo8Qglf6vMKPD/1IFZcqfB32NUO+HcLt1Nu5K48aBTNnmpdt2gSLFxe73ytXrhAbG4unp6faO+JA2FKRHAL8hBDNhRBuaCHoNxlOSm33fC0pZTMpZTO0UCwjZR6mLYV9065dOwCj3btAsrNzhUFJa92STu6r2B+9nyY+Tdj71F6G+g0tC1EVFoxtO5adT+6knlc9dkTsIHhlMBfi81jO/cEHWlIxU155BY4cKVZ/+3OSZ3Xt2hUXF5eSiq0oZ2ymSKSUWcB0tERZZ4ANUspTQoi3hRAjbSWXwvr4+fnh4eHB9evXuWGZW92Sr76Co0fNisb1jeFi8hW6N+zOgSkHaFenXRlKq7Cka4OuHJxykKC6QZy7dY4eK3qw+8pu80pubtr+Eh+fu2WZmTB+PJj4Twri9u3bhIeH4+TkRDdLpaSwa2y6j0RKuUVK6S+lbCmlfCenbL6UclMedQeo2Yhj4uLiQps2bYBCZiU3b8Jrr5kVbWgn+G+jOzzU9iFCnwilnpcK52YLGvs0ZveTuxnuN5z41HgGhQxi01mLj2nz5rlzu58/r4X9LwIHDx4EtCW/juCcVtxF7WxXlAsGe/fJkyfzDy3/2mtw+64NPtkVXhwkeannS3w/7nuHzV5YUfB29+bXR3/lmS7PkJaVxpj1Y1gdttq80tixMHWqednq1Voo+gJIT0/naM5MtIdlCBaF3aMUiaJcaNq0Kd7e3iQkJBAdnUemvkOHtEi+JizsDzPGvs+iwYsqfO4QR8HZyZkvhn/BvL7zyJbZPPnrk3y450PzSh9/DFXG0KcAACAASURBVDkzUCPTpkEBGTPDwsLIyMigadOmKly8A6I+nYpywcnJKX+nu16vOdhNZirhtaDNO18yp7dFqleFzRFCsPCehXwy5BMA5myfw5xtc+7OND094fvvwd397kVJSfDYY+ZRCnLQ6/UcyNnEqGYjjolSJIpyw2DeOnXqFNnZ2XdPfP21NiMxIf69Bfyju4WJRGFXzOgxg7Vj1uLi5MKHez/kqU1P3U3jGxQEixaZX3DgALz5Zq52zp8/z+3bt/H19TUuFVc4FkqRKMqNevXqUatWLe7cucMlg5kjPh793FfM6sUN6Uevp3J/4Sjsj8faP8Zv43/D09WTVWGrGLthLKmZOXHVnnsORowwv+C99+Cvv8yKDEt+u3fvjpOT+kpyRNS7pig3hBDGWYnBvJU692Wcbt0NP6738KD2lyE2kU9RMoa0GsL2idup7lGdTWc3MWTtEBLTEkEIbbbZoMHdylLC449rK/TQwqFERETg5uam4mo5MEqRKMoVg58kPDyc6D834b5ildl5p3nzoEkTW4imKAU9G/dk15O7aOjdkJ2RO+m/uj83Um5ArVoQEqIpFQMxMfDkkyCl0TfSsWNHPHLyyygcD6VIFOVKjRo1aNSoETfSY4l9ahxOpiuBW7WCl1+2mWyK0hFYJ5A9k/fgX9Of49eP029VP6KTouGee+DVV80rb95M+n/+Y5yZKie7Y6MUiaLcqdqsKqknltM10mIFz5Il5it9FA5HU9+m7HpyF0F1gzh76yx9V/XV8sEvWJArRa/ra69R6+pVWrduTY0aNWwjsMIqKEWiKFeOxhzl1d3P8va2dPMTI0fCUBU/qyJQp2oddjyxgx4NexCREEHfVX05k3BB25RoElreKTOTsT/+SLAKzujwKEWiKDf2Ru3lnjX3MOP329RNMTnh7l6iSLEK+6VGlRpsm7iNAc0GcE13jX6r+3HMIwG+/NKsXu2bN2lqpayKCtuhFImiXPjz0p8MDhlMoyuJzDhokSBp7lwtTpOiQuHt7s2Wx7YwtNVQbt65ycA1A9nXuynyH/8wqydWrtQCPiocFqVIFGXOb2d/Y/h3w0nJSGHDrno46+962BN8fEh45hkbSqcoS6q4VuGXR39hbJuxJKYnMihkED883pebNWuaV5w6FS5fto2QilKjFImiTFl/cj1jNowhPTudFemDaXsy1uz8H0OGcPLiRRtJpygP3Jzd+H7c9zzR4QlSMlN4fM80/jOuK3pX17uVCgihorB/lCJRlBmrjq3isZ8fI0ufxRudZzH529Nm51N69yY8IIATJ07kHxFYUSFwcXLh6we/ZmLARDJlJh/U38aRGQ+bV9q/X1vdpXA4lCJRlAmfHvyUyZsmo5d6Fg5cyFt73RGmUX9dXfFYvhwvb2/i4uKIiIiwmayK8sFJOHFP6j30pjd69AR7f0dU3w7mlf7971whVBT2j1IkCqvz/u73eX6rlszo4/s/Zl79RxAffWReadYsnNu2pWvXrgDGHc6Kisvly5eJjIzkAfcHeLPvm+iRdA4+Tkqtu0uCLUOoKBwDpUgUVkNKyRt/vcHcP+ciECx/YDkv9JgJM2dCRsbdivXrw7x5AHTp0gVnZ2fOnj1LfHx8Pi0rHB0pJX/lzDR69erFgnsW8NHgj7hZFUYMS0LmE0JF4RgoRaKwClJKXvzjRf616184C2dCRofwdJenYfNm2LrVvPKiReDtDYCXl5cx/pYh1aqi4nHhwgWio6Px9PQ0hkOZ1XMWXz7wJaEtBO/2sVAamzfD0qU2kFRREpQiUZSabH02z2x+hsUHFuPq5MoPD/3AhKAJkJamzUZM6dsXxo83KzJ8sYSFhZGebrHjXeHwSCkJDQ0FoHfv3ribhMGZ2mUq34z+hrcHCvY1srhw9mw4dqz8BFWUGKVIFKUiS5/FE788wVdHv8LDxYNN4zcxus1o7eSHH5rvDXBygk8/NY8EC9SvX58mTZqQnp5OWFhYOUqvKA/Onj3LtWvX8PLyolu3brnOPx70OOse/ZFJD7mQaBpqLSMDHn5YWxqssGuUIlGUmPSsdB7+4WHW/r0WLzcvfp/wO0NaDdFORkZqK3BMee45LXNeHhhmJQcPHlRLgSsQUkp27NgBQJ8+fXA13Ttiwpg2Y1jyz008N8ri/IULMGWK8pfYOUqRKEpEyv+3d+ZhVVXrH/8sBlFRgRxJFGfBIVEUHBA1zTGH63StzDRMbbBJ++XtNmjdbqPdNG82kKWlmeJYaomm5BUHBgEHUhE1RcOJUWRevz/2ATlHRjmcfaD1eZ79cM7a6+z9ZbE5797rfdf7Zt9k7NqxbPp9E861nQl+NJgBrQZoO6WEZ56BW7duf6BRI1i0qMTjeXh44OTkxI0bNzh9+nQVq1dYihMnTnDlyhUaNGiAt7d3qX1HtB/BzHd3sqKXnfGO9evh00+rUKWisihDoqgwSbeSGPrdUH458wuN6zZmz2N76O3W+3aHTZs0Z2lR3n0XXFxKPKaNjU3htIcKBa4Z5OfnF/pG+vfvj52dXekfAAa2Gkjn1cEcdTX5anrhBQgLqwKVCnOgDImiQvyZ/icDVw4k9EIoLRq0YN+MfXg187rdITUV5s41/lC/flo4Zxn06NEDe3t74uPjuXLlipmVKyzN0aNHuXbtGs7OzhUqo+vbfiD2GzaT5lDEl5aTo/lLkpKqQKmisihDoig3Z5PO4rfCj5jEGDo27Mj+x/fTsVFH406vvgqXLt1+b2enpQ63KftSq1OnDvcZfCjqqaR6k5eXR0hICAADBgzA1ta2Qp/36DOa9OVLjBvPnYPp05W/xApRhkRRLo5fOY7f136cSTpDD9ce7JuxjxZOLYw7hYVpUVlFeekl6Ny53OcpcLrHxMRwq6iPRVGtiI6OJikpiYYNGxbeHFQU1xlzSZ9t8iS7dSuYZklQ6I4yJIoyOZxwGP9v/LmUdokB7gPY89geGjs2Nu6UmwuzZxvfLbZpU7iCvbw0btyYtm3bkpubS0REhBnUKyxNbm4uv/32G6A9jdiU42m0JOotWU6ut/G0mFywAEJDK6VRYV6UIVGUSkRSBPevvJ8bt24wusNodjyygwYODe7s+Mkndy4e+/RTqFu3wucseCoJCwsjPz//bmQrdOTIkSOkpKTQuHHjwqwFd42DA3ZBG5HOzoVNIjeXrIl/wz4lpZJKFeZCGRJFiWyK3cQ/jv5DqyFx31Q2TN5AHfs6d3a8cAFee824bcoUGDbsrs7brl07GjZsSGpqKrGxsXd1DIU+ZGVlFT6NDBw4EGGy+PSuaNUKsXKlUZPD5Su4Lvo/UDcaVoEyJIpi+Tz8cyaun0iOzGGuz1xWjluJvW3xi8mYOxduFinC7uQElajDLYTAx8cHUE736sbevXtJT0+nefPmeHp6mu/AY8bA/PlGTW2OnCLqub+b7xyKu0YZEoURUkpe/fVV5mybQ77MZ7r7dJYMX4KNKOFS2bwZtmwxbnvvPWjWrFI6unXrhoODAxcuXOBS0SgwhdWSmJjIoUOHEEIwatQo8zyNFOXf/4a+fY2a7lsWxA8fzlDZEHRGGRJFIdl52UzfMp23972NrbAlcHQgj7V6rOQvhLS0O9eM9OkDTzxRaS0ODg6Faw/UU4n1I6Vk27ZtSCnp1asXrq6u5j+JvT388AMUqfduAwx79RsWfa5V4lTogzIkCgBSs1IZtWYUq6JX4WjvyI8P/UhAj4DSP/T661C06mEF1oyUh4LprWPHjpGWlmaWYyqqhqioKC5cuICjoyODBg2quhO5ucH33xtdY85ZMOXVtUz9ejQ3s2+W8mFFVaGrIRFCDBdCnBRCxAkhFhSz/0UhxAkhRIwQYrcQwl0PnTWdhNQE+n/dn13xu2jq2JSQ6SGMaD+i9A9FRsLSpcZt8+ZB165m0+Xi4oKnpyf5+fmFDlyF9XHr1i127doFwNChQ6ldu3bVnvCBB7TM0kXwuA7T3v2ZId8M4spNlRXB0uhmSIQQtsB/gRFAJ+AhIUQnk25HgJ5SyvuAIOB9y6qs+Ry/cpw+X/UpXK1+IOAA3veWnlyPrCwt5UnRiJlWrbQnFDMzaNAghBBERERwTZVftUp2795NRkYGrVq1oqsZbyRK5YUX+HPoUKOmkXEwdlUYfb/qS9yNOMvoUAD6PpH4AHFSyngpZTawFhhbtIOUco+UMsPw9iBgWvpGUQn2nttLvxX9uJB6gX4t+rH/8f20dmld9gdfew1iYozb7nLNSFk0btwYLy8vo1KtCushISGBiIgIbGxsGDlypPkd7CUhBKfmzQPD9GcBC/aDT8gZ+nzVh0MXlW/NUgi9oh2EEBOB4VLKmYb3jwK+UspnSui/DPhTSvmvYvbNAmYBNG7c2HvdunVVJ9xMpKenU69ePd3OH5wYzAcnPyBH5uDfyJ9XPF7Bwdbhjn6mOp2iovB68UVEkesmcfBgYiu4gr0iZGVlcfjwYfLz8/Hy8sLJyalMndZIddAI5dcppSQyMpL09HRatGhBmzZtLKDuNunp6dyTmYn3nDk4XL9e2J5pL/CbLjnWwoFXPF7Bv7G/RXWZUl3+7oMGDYqQUva8qw9LKXXZgElAYJH3jwKflNB3KtoTiUNZx+3QoYOsDuzZs0eX8+bm5cqXdr4kWYhkIfK5Hc/J3LzcEvsb6UxOlrJlSym1RCja5uYmZVJSlevetWuXXLhwoVyxYoXMz88vXaeVUh00Sll+nYcPH5YLFy6UH330kczKyqpaUcVQqPPgQSkdHIyuy+sNHWXTedo1vnDPQpmXn2dxfXfotHKAcHmX3+d6Tm1dBIpm/XMD7lgwIIQYAvwTGCOlVAW9K0FyZjKjvx/NB6EfYGdjx6cjP+Xj4R9ja1POzKzPPgt//GHctnIlFElfUVX069ePOnXq8Mcff3Dq1KkqP5+idNLT09m9ezcAw4cPp1atWvqJ8fWFL74warrn+k0idrpTO0+wMGQhk9dPJj07XSeBNR89DUkY0F4I0VoIUQuYAmwt2kEI0R34HM2IqFCMSnDq+il6B/ZmR9wOGtZpSPCjwTzZ68nyHyAoCFatMm578UW4/37zCi2B2rVr4++vTVHs2rVL5eDSmV27dpGVlUW7du3w8PDQWw5Mm6YVvypC86PnORX7AA1q1WdD7Ab6rejHueRz+uir4ehmSKSUucAzwC9ALLBOSnlcCPGmEGKModsHQD1gvRAiSgixtYTDKUrh57if8fnSh5PXT9K1SVfCnghjYKuB5T/ApUtaZt+idOkCb79tVp1l0bNnT5ydnbl27RpRUVEWPbfiNufPnyc6OhpbW1tGjBhhOQd7Wbz/vhYaXIQWQTs5nfEEHRp2ICYxhl5f9iLkXIhOAmsuuq4jkVJul1J2kFK2lVK+bWh7XUq51fB6iJSyqZTSy7CNKf2IiqJIKVkcuphRa0aRkpXC3zz+RmhAaPkis24fRAv1vXHjdlutWvDdd1DV6wVMsLOz437DE9DevXvJzs626PkVWsGqbdu2AeDn58c999yjs6Ii2NlpK9/btTNqbvKvjzhi9wzD2g7jWsY1hnw7hOVhy3USWTNRK9trKJm5mTy2+THmB88nX+bzxoA3CJocRL1aFYseab55M+zcadz4r39Bt25mVFt+unTpgqurK2lpaRw8eFAXDX9lQkJCuHr1Ki4uLvj5+ekt505cXLTiVw2MSx3Uffp5ttWdxbw+88jNz+Wp7U/x5E9Pkp2nbkbMgTIkNZCzSWfx/9qfb2O+pa59XYImBbFw4MKSEy+WxO+/0+azz4zbBgzQfCM6IYTgAcP0xf79+7l5U6XEsBRnz55l3759CCEYO3YsdnZ2eksqHk9P+PFHcCgSzp6fj+3DD/Nh7TGsHLcSB1sHPov4jMGrBnMx9WLJx1KUC2VIahhBJ4Lo/nl3wi6F4e7kTujjoUzoNKHiB8rOhqlTsS06fdSggRalVcH62+amdevWtGvXjuzsbJU6xULcvHmTjRs3AuDv74+7u5VnK/L316a5iuZ9y8qC0aOZRjdCpofgWs+V//3xP7w+82LbqW36aa0BKENSQ8jMzeSpbU8xaf0kUrJSGOcxjsjZkXRrdpdTUG++CaalbpctAyv5AhkyZAgA4eHhJCUl6aymZiOlZPPmzaSnp+Pu7l4YPWf1jB17R1gwqakwfDi+2Y2JmhPF0LZDuX7rOg9+/yDzd85XU113iTIkNYCT107iG+jL8vDl1LKtxdLhS9k4eSP31LlLR+hPP2m1H4oycSJMnVp5sWaiadOmdOvWjfz8fJU6pYo5ePAgcXFx1KlTh/Hjx1eqBrvFCQiAd94xbvvzTxg6lCbpkh2P7ODdwe9iK2xZfGAx/b/uz9mks/porcZUoytCURzfRn+L9xfexCTG0O6edhwIOMBc37l3H5J57Bg89JAWrVWAqyt89hlYS5ingUGDBmFra6vSzFchly5dKszsO2bMGBqYOLGrBS+/DM8/b9x25gyMGIFNWjov+73MbzN+o6VTSw4nHKb7590JOhGkj9ZqijIk1ZT07HSmb57OtM3TuJlzk4e6PETkrEh6uPa4+4NevQqjR0P67RXA0sYGvv3WqJiQteDk5ISvry8Ap06dIi8vT2dFNYusrCyCgoLIz8+nV69e1rHw8G4QAhYvhkceMW4/cgTGjYPMTPq26MuR2UcY5zGOlKwUJq2fxFPbniIzN1MfzdUMZUiqIWEJYfT6shcro1dSx64OgaMDWT1+NfUd6t/9QbOzYcIEOHfOqDnumWdg8ODKCa5C/P39cXZ2Jj09nb179+otp8YgDRUPk5KSaNq0KUNNUrZXO2xs4OuvYYRJnZ09e2D8eMjI4J4697Bx8kaWDl9KLdtaLA9fTu/A3sQkxhR/TEUhypBUI27l3OLl4Jfp/VVvfr/2O50adyLsiTACegRUbnWxlPDUU7Bvn3H77NkkjBtXOdFVjIODA+MMGvfv388fprnAFHdFdHQ0R48exd7enokTJ1pvqG9FsLeH9euhd2/j9h07NAOTmooQgrm+czkQcIB297QjOjEa7y+8Wbh3oXLEl4IyJNWE/X/sx+tzL94P1Wp7zeszj7AnwujcpHPlD/7xx/DVV8ZtgwbBJ59YnV+kONzd3WnZsiVSSjZt2kRWlsrtWRkyMjLYvn07ACNGjKBRo0Y6KzIjjo5aMImnp3H7b79peeMMxdN6uPYgclYkT/d6mtz8XBaFLKLnFz0JvxSug2jrRxkSK+dm9k2e2/Ec/b/uz6nrp+jUuBOhj4fy4dAPqWtvhkJSO3bA/PnGbW3bandu9vaVP76FcHd3x9XVleTkZHbs2KG3nGpLbm4usbGx5OTk0KVLF7y8vPSWZH4aNtSmtO67z7g9IkJbf5KQAEB9h/osG7mMvY/tpa1LW45eOYpvoC8Ldi1QvhMTlCGxYn49+ytdl3dl6eGl2AgbXu3/KpGzIvF18zXPCWJjYcoU45K5DRpoq4Kt0LleGjY2NowfPx47Ozuio6M5fvy43pKqHVJKduzYQXp6Oi4uLjz44IPWk5DR3DRtCnv33jnNFRsL/ftDfHxh04BWA4h5MoYXe7+IlJL39r+H12dehF4ItaxmK0YZEiskJTOF2T/OZvCqwZxNPku3pt0IeyKMt+5/Cwe7O6sY3hXXr2sRWqmpt9tsbLTVwKaP/dWERo0aFTqFf/rpJ1KL/m6KMgkJCSEyMhIbGxsmTJiAg4OZrjVrxcUFgoPvDCY5exb8/LRQeAN17euyeNhiQgNC8WzkycnrJ/Fb4cfzPz/PzWyVpkcZEisiLz+PLyO+pMOyDnwR+QX2Nva8Negtwp4Io7trd/OdKDtbW2B45oxx++LFMHy4+c6jAz179qRdu3ZkZmayZcuWggqbijIIDw8nJCQEIQSenp40b95cb0mWoV49zWcydqxx++XLWl65sDCj5t5uvYmcHckrfq9gI2xYcmgJHZZ14Nvob8mXf90aOcqQWAm/nv2VHl/0YNZPs7hy8wr9WvTjyOwjvOr/Kva2ZvRV3Lqlxc6bhsoGBMBzz5nvPDpRkFCwbt26xMfHc+jQIb0lWT2xsbGFzvVRo0bVLOd6eahdWyvc9uijxu03bmgO+D17jLvb1ebtwW9z+InD9Ly3J5fSLjFt8zR6B/b+y053KUOiM6evn2bc2nEMXjWYmMQY3J3c+WHiD+ybsc88EVlFSU3VwhxNndH9+8Onn1aLCK3yUK9ePUaPHg1olfyuXFHFNUvi3LlzbNiwASklAwcOxNvbW29J+mBnB998A08/bdyeng5Dh8KSJcbZHtAiuw7NPMTKcStxredK2KUw+q3ox5SgKZxPPm857VaAMiQ6kZ6bzvyd8+n8aWe2nNyCo70jb9//NrFPxzK582TzOzmvX4chQyDEpDpc+/awYYNWrKoG4eHhQffu3cnLy2Pjxo3k5ubqLcnqSExMZO3ateTl5dGzZ8/qk4yxqrCx0ULe//lP4/bcXC3FypQpYJKKx0bYMK3bNE7NPcVr/q9R2642Pxz/AY//evDqr6/+ZerEK0NiYbJys/g07FOmHp7K4gOLyc3PZYbXDE7PPc0r/V+hjn0d85/08mUYOPCO+V66dtUWITZubP5zWgHDhw/HxcWFxMREdu/erbccqyI5OZnvvvuOrKwsPD09ratkrp4IoRVue//9O/etWwe9ekExEYH1atXjzUFvcvKZkzzU5SEyczN5e9/bdPikA9subyMnL8cC4vVDGRILkZGTwZKDS2iztA1Pb3+alJwU+rfsT/iscFaMXYFrfdeqOfH581psfJEIFAB8fTU/SdOmVXNeK6BWrVqMHz8eIQQHDx7k8OHDekuyCjIyMvjuu+8K08JXu4y+luCll2DTpjsqLXLyJPj4wOrVxX6spVNL1kxYQ+jjofg09+Fy+mU+PPUh7T9pz2fhn9XY9Sfq6qli0rLSeO9/79Hq41Y8/8vzXEq7RNcmXVnUaREh00Mql2SxLE6e1MIY4+KM2wcN0sIeranedhXh5ubGqFGjANixYwdRUVE6K9KX7Oxs1qxZw/Xr12natClTpkypGelPqoJx47RFiqZlpTMytJIKTz2lFcsqhj4t+nAg4ACrx6+mZd2WnE85z5PbnqTt0rZ8fPBjMnIyLPALWA5lSKqIpFtJLNq7CPeP3VmwewFXM67S896ebJmyhag5Ufg39q/aqYToaM2JftGkjOioUbBtG9SvRILHaoa3t3fh+pKtW7f+ZRcrZmdns27dOhISEnB2duaRRx6hdu3aesuybtq1gwMHYMaMO/ctX679j50v3rFuI2x4uOvDrOi5gnUT13Ff0/u4lHaJF355gVYft+Ld/71LalbNWOukDImZuZh6kX/s+gfuH7uzMGQhSZlJ+LX045epv3B45mHGdBxT8drpFWXPHs0ncvWqcfvkybBxI9SpAj+MldOnTx8GDhyIlJKNGzdy6tQpvSVZlLS0NL755hvOnDlD3bp1mTp1KvX/QjcTlaJOHVixQstHZ2p4w8Kge3etEmMJZQxshS2TOk8ianYUW6dsxae5D1czrvKP3dr3xBt73uDP9D8t8ItUHcqQmIF8mc/PcT8zbu043D92593975KWncYDbR4gZHoI+2bsY2jboVXvzMzMhBdf1GLfk5ON9wUEwJo1NS46qyL4+/vTt29f8vPzWbduHWfP/jUq4SUmJhIYGMjly5dxdnZmxowZNKxmKXCsgscfh9BQaNPGuD0pCWbP1tKtlOKHE0IwuuNoDgYcZOfUnfi7+5Ocmcybv71Ji/+0YPL6yeyO310tFzYqQ1IJEtMTeWffO7Rd2pYRq0ew5eQWbIQNkzpN4kDAAXY+ql0sFiEyEry94T//uXPf88/Dl1+Cra1ltFgpQgiGDBlCz549ycvL4/vvv+fChQt6y6pS4uLiWLFiBampqbi5uTFz5sy/3oJDc9K9u+Y3GTPmzn3h4ZoxmTWrMItwcQgheKCtdpMZMj2EcR7jkFKy/sR6hnw7BI9lHnwY+iHXMko+hrWhDEkFkVLy69lfmbx+Mm7/ceOVX1/hXPI5Wjm34p3B73DxhYusm7SO3m69yz6YOcjN1cIVfX3hxIk79y9aBB99VGMWG1YWIQQjR47kvvvuIycnh9WrV3P58mW9ZVUJERERrFmzhuzsbDp37sy0adNwdHTUW1b1x9kZNm/WUgrVNcnALaV209axI3z+eYnTXQX4u/uz6e+bOP/8eRYNXIRbAzdO3zjNS8Ev0fyj5kzdOJV95/dZfaofZUjKgZSSgxcPMn/nfFovac3gVYNZf2I9UkrGeYzj50d+5syzZ1jgt4Cm9SwYTnv6tObse+01zaAUpWVLzVfy+uvKiJhQkEbF09OTrKwsvvvuO66a+pOqMVJKgoOD+emnn5BS4ufnx4QJE7CvRmUBrB4htGnk33/X8taZcuMGzJkDvr7UL+4Gz4TmDZrz+oDXOfvcWbZO2crI9iPJycth9dHV+H/jT/tP2rNg1wIiLkVYpVFRcX8lkC/zOXjxIEEnggg6EcSF1NtTIC0atGBmj5kEdA+geQMdkttJqUWMvPSSFopoyvTpWrEqJyeLS6suFGS4Xbt2LXFxcaxatYqHH34YV9cqWs9jIXJycti0aROxsbHY2Njw4IMP0r27GRN+Koxp0UKr3RMcDHPnaiH3RYmIwDsiAn7+GV54QQuCKeXGzs7GjtEdRzO642jOJZ8jMDKQFUdWcCbpDO/tf4/39r9Ha+fWTOw0kUmdJtHz3p5WsZBUGZIi5OTlcODiATbGbiToRBAJaQmF+9wauDHRcyKTOk+it1vvqo+8Ko78fNi+Hd55R3P6mdKokRY98re/WV5bNcTW1pbJkyezZs0azp07R2BgIIMHD6ZPnz5W8c9ZUZKTkwkKCiIhIQEHBwcmT55MG1PHsKJqeOABiInRfJRvvQU3TVLL//ijtnl53U63Ukaa/lbOrfjX/f9i0cBF/O+Pt+yCNgAADpVJREFU/7H+xHo2xG7gbPJZPgj9gA9CP8DdyZ2JnSYy3nM8Ps19sLPR5yv9L21IpJScuHqCXfG72HV2F3vP7TXKjdOiQYtCy+/r5quP8QDIyYHvv9fSNpS0BmL0aG1utgavVK8K7O3tefjhh9m5cyfh4eEEBwdz5swZxo0bV23CY/Py8jhw4AAhISHk5ubi7OzMww8/TOMamvrGaqlVC15+GR55BObN01KqmBIVpc0YLFigLWicM6fMFEW2NrYMaDWAAa0GsGT4EkIvhLL+xHqCTgRxPuU8iw8sZvGBxTRwaMCgVoMY0mYID7R5gA4NO1jshugvZ0gSUhPYfXY3wfHB7IrfdUf8tkcjD0a1H8WkTpPwae6j753pzZsQGKg5y//4o/g+9etrmUmnT1e+kLvE3t6eUaNG0a5dO7Zu3Up8fDzLly9n7NixdOzYUW95pXL+/Hm2bdtW6OPp0qULw4cPV051PXFz0wrEPfGEZjAiIu7s8+efmv/y3//WVskHBGipV8pIVWNrY0t/9/70d+/Px8M/1ozK8fXsiNvB6Run2XJyC1tObtFkNHBjSJshDGk9hMFtBtOsXrOq+G2BGm5I0rPTibwcyeGEw4Xb+RTjVajN6jUzGmy3Bm46qS3C1avw3/9qmUhv3Ci534gRWvr3Vq0sJq0m07FjR+bMmcPmzZuJj49n7dq1eHt7M2zYMKtzVGdkZBAcHFyY8sXFxYVRo0bRtm1bnZUpChkyBMLCOPLJJ3Tfu1eL9DJ1lGdmajeLgYHabMLo0VqRrcGDy1w4bCNs8Gvph19LP5awhPPJ5wtnV3bF7+Ji6kW+ifqGb6K+AaCNSxt63dsLn+Y++DT3oYdrD+ra1y31HOWlxhmSlJwUZm6dyeGEwxy/evyOxT31atVjgPsAzXi0GULnxp31nw+XUptf3b5d20JDjeuoF8XGBiZNgv/7P+hRhXm6/qLUr1+fqVOncvDgQXbv3k1ERATnz59nwoQJNGtWdXd05UVKSVRUFMHBwdy6dQtbW1v8/Pzw8/NTObOsESFIue8+ePZZrQ780qXaCvn0YtLLJybeNip16mh1UMaO1dIaNWlS5qncnd0J6BFAQI8A8mU+MYkxmmGJ38W+P/YRnxRPfFI8Pxz/AdBW3Hdp0qXQsFSGGnflJWYm8tWRrwAtAsKrmRc+9/rQq7lmiT0beWJro//CPNubN7V0Jdu3a4WmLl0q/QO1a2v5fubNA3XXWaUIIejTpw+tW7dmw4YNXLt2jcDAQHx9fenVqxfOzs4W1ySlJCEhgeDgYP4wTHO2bt2aUaNGqVXq1YU2bbRoykWLNGOydGmJebq4dQu2bNE2IbSbRm/v21uXLqU6622EDV7NvPBq5sX8vvPJzc/l+JXjhF0KK5ydOXblGNGJ0UQnRvNl5JeV+tVqnCGpb1+ft4a9hU9zH7yaeVVNfY+KIKU2VXXixO0tJoZ+oaFlLlYCtMVPTz2l3dEoR7pFadasGbNmzeKXX34hIiKC0NBQQkNDad++Pb169aJt27ZVnn49LS2NmJgYoqKiuGZYLe3o6MiwYcPo0qWL/k/Tiorj5KStQXn2Wc1Q/PCDFh5sUjSrECk1P0tRX4u9vWZMCgyLl5c2xd2kSbF+FjsbO7o160a3Zt2Y2WMmADezb3LkzyMcTjhM2KUw1rL2rn+lGmdIXGu78lxvC9Yez8vTqg9euaIZjKtXISFBW6hUYDiK8XOU+fXTubP2BDJr1l8qU6+1YW9vz4MPPoiXlxdhYWEcP36c06dPc/r0aZydnfH29qZ79+5mdW7n5uZy8uRJoqKiOHPmTOECNEdHR7p164afnx91/oKJN2scdnYwYYK2ZWVp1Uu3bIGtW+/M2m1KTg4cOaJtgYG32x0ctLUt7u7aouSCny1bassDXFy0rV49HGs5FvpYgOprSIQQw4ElgC0QKKV812S/A7AK8AauA3+XUp4r7Zi2t27B/v2aFc/PN/5Z8Do3t+QtJ0dzgGVkaI+XGRm3t4L3KSmawbhyRTMS5lhpWreu5pwbOVJzordsWfljKsyGm5sbbm5uDB06lKioKMLDw0lOTmb37t3s3buXTp060bVrVxo2bIiTkxO2FchrJqUkLS2N69evc+LECY4dO0ZmplYAycbGBg8PD7p160a7du0qdFxFNcLBQfOJDB0Ky5ZpYcJbt2qG5ciR8h8nK0urP2Rag8gUW1tttqPAsLi4VEq+boZECGEL/Bd4ALgIhAkhtkopi+YTCACSpJTthBBTgPeAv5d23LoXLmjFnKoDHTveNhz+/mUuUFLoj6OjI/369aNv377ExcURHh7OqVOnOHr0KEePHgU0H4uTkxMuLi44Ozvj4uKCi4sLycnJHDt2jOTkZJKSkkhOTiY5OZmUlBTyTKY5XV1d6datG127dqWuaT4nRc1GCC05ZPfu8MYb2g1rwdRWwVbZZKMFMynXr5tFsp5PJD5AnJQyHkAIsRYYCxQ1JGOBhYbXQcAyIYSQ1phspjTq1AFPT+jUqfDnwcxMek+ZorcyxV0ihKB9+/a0b9+e5ORkIiMjuXDhAklJSaSkpBQaCVOio6OLPZ6joyPOzs60aNECLy8vmip/mKKAJk20m80RI263Xb2qZfwuMCxxcZrjPiVFF4l6GpLmQFGzehHwLamPlDJXCJECNASM8isLIWYBswxvswSYFCjXmVu3tD96ZGTR1kY89FB1yBPdCJPxtlKqg87qoBGUTnNTXXTe9epbPQ1JceEmpk8a5emDlPIL4AsAIUS4lLJn5eVVLUqneakOOquDRlA6zU110nm3n9UzjfxFoEWR926A6WKKwj5CCDvACShlqbdCoVAoLI2ehiQMaC+EaC2EqAVMAbaa9NkKPGZ4PRH4tdr5RxQKhaKGo9vUlsHn8QzwC1r47wop5XEhxJtAuJRyK/AV8K0QIg7tSaQ83ukvqky0eVE6zUt10FkdNILSaW5qvE6hbvAVCoVCURlUqV2FQqFQVAplSBQKhUJRKaq9IRFCfCCE+F0IESOE2CSEKDY1qxBiuBDipBAiTgixQAedk4QQx4UQ+UKIEkMBhRDnhBBHhRBRlQnHu1sqoFPv8bxHCBEshDht+FlsjgchRJ5hLKOEEKbBHFWlrdSxEUI4CCF+MOw/JIRoZQldxegoS+d0IcTVIuM3UweNK4QQV4QQxa4NExpLDb9DjBBCl9oK5dA5UAiRUmQsX7e0RoOOFkKIPUKIWMP/+R2JCe9qTKWU1XoDhgJ2htfvAe8V08cWOAO0AWoB0UAnC+v0RFvwsxfoWUq/c0AjHcezTJ1WMp7vAwsMrxcU93c37Eu3sK4yxwZ4CvjM8HoK8IMOf+fy6JwOLLO0NhMN/kAP4FgJ+0cCO9DWnPUGDlmpzoHAT3qOpUGHK9DD8Lo+cKqYv3uFx7TaP5FIKXdKKXMNbw+irUcxpTAdi5QyGyhIx2IxpJSxUsqTljzn3VBOnbqPp+F8Kw2vVwLjLHz+kijP2BTVHgQMFpbPB28Nf8MykVL+Rulrx8YCq6TGQcBZCOFqGXW3KYdOq0BKeVlKGWl4nQbEomUQKUqFx7TaGxITHkezpKYUl47FdPCsBQnsFEJEGFK/WCPWMJ5NpZSXQfvnAEoqIVdbCBEuhDgohLCEsSnP2Bil/gEKUv9YkvL+DScYpjeChBAtitmvN9ZwLZaXPkKIaCHEDiFEZ73FGKZUuwOHTHZVeEyrRT0SIcQuoLg6p/+UUm4x9PknkAusLu4QxbSZPe65PDrLQT8p5SUhRBMgWAjxu+Fux2yYQafu41mBw7Q0jGcb4FchxFEp5RnzKCwWs6X+qWLKo+FH4HspZZYQYg7aU9T9Va6sYljDWJaHSMBdSpkuhBgJbAba6yVGCFEP2AA8L6VMNd1dzEdKHdNqYUiklENK2y+EeAx4EBgsDZN8JpQnHUulKUtnOY9xyfDzihBiE9oUhFkNiRl06j6eQohEIYSrlPKy4bH7SgnHKBjPeCHEXrQ7sKo0JBVJ/XNRx9Q/ZeqUUhbNMf4lmg/S2rDItVhZin5ZSym3CyE+FUI0klJaPJmjEMIezYisllJuLKZLhce02k9tCa041svAGCllRgndypOORXeEEI5CiPoFr9ECCawrk7GGNYxn0fQ5jwF3PEkJIVyEVhwNIUQjoB/GZQqqguqS+qdMnSbz4mPQ5tOtja3ANEOkUW8gpWDK05oQQjQr8IMJIXzQvnvNUwykYjoEWsaQWCnlRyV0q/iY6h1FYIYohDi0+bwow1YQDXMvsN0kEuEU2t3oP3XQ+Tc0S58FJAK/mOpEi6CJNmzHrVWnlYxnQ2A3cNrw8x5De0+0apsAfYGjhvE8CgRYSNsdYwO8iXazA1AbWG+4dg8DbSw9fuXU+Y7hOowG9gAeOmj8HrgM5BiuywBgDjDHsF+gFcg7Y/gblxgRqbPOZ4qM5UGgr046/dCmqWKKfGeOrOyYqhQpCoVCoagU1X5qS6FQKBT6ogyJQqFQKCqFMiQKhUKhqBTKkCgUCoWiUihDolAoFIpKoQyJQqFQKCqFMiQKhUKhqBTKkCgUCoWiUihDolBUIUKIAUIIKYQYUaSttaEI0lI9tSkU5kKtbFcoqhghxK9AbSllXyGEExAKnAXGSinz9FWnUFQeZUgUiipGCNEfLYPzMGAe0BTwk1Km6ypMoTATypAoFBZACBGMlkQyGfCVUl7UWZJCYTaUj0ShsAxxQF3gDWVEFDUN9USiUFQxhpLJn6DV88iUUvbWWZJCYVaUIVEoqhAhxAPANmAmWu2PA8BIKeUOXYUpFGZEGRKFoooQQnQG9gPLpJSvGtqCAScppY+u4hQKM6IMiUJRBQghmgCHgHBgsiwoPSeEPxACPCil3KajRIXCbChDolAoFIpKoaK2FAqFQlEplCFRKBQKRaVQhkShUCgUlUIZEoVCoVBUCmVIFAqFQlEplCFRKBQKRaVQhkShUCgUlUIZEoVCoVBUiv8HN6/GA87GxjQAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "g = 0.1 Perturbative partition function: 0.355151471602 Monte Carlo partition function 0.4632873946110713\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "g = 0.2 Perturbative partition function: 0.327758771651 Monte Carlo partition function 0.4434214265268955\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "g = 0.3 Perturbative partition function: 0.327846128879 Monte Carlo partition function 0.43064078167185016\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "g = 0.4 Perturbative partition function: 0.362552298949 Monte Carlo partition function 0.4215268585206015\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "g = 0.5 Perturbative partition function: 3.94705133132e+25 Monte Carlo partition function 0.4146751678730463\n" ] } ], "source": [ "import math, numpy, pylab\n", "from numpy import *\n", "\n", "# Define the anharmonic (quartic) potential\n", "def V_anharmonic(x, gamma, kappa):\n", " V = x**2 / 2 + gamma * x**3 + kappa * x**4\n", " return V\n", "\n", "# Free off-diagonal density matrix:\n", "def rho_free(x, xp, beta):\n", " return (math.exp(-(x - xp) ** 2 / (2.0 * beta)) /\n", " math.sqrt(2.0 * math.pi * beta))\n", "\n", "# Harmonic density matrix in the Trotter approximation (returns the full matrix):\n", "def rho_anharmonic_trotter(grid, beta):\n", " return numpy.array([[rho_free(x, xp, beta) * \\\n", " numpy.exp(-0.5 * beta * (V_anharmonic(x, -g, g) + V_anharmonic(xp, -g, g))) \\\n", " for x in grid] for xp in grid])\n", "\n", "# Exact harmonic oscillator quantum position distribution:\n", "def p_quant(x, beta):\n", " p_q = sqrt(tanh(beta / 2.0) / pi) * exp(- x**2.0 * tanh(beta / 2.0))\n", " return p_q\n", "\n", "# Perturbative energy levels\n", "def Energy_pert(n, cubic, quartic):\n", " return n + 0.5 - 15.0 / 4.0 * cubic **2 * (n ** 2 + n + 11.0 / 30.0) \\\n", " + 3.0 / 2.0 * quartic * (n ** 2 + n + 1.0 / 2.0)\n", "\n", "# Partition function obtained using perturbative energies\n", "def Z_pert(cubic, quartic, beta, n_max):\n", " Z = sum(math.exp(-beta * Energy_pert(n, cubic, quartic)) for n in range(n_max + 1))\n", " return Z\n", "\n", "# Construct the position grid:\n", "x_max = 5 #maximum position value\n", "nx = 100 #number of elements on the x grid\n", "dx = 2.0 * x_max / (nx - 1) #position differential\n", "x = [i * dx for i in range(-(nx - 1) / 2, nx / 2 + 1)] #position grid\n", "\n", "beta_tmp = 2.0 ** (-5) # initial (low) value of beta (power of 2) (high temperature)\n", "beta = 2.0 ** 1 # actual value of beta (power of 2)\n", "\n", "#g = 1.0 #-cubic and quartic coefficient\n", "\n", "for g in [0.001, 0.01, 0.1, 0.2, 0.3, 0.4, 0.5]:\n", " \n", " Z_p = Z_pert(-g, g, beta, 15)\n", " \n", " rho = rho_anharmonic_trotter(x, beta_tmp) # density matrix at initial (low) beta (Trotter decomp.)\n", "\n", " # Reduce the temperature by the convolution property (matrix squaring):\n", " while beta_tmp < beta:\n", " rho = numpy.dot(rho, rho) #matrix squaring (convolution)\n", " rho *= dx #also multiply by the differential since we are in position representation\n", " beta_tmp *= 2.0 #reduce the temperature by a factor of 2\n", " #print 'beta: %s -> %s' % (beta_tmp / 2.0, beta_tmp)\n", "\n", " # Output position distribution pi(x) at the final beta onto a file:\n", " Z = sum(rho[j, j] for j in range(nx + 1)) * dx #partition function\n", " pi_of_x = [rho[j, j] / Z for j in range(nx + 1)] #the diagonal element of the density matrix\n", " f = open('data_anharm_matrixsquaring_beta' + str(beta) + '.dat', 'w')\n", " for j in range(nx + 1):\n", " f.write(str(x[j]) + ' ' + str(rho[j, j] / Z) + '\\n')\n", " f.close()\n", "\n", " # Plot the obtained final position distribution:\n", " T = 1 / beta\n", " x = linspace(-x_max, x_max, nx+1)\n", " y2 = [V_anharmonic(a, -g, g) for a in x]\n", " y1 = [p_quant(a, beta) for a in x]\n", " pylab.plot(x, y2, c='gray', linewidth=2.0, label='Anharmonic potential')\n", " pylab.plot(x, y1, c='green', linewidth=2.0, label='Harmonic exact quantum')\n", " pylab.plot(x, pi_of_x, c='red', linewidth=4.0, label='Anharmonic matrix squaring')\n", " pylab.ylim(0,1)\n", " pylab.xlim(-2,2)\n", " pylab.title('Anharmonic oscillator position distribution at $T=$%.2f' % T, fontsize = 13)\n", " pylab.xlabel('$x$', fontsize = 15)\n", " pylab.ylabel('$\\pi(x)$', fontsize = 15)\n", " pylab.legend()\n", " pylab.grid()\n", " pylab.savefig('plot_T_%.2f_anharm_g_%.1f_prob_matrix_squaring.png' % (T,g))\n", " pylab.show()\n", " print 'g =', g, 'Perturbative partition function:', Z_p, 'Monte Carlo partition function', Z" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Path integral Monte Carlo" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "data": { "image/png": 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qBMDGjRvZunUrDRs2pGfPnvzyyy/06tULgNq1a/P777/z2muvMXPmTN5++21at27NihUrCA0NZfHixUydOpX58+cDsHr1ajZt2kRsbCzLli3jjz/+YNu2bcTGxtK8eXPGjRvH2rVreemll3jllVd48cUXmThxIjfeeCNjxozh3XffZdKkSSxcuBCAw4cPs2rVKrZv386QIUMKDKHNnj2bvXv3snHjRkJDQzl5svCE+Onp6fz666+sWLGCCRMmsHjxYp588kk6duzIwoULWbJkCTfeeCOJiYlMmDCB6Oho7rvvPgCuu+467r77bnr16sX+/fu59NJLXWuwtm/fztKlS0lNTeW8887jtttuY8aMGWzZsoXERKOwalJSkkuPunXr8tNPPxEZGcmuXbsYNWoUOjdkcKADKfyXoDNUVjFv3jzuuusuAK699lrmzZvnMlQXXHABjRs3BiAhIYGkpCSXoRo2bBgAnTt35ssvvwSMN8MxY8awa9cuRIScnBzXeS655BJiY2Nd2127dnWtV2rRogUDBw4EID4+nqVLlwKGccvr+4YbbmDy5Mmu44cOHYrNZqNt27YcOXKkwOdavHgxEyZMcGWhdj+3O6NGGeu7+/TpQ2pqKikpKaxZs8ZlEPv378+JEydcb735z/Hnn3+6tk+fPk1qaioAgwcPJiIigoiICOrWrVuoju7k5OQwceJEEhMTCQkJYefOncW21wQOeg2V/xJ0hqokz8cbnDhxgiVLlrBlyxZEBLvdjojwzDPPABAREeFqGxISYppfytvnLn/44Ye56KKLWLBgAUlJSaYs5PlLZ7j3bbPZXNs2m63IeSz3EGr34wurBq2UKlXIdf42IlLoHFVhfTkcDlavXk2VKlUK7Cvu2hXGCy+8QL169fjjjz9wOBxERkaWqLsmMNBrqPwXPUdVCXzxxRfceOON7Nu3j6SkJA4cOECzZs1YtWpVufpLSUmhUaNGgDEvVVF69Ojhmjf76KOPXN5caRg4cCBvvPGGy0AUNfT36aefArBq1SqqV69OTEwM3bt356OPPgKMubratWsTExNDtWrVXB5T3jleffVV13bekF5R5D/enZSUFBo0aIDNZuODDz4oMvJQE3jooT//RRuqSmDevHlcddVVJtnw4cP5+OOPy9Xf5MmTefDBB+nZs6dHHrQvv/wy7733Hu3bt+eDDz7gpZdeKvWx48aN45xzzqF9+/Z06NChyM9Us2ZNevTowYQJE3j77bcBuOeee1i/fj3t27dnypQpzJ07F4ArrriCBQsWuIIpXn75ZVe7tm3b8sYbbxSrU61atejZsyft2rXj/vvvN+27/fbbmTt3Lt27d2fnzp26eGMQoYMp/BcpbDjHnymscOK2bdto06aNRRpp+vXrx8yZM+nSpQtgDBf+888/KKWoX7++K1w9WNDfR2uYOXMm6enp3H333dqrKgQR2aCU6mK1HoURXE8IjU8Q7GmUNJVPbm4u6enp2Gw2V000jf8QdMEUmspn2bJlBWQ2mw273Y7dbndFDGo03iJvfqpatWpB58EHAvqOaSwhLzOA9qg0lYGO+PNvtKHSWIIe+tNUJnoNlX+jDZXGEvIMlQ4P11QGOjTdv9GGSmMJeuhPU5no0HT/RhsqH2XOnDkcOnTItV2akh/r169n0qRJxbbJn1ncm8yZM4eJEycWKo+OjmblypUuQ5VXAqW8Wc7Lm3F97dq19OnTh/POO4/WrVszbtw4MjIySn28Lg/iH2iPyr/RhspHyW+oSkOXLl1cGcSLwtOGqrzlRNq1a8dXX33lGvr75JNP6NChQ7n1KI+hOnLkCCNHjuTpp59mx44dbNu2jUGDBhWZ1SI/3iylovEs2qPyb4LLUIl4968IkpKSaN26NWPGjKF9+/aMGDHC9db++OOP07VrV9q1a8f48eNRSvHFF1+wfv16Ro8eTUJCAmfOnAEKL/nhzrJly7j88suB0pfAAHj22Wfp2rUr7du3N+VCnD59Oq1bt+aSSy5h1KhRzJw5EzAW8E6dOpW+ffvy0ksv8c0339CtWzc6duzIxRdfXGJiWIBevXqRmJhIVlYWaWlp7N69m4SEBNf+n3/+mY4dOxIfH8/NN99MVlYWYHiWjz76qOk6lKU0iDuzZs1izJgxXHjhhc6vhzBixAjq1atX6lIq7mRmZnLTTTcRHx9Px44dXUl/NdajPSr/JrgMlYXs2LGD8ePHs2nTJmJiYlxezcSJE1m3bh1btmzhzJkz/O9//2PEiBF06dKFjz76iMTERFcy1rySH7fddpvLaBTH9u3b+eGHH1i7di2PPfYYOTk5zJgxgxYtWpCYmMizzz7Ljz/+yK5du1i7di2JiYls2LCBFStWsH79eubPn8/GjRv58ssvC5TCSE5OZvny5dx777306tWLNWvWsHHjRq699lpXst3isNls9OrViyVLlrBw4UKGDBni2peZmcnYsWP59NNP2bx5M7m5ubz++uuu/fmvQ1xcHBMmTODuu+8mMTGR3r17c+edd3L33Xezbt065s+fz7hx4wrosGXLFjp37lyofnmlVDZu3Mjjjz/O1KlTXftWr17N3LlzWbJkiemYWbNmAbB582bmzZvHmDFjyMzMLPFaaLxLdnY2mZmZhIaGEhUVZbU6mnKgDVUl0aRJE3r27AnA9ddf70pIu3TpUrp160Z8fDxLlixh69atRfbhXvLDvcZSUeSVwKhdu3aRJTB+/PFHfvzxRzp27EinTp3Yvn07u3btYtWqVVx55ZVUqVKFatWqccUVV5iOu+aaa1z/P3jwIJdeeinx8fE8++yzxX4Gd4YOHcpXX33FJ5984ioDAoZRb9asGa1atQJgzJgxrFixokzXYfHixUycOJGEhASGDBliKg1SGlJSUhg5ciTt2rXj7rvvNn2m/KVU8li1ahU33HADYBi6pk2b6jIiPoB7aHppMv1rfA9tqCqJwspcZGZmcvvtt/PFF1+wefNmbr311mLfwAsr+VEcpSmBoZTiwQcfJDExkcTERHbv3s0tt9xSaEkPd9yTud5xxx1MnDiRzZs38+abb5bKixAROnfuzPbt2zl+/LjLKOXpVJrPVdx1yCsNkve5/v77b6pVq2Zqc/7557Nhw4ZCj88rpbJlyxa++eYb02cqKpFtoOXNDBT0sJ//E1yGSinv/hXD/v37Wb16NWBkU+/Vq5fr4Ve7dm3S0tJMEW/FlaqoCPn7vfTSS3n33XdJS0sD4O+//+bo0aP06tXL9YBOS0tj0aJFRfbpXnYkLwN6abDZbDz44IMFqi63bt2apKQkdu/eDcAHH3xA3759y/S5SlMaZOLEicydO5fffvvNJfvwww/5559/ylVKpU+fPq6yJTt37mT//v2cd955pTpW4z10IIX/E1yGykLatGnD3Llzad++PSdPnuS2226jRo0a3HrrrcTHxzN06FC6du3qaj927FgmTJhgCqbwBPlLYAwcOJDrrruOCy+8kPj4eEaMGEFqaipdu3ZlyJAhdOjQgWHDhtGlS5cif+jTpk1j5MiR9O7dm9q1a5dal5CQEPr370+fPn1M8sjISN577z1GjhxJfHw8NpuNCRMmFNtXeUqD1KtXj08++YT77ruP8847jzZt2rBy5UpiYmLKVUrl9ttvx263Ex8fzzXXXMOcOXNMXq3GGrRH5f/oMh+VQFJSEpdffjlbtmyxTIfykJaWRnR0NBkZGfTp04fZs2fTqVMnj/WfkpJCeno6MTExQZXR2urvY7Dx1VdfkZiYyODBg12lZjQF8eUyHzpttaZIxo8fz59//klmZiZjxozxqJGCs9kp9HokjTfRCWn9H22oKoG4uDi/86aAclcgLi15hkrn+9N4Ez305//oOSqNZeTVodKGSuMtlFI6mCIA0IZKYxnuHlWgzZVqfIPMzExycnIIDw/XgS1+jDZUGsuw2WyICEopnUVd4xXch/30Yl//RRsqjaXoeSqNN9HDfoFBUAZTxE0pevFqeUiaMdij/eUnMTGRQ4cO8a9//avQ/evXr+f9998vMXO6VRw6dIhJkyYVWsIjNDSU3Nxcbag0XkEHUgQGlnpUIjJIRHaIyG4RmVLI/nNEZKmIbBSRTSJS+JM6wElMTOTbb78tdF9ubm6pyntYRW5uLg0bNiyyzpT2qDTeRHtUgYFlhkpEQoBZwGVAW2CUiLTN1+y/wGdKqY7AtUDlVPzzMHllPsaNG0e7du0YPXo0ixcvpmfPnrRs2ZK1a9cCFFpaIjs7m0ceeYRPP/2UhIQEPv30U6ZNm8b48eMZOHAgN954o6m8x6RJk3j88ccB+OGHH+jTp0+B+Z/ly5eTkJBAQkICHTt2JDU1FaUUEydOpG3btgwePJh//etfLuPiXrRx/fr19OvXr0h9oWApDPfignPmzGHYsGEMGjSIli1busqK2O123nnnHVq1akW/fv249dZbCy26qNGUBe1RBQZWDv1dAOxWSv0FICKfAFcCf7q1UUDeN6w6ULZKgj7E7t27+fzzz5k9ezZdu3bl448/ZtWqVXz99dc89dRTLFy40FVaIjQ0lMWLFzN16lTmz5/P448/zvr1612566ZNm8aGDRtYtWoVVapUYdmyZa7zzJgxg65du9K7d28mTZrEt99+i81mfh+ZOXMms2bNomfPnqSlpREZGcmCBQvYsWMHmzdv5siRI7Rt25abb7652M9UlL5glMLYtGkTsbGxBTKcJyYmsnHjRiIiImjVqhWjR4+mSpUqTJ8+nd9//51q1arRv3//ChVS1GhAL/YNFKw0VI2AA27bB4Fu+dpMA34UkTuAqsDFhXUkIuOB8QDnnHOOxxX1BM2aNSM+Ph4wsnYPGDAAESE+Pt71IE9JSWHMmDHs2rULESEnJ6fI/oYMGeKqU+VOVFQUb731Fn369OGFF16gRYsWBdr07NmTe+65h9GjRzNs2DAaN27MihUrGDVqFCEhITRs2JD+/fuX+JmK07eoUhgAAwYMcD042rRpw99//01ycjJ9+/Z1HTNy5EhdIkNTYdxLfGj8FyvnqAqLFc2/mGYUMEcp1Rj4F/CBiBTQWSk1WynVRSnVpU6dOl5QteK4r+Gw2WyubZvN5kohVFxpifwUVWoCjMJ9tWrVKrKU/ZQpU3j77bc5c+YM3bt3d1ULLip8NzQ01DV86K5TeUphgPla5AVT6PB0jadRSmmPKkCw0lAdBJq4bTem4NDeLcBnAEqp1UAkUPr03H5GUaUlylLyY9++fTz33HNs3LiR7777zlTCIo89e/YQHx/PAw88QJcuXdi+fTt9+vThk08+wW63c/jwYVMZ9bi4OFfdpryhveL0LQsigojQoUMHli9fzqlTp8jNzTWdR6MpDxkZGdjtdqpUqUJYWJjV6mgqgJVDf+uAliLSDPgbI1jiunxt9gMDgDki0gbDUB2r6Im9HU5eXiZPnsyYMWN4/vnnTUNvF110ETNmzCAhIYEHH3ywyOOVUtxyyy3MnDmThg0b8s477zB27FjWrVtHZGSkq92LL77I0qVLCQkJoW3btlx22WWEh4ezZMkS4uPjadWqlan+06OPPsott9zCU089RbduZ0dni9K3rNhsNho0aMDkyZPp1q0bDRs2pG3btvotuBy4L73w1e95ZaGH/QIHS8t8OMPNXwRCgHeVUk+KyOPAeqXU184owLeAaIxhwclKqR+L69MXy3z4I2PHjuXyyy9nxIgRXj/XyZMnyczMJCwsjDp16pCbm8tVV13FzTffzFVXXeX181c23vw+lsZQBYsx27ZtG5999hmtWrVi1KhRVqvj8+gyH0WglPoW+Daf7BG3//8J9KxsvTSVS95aqunTp7NixQoyMzMZOHAgQ4cOtVgzjT+jQ9MDh6DMTKEpmfLOOZUHd0Olh/s0niI5ORnQgRSBQNDk+tPZuX2XYCqgqL+HlceJEycAqFWrlsWaaCpKUBiqyMhITpw4oR8SPkqwpFFSSnHixAlTYIvGe+RlU6ldO2ADhYOGoBj6a9y4MQcPHuTYsQoHDGq8QF5xOxFxvQUHKpGRkTRu3NijfXo6yXIgkJubS3JyMiJS5MJzjf8QFIYqLCyMZs2aWa2GpgiUUsyYMYPs7Gzuv/9+oqKirFZJ4+ecPHkSpRR4SNDxAAAgAElEQVSxsbEuj13jvwSFodL4NiJCjRo1OHr0KMnJydpQFUGwhJV7Aj3sF1gExRyVxvepUaMGcDZSS6OpCNpQBRbao9L4BHmGKi+bgKZ49LxU8WhDFVhoQ6XxCbRHdRY9xFdxtKEKLLSh0vgEeYsytaEqBIcD/vyT639fRO2MZHbUbsqqZh1JjSg6Q30wo5RyGSq9hiow0IZK4xNoj+osofZczj+yhwsObIUrZ8PKlXDqFE+4tcmxhbChURuWNe/C0hZd2FG7KRRRpiXYSE1NJScnh6ioKB2YEyBoQ6XxCdwNlVKqyNpYAcupUzB7NixezB/LV1E1p+haZABhDjvdD2yh+4EtTFk+h0PVarOseReWNe/MqrgEMsILFtUMFvSwX+ChDZXGJ6hSpQrh4eFkZ2eTmZlZaPXigGX1arj6ajh4EDBKWZeVhqnHue6P77nuj+9JiajKtIv/DQTn/JY2VIGHDk/X+AR5a6kgiIb/lIIXX4Q+fVxGqkiqV+fnFl15v+NgdtVqUnzTrHReWPQ8TJoEOTkeVNg/0IYq8NAelcZncF/026BBA6vV8S4pKXDLLVBEJeNjVWvwW+N2XP6fqw1D1q4dtzz0vWt/4+R/6PfXBi76az099m2iSm5WwU5eeQU2boTPP4f69b31SXwObagCD22oND5D0ET+/fEHjBgBu3cX3HfXXfRLb0NSzYYgwuV3FD58d7BGfT7sNJgPOw0mIjebbvs3c9Ff6xn1xw9E5mafbbhqFUdank+9H/8HF17opQ/kW2hDFXjooT+NzxDwQ39KwTvvQPfuBY1U9eqwYAG88AJJsY3KFMGXFRrOiuadeezifzN89DMcjKlr2l8v7ST07QtvvGHoUARxUxb5/ULirKwsUlNTCQkJ0XWoAghtqDQ+Q6Blp8h78MdNWQQZGXDTTTBuHGSaI/q21GsBGzaAByoab61/LpePfZEVcR3NO3Jy4Lbb4JZbiHD3uAIM9xpUNpt+vAUK+k5qfIZA9ahqZqQYw25z5xbY93GHQQy//llo0cJj50uuEsPYkdN4rfuIgjvfe4/PPnqAhqePeux8voQe9gtM9ByVxmcIxLVUofZcZn31NOzfZN4RFcXdF01gQbv+gOdz9zlsITzTdyyb6rfkuUUvmNZldfhnF19+cB9X3vi8R8/pC2hDFZhoj0rjM1SpUoWwsDCysrLIzCx+wau/MHXpu/TIb6Rat4a1a11Gypt8f15PwyC1amWS1087yZsLniowDOnv5A39aUMVWGhDpfEZAm0t1fDNP3Pzhq9Nst8anw9r18L551eaHrtrn2Occ8gQkzzh8E5j3qqYAAt/Q3tUgYk2VBqfImAM1bp1PPXDqybR39XqcPvQB6FatUpXJ+7/VtH8vFtY2ryzececOfDqq4Ue4284HA5TMIUmcNBzVBqfIiAM1ZEjcNVVRNjPZoXIDA3n38Me4kTVGpaFgDtsIdx5xf0sfP8emp865JLn3nkX169Og3PaW6KXp0hOTsZutxMTE0N4eLjV6mg8iPaoND6F34eoZ2cbi3n//tsknjLoDrbUP9cipc5yOjKaW4c9TKpb0tpQ5WDWwhk0SvHvSEA97Be4aEOl8Sn83qO6+25YtcokeqvrUBaef1G5ujOtxfIQe2o34e7L7zPJap05zewvnyCyhKztvoyuQRW4aEOl8Sn8Oo3S22/Da6+ZRKuadmBGv5ssUqhoFrfsxvO9Rptk5x/9i2e+e9lvgyu0RxW4aEOl8Sn81qNavRr+8x+T6ED1eky88gHsthCLlCqeV3pcww8tu5tkQ7atgJkzLdKoYujQ9MBFGyqNTxEVFeUXa6lMQ3KHDsHw4cb8VB5RUYwf9hDJVWKsU7IElNi4Z/A97Kx1jnnHlCnwww/WKFUBtEcVuGhDpfEp/G4tlVIwejQcPmwS/+fiO9hWt7lFSpWe9Igobh3+X1Ii3Mo1Ohxw7bWFZ3f3UTIyMsjIyCA8PJxqFoT/a7yLNlQan8OfDNVVW5fCsmUm2WvdR7CoTW9rFCoH+2o25I4hk7GL2+MgOZm1F11pGC0/wN2bCoTUWxoz2lBpfA5/CaiIyUxj6tJ3TbKVTROY2fsGizQqPyuad+aZvjeaZBcc/BPee88ijcqGHvYLbLSh0vgc/uJR3bvyA+pkuOkYEcFDl/4Hh48GT5TEmxcML5i5YvJkOHbMGoXKgA5ND2y0odL4HP6w6LfdP7u5fuN3ZuHUqeyv2cAahTyBCA8PvJ0zoRFnZSdPwn33FX2Mj6Aj/gIbSw2ViAwSkR0isltEphTR5moR+VNEtorIx5Wto6by8XmPyuHgiR9fI0S5zd+0aGF4H37Ower1eLHXKLPw/fdhyRJrFColeugvsLHMUIlICDALuAxoC4wSkbb52rQEHgR6KqXOB+6qdEU1lY7PG6q33zYyj7vz6qsQGWmNPh7mnS5D2VYnziy87TbIyrJEn5LIzc3l1KlTiAixsbFWq6PxAlZ6VBcAu5VSfymlsoFPgCvztbkVmKWUOgWglPLvZGSaUhEVFUVoaCiZmZm+t5bq2DFjnZE7w4bBoEHW6OMFckNCeWigefEyO3fCjBnWKFQCJ0+eRClFzZo1CQ3VebYDESsNVSPggNv2QafMnVZAKxH5RUTWiEihTwMRGS8i60Vk/TE/mPjVFI9Pr6WaMgVOnXJtpodFwosvWqiQd/i9cRs+Ssj3c3vqKdixwxqFikHPTwU+VhqqwhY75E8yFgq0BPoBo4C3RaRGgYOUmq2U6qKU6lKnTh2PK6qpfHzSUP36K7xrDkd/uee10KSJRQp5l6f7joW6dc8KsrN9stCijvgLfKw0VAcB9194Y+BQIW2+UkrlKKX2AjswDJcmwPE5Q5Wbazyk3dhVqwnvdsk/Wh04nI6MhhdeMAuXLoUPPrBGoSLQgRSBj5UDuuuAliLSDPgbuBa4Ll+bhRie1BwRqY0xFPhXpWqpsQSfC1GfNQs2bTKJHh54GzkhYZYVQqwM4v6I4f24jvRJ2nhWeO+9JGwIc+UxTJox2CLtDLShCnws86iUUrnAROAHYBvwmVJqq4g8LiJDnM1+AE6IyJ/AUuB+pdQJazTWVCY+5VEdPgwPP2wSLWjbjzV+XhG3VIjw8MDbyAoJOys7fpwpy+ZYppI7SiltqIIAS9dRKaW+VUq1Ukq1UEo96ZQ9opT62vl/pZS6RynVVikVr5T6xEp9NZWHrxiquCmL+GrAKEhNPSuMieGpi26xTqlKZl/Nhrzc41qT7NpNP9L1wBaLNDpLWloa2dnZVKlShaioKKvV0XgJnZlC45P4Sr6/rge2cOW25Wbh9Okci65pjUIWMbvbMGjTxiR76odZhNpzLdLIQHtTwYFedKDxSapWrWpaSxVZiYtpXXNOSvHpinyBAwkJcPvt8F//q9dUEXJCwuCNN6BvX5es5YkDXL35Jwouf6w8tKEKDrRHpfFJ3NdSWRVQ0TtpI90ObjULX34ZgnRRady3qXze7mKT7M5f5kFGhkUaaUMVLGhDpfFZLJ2nUop7V35olg0aBL39p86UN5jZ53oyQ8Nd2/XSTsJLL1mmjzZUwUGZXw1FJB4j/VF9IBI4CewEfs1LdaTReAIr56kG7FlbIJ/fFXUvZXMAh6KXhiPVajOn8xVM+G2+S3b6sSfp/U8zUqpUq/RQdW2ogoNSeVQi0lxEnhWRQ0Ai8AZGgtibgOnAN8AxEflZREaJiPbUNBXGKo9KlKOAN/Vjy+5sbqDXmgO81n2kqXR9TFY6t635vNL1yM7O5vTp04SEhLi+K5rApESDIiJvA1uBBOBxoCMQqZSqo5RqrJSKBuoCVwCbgWeAbSLSy3tqa4IBqwzVoB2/0vboXpPs+V6jK1UHX+Z0ZDSvdx9pko39/X/UP328UvXIy/EXGxuLzabfjQOZ0tzdTKC1UuoSpdQbSqlNSim7ewOl1HGl1HdKqbuApsAjFEwwq9GUibySDXkPpErBbueeVR+ZRN+07s32us0qTwc/YE7ny/kn+mxJjcjcbO76pXLLxelhv+ChREOllJqolNpX2g6VUg6l1KdKqU8rppom2MlLMHz8+HFycytpvc68ebQ8cTapv11svNgrf2YvTWZYJC/2NF+XkZsXw7ZtlaaDNlTBQ5n8ZRF5UUQKy3qu0XicsLAwYmNjTWlyvEpODkybZhItPL8fe2oFZnb0ivJ5+0vYE9vYtR2iHPDQQ5V2fm2ogoeyDuyOAhaKSKG5SkTksoqrpNGcpV69egAcPVoJNTPffx/27HFt5thCeKnHqGIOCG7sthCe7XODWbhgAaxZUynn14YqeCiroeoOnAusFJEGeUIRuVREfgP+50nlNJq6znpIR44c8e6JsrLg8cdNos/jL2Z/zQZFHKAB+L5VDxLzR0NOmeL1mlV2u901d6nrUAU+ZTJUzppQPYDjwFoRuVlEfgW+A1IwChxqNB6j0jyqt9+G/ftdm1khobza4xrvnjMQEDEKLLqzfDl8/71XT3vkyBHsdju1atUiIiLCq+fSWE+ZYzqVUinATKAm8BbGot8LlVIDlVIrPayfJsipFI/qzBl48kmT6OOEyzgUU7eIAzTurG7agRVxHU2yP8f+BxwOr53zwAEj4KVx48YltNQEAmUNprhURFYB3wO/Am8CbTGGAzUaj1OzZk3CwsJITU3lzJkz3jnJ668bNaecZIaG81q+dUKa4nm631jTdtuje+ET71Xl+fvvvwFtqIKFsnpU3wFZQF+nB3U7MAl4V0Qe87h2mqDHZrO5wtS94lWlpcH//Z9JNLfT5RxzWyOkKZmt9VrwdZs+ZuHDD0N2tlfOpz2q4KKshqqfUmqAUmpVnkApNRu4HJgkIrqwocbj5A3/eWWe6uWXwT30PTqaN7sN9/x5goDnel9Pji3krOCvv+Cttzx+nrS0NJKTkwkPD3d9NzSBTVmDKVYUIf8J6IWRrFaj8Sh5ARUe96jS0uC558yyO+/kZFR1z54nSNhXsyHzOgwyC596CjIzPXqegwcPAtCoUSOdOilIKE2uvxtEJKSkdkqprUA35zHnikhw10PQeAyvRf699RacPHl2OyYG7r3Xs+cIMl7pca2pDAiHDsE773j0HO6GShMclOZ15F5gj4hMF5EORTUSkVrAQBH5BtgI6AUoGo/gPvSnPLU+JyuLw4+YI/1ePX8QcU//6pn+g5Rj0TX5KMG87v/Qg9OMdWoeIs9QNWmiM4YEC6XJ9ZcAPABcBGwUkdMi8puILBKRL0VkiYjsBY4CLwF7MJLYfuZVzTVBQ9WqValatSrZ2dmey6T+wQc0SDub7PZMaATvdR7imb6DnDe6DTd5VQ1Tj8O773qkb4fDoSP+gpBSDfA6k8z2AloB92PUpMoFqgJHgLnAIKCBUuoupdTfXtJXE6R4dJ7KboennzaJPukwkBNVdU0jT3AsOpZ5HS41C//v/zziVR05coTc3FxiY2OJiio0k5smACnrTGSWUupNpdS/lVJXKqUuVUqNUkpNU0r9pJTK8YqWmqDHo5F/X3wBu3e7NnNsIbx1wVUV71fj4vVuI8gKCTsrOHCAqVfeS1wFKyTrsPTgpKyGKklEunhFE42mGDwWUKFUgXVTC86/SGeh8DBHq9Uq4FXdvvozwuwVe5fVw37BSVkNlQALnPNTTzsjAjuKSITz7w9vKKnReGzo77vv4I+zX1MHwhvdRlSsT02hvNFtBFkhoa7txqePMXzzzxXqU3tUwUl5FiH8AKQDVwLvAeuBNIy5qjiPaabRuFG7dm1EhBMnTlSsiGI+b+q783rwVy390PMG/8TU5tP2Zq/qP2s+N+p+lYP09HROnTpFWFiY68VFExyUx1DNVkpdrZRqDURjLPIdBzwLXOtJ5TSaPNyLKB47dqx8naxcCatWmUQ6p593eb37CLJtZ72qJilHjLpf5UAv9A1eKnS3lVKZSqkNSqm5SqknlVLfeUoxjSY/FZ6nyudNLW/Wia31dT5lb3I4pg6ftb/ELHzyyXJ5VXqhb/BSHkM1WkSuEJHmHtdGoymGCpX82LjRmJ9yQ3tTlcNrF440eVXs3QsffljmfvRC3+ClPIbqeuArYJeIpIrIWhF5T0TuFZFLSzpYoykvFfKoZswwba5v1IbfmrTzhFqaEjgUU5cv4i82C598Esow16gX+gY3ZTVUPwP9MYom9gHuA9YATYHJwLce1U6jcaPcHtXOnfD55ybRa91HgoinVNOUwGsXjjRnVt+zBz76qNTHHz16lJycHGrWrEnVqlW9oKHGlylr9vRLlFJ/KKVSlFK/OBf/TlJK9VdK1QPqe0lPjcZVRDEtLY2MjIzSH/jMM8b6KSfb6sSxpEVXL2ioKYqD1evxRbsBZuETT5Taq9Jh6cGNR0NnlFLlDMfSaEpGRMrkVcVNWUT32+cWiDJ7XXtTljDrwqvNXtXu3TBvXqmO1cN+wY2O8dT4FWVNpXTrugWmCLOkGg1Y1LqXV3TTFM/BGvX58vz+ZuH06UbuxRLQHlVwow2Vxq8oS4aKmhkpjPrje5PszW7DsdtKLK+m8RKv9rgGQtyu/65d8OmngOEB5/25k5GRwcmTJwkNDdULfYMUSw2ViAwSkR0isltEphTTboSIKJ1nUFOWyL+xG/5HVI5bxu4GDZiff55EU6kcqFGfz9tcZBY+8QQ4HEUe475+KiREv2QEI5YZKmfV4FnAZUBbYJSItC2kXTVgEvBb5Wqo8UVKXUQxLY0xv39jlt17L9mhYYW311Qar/a4Gru4PXq2bYP584tsrxf6aqz0qC4Adiul/lJKZQOfYOQPzM904BkgszKV0/gmUVFRVKtWjZycHE6dOlV0w9mzqZGZdna7Zk0YP977CmpKZF/NhnzVtq9ZOH06ogr3qvRCX42VhqoRcMBt+6BT5kJEOgJNlFL/K64jERkvIutFZH2588Bp/IYSAyqysuC558yyiROhWjUva6YpLbMuvBoHbpGXmzczcNeaAu30Ql8NWGuoCosPdo3liIgNeAG4t6SOlFKzlVJdlFJd6tSp40EVNb5IiSHqH34Ihw6d3a5SBSZNqgTNNKVlT60m/K9Nb5Psjl8/Na13Azh27BjZ2dnUqFGD6OjoylRR40NYaagOAu6+fGPA7elCNaAdsExEkoDuwNc6oEJTbECF3W4s8HXn1luhdu1K0ExTFl658BrTdrsje+i/Z51JpsPSNWCtoVoHtBSRZiISjlEi5Ou8nc7sF7WVUnFKqTiMVE1DlFLrrVFX4ysUG6K+cKGRMslJji0E7i3RKddYwK46TWH4cJNs0q/zTF6VHvbTgIWGSimVC0zEKMS4DfhMKbVVRB4XkSFW6aXxffKKKJ48eZIc93IRhZSZ/6ptPzjnnMpVUFN6/vtf02bC4V302fu7a1t7VBqweB2VUupbpVQrpVQLpdSTTtkjSqmvC2nbT3tTGoDQ0FBq1apVsIjizz/Dhg2mtm90G47Gh0lIgCvNwb53/mJ4VWfOnOHEiROEhoZSv75OIxrM6MwUGr+k0HmqfKU8fmzZnd21tTfl8zz8sGmz86HtsGSJKyy9YcOGeqFvkKMNlcYvcY/8i5uyiCFjXjA8Kjde7zbCCtU0ZaVzZxg82CybPl0v9NW4CC25iUbje5g9qlhuW/OFaf/qc+LZ2Ki1BZppykJeXr+E2P4sxC3H3/LlZC9eDOHheqGvRntUGv/EPfKvxYkDXLpztWm/LjPvXyQ2PI8VcR1NslbOZLU6kEKjPSqNX1K9enXCw8NJT0/n9t++w3Z2rThb6rVgpdtDL382bo1v8lLPUfRJ2ujabrZnD61PnqSazigS9GiPSuOX5BVRjElJYcjW5aZ9r3cboQsj+iEbGrfll6btTbK+K1ZYpI3Gl9CGSuO31KtXjwtXrybMcbbw3t6aDfjuvB4WaqWpCC/3GGXarp+YCGvXWqSNxlfQhkrjtzSMiKBTvnVTb14wHIcujOi3/HZOPOsa56v28+ij1iij8Rm0odL4Lc0XLSLcLTPFkehYvtSFEf2ez3pfbhZ8/z2sWmWNMhqfQBsqjX+SkkL1uXNNore7DNWFEQOAky0akNS0qVn43/8WyKyuCR60odL4Jy+/jCQnuzZTIqOZlzDIQoU0niAUOw1DTrPkov7mHcuXw5Il1iilsRxtqDT+R0oKvPCCSfTlBZeQFhFlkUIaT9EkJIVQUaxvcj7Lm3Uy79ReVdCiDZXG/3jlFXArQ38mMpLfLuhmoUIaT9HUZtzXJHsNnut9vXnnmjXw7bcWaKWxGm2oNP7F6dPw/PMm0ZoLL6RG1VzcCkRr/JAQHDQOSQFgn6Mmmxq04seW3c2NHn4YHA4LtNNYiTZUGv8inzeVElGVJV17U0VyqSlnLFRMU1Ea2VIIEwfHHFGkqwgAnu812txo40ZYsMAC7TRWog2Vxn8oxJt6p+tQ9obXAaBhyGkrtNJ4iLgQ4wVkn72mS7a9bjO4xlyyfue/7wG7HU3woA2Vxn949VU4edK1eTqiKnM6X8EhRwwADW3aUPkrNhw0cQ77JbkZKgCmTQPb2UdVqxP7Yd68StROYzXaUGn8g9RUeO45k+idLldyOjKaw3YjaWk9Wxo29PyFP9LQdppwsXPSUYVUFWne2bo13HCDWTZtGrgt9tYENtpQafyDQryp97oMAeAM4ZxyRBImDurY0q3SUFMBmoYYa+IKeFMY2e97R/Ymxz011p49kG/BtyZw0YZK4/sU4k2922UIpyOjXdt5w38N9PCf3yEoznEaqn2FGCqAAzXq81n7S8zCxx+HrCxvq6fxAbSh0vg+s2bBiRNnt6tX590uV5qaHLbreSp/pb4tlUjJJdkRSXL+YT83XrnwWrJC3FJkHTgAb71VCRpqrEYbKo1vk5YGM2eaZXfeafKmAP5xVMOhoI4tnTB0RJg/YY72K7qO2D8xtfko4TKz8MknISPDi9ppfAFtqDS+TX5vKiYG7rqrQLMcQjjuqIpNoJ4ttRIV1FQEY9gvLxtF4cN+7rzefSQZYRFnBf/8w5OD7yBuyiJdyTmA0YZK47sU4U1Rs/AHmitMXa+n8hvq2tKIklxSHeGcVFVKbH8suiZzO11hkt2+5nOqn9EvJ4GMNlQa3+W11+D48bPbRXhTeZxdT6UfWv5CU5M3VfSwnztvdhtGavhZo1YzM5W7fvnYG+ppfARtqDS+SVoaPPusWTZpEsTGFnnIMUdVcpSNmrYzVEGvsfF9FE1txUf7FUZylRhe7z7SJLvh90W0OH7Ao9ppfAdtqDS+ydNPm72patXg7ruLPcSBjSMOI8iigR7+83lqSzrRtmzSVRjHVNUyHftO16Hsr17PtR2qHDyy5C1dBiRA0YZK43scOFBgbuql+MHFelN56PVU/kNpo/0KIys0nKcuutkk67v3d10GJEDRhkrjezz4IGRmujaPVq3Jm92Gl+rQs+upUtFlP3wZVWw2itLwfaserGnSziy85x7Izq6ochofQxsqjW+xdi189JFJNLP3DWSEV3GFIBcXhnxSVSFThRJtyyZGdNYCXyVWzhBjy+KMCuWoI7rkAwpDhMcHjMfh7o3t3GksadAEFNpQaXwHpYw3Yje21Ynji/gBZehEXElq9fCf79LUbdhPlXHYz50/6zXnkw4DzcLHHoNjxyqinsbH0IZK4zvMnw+//GISTe8/Dod7MtJSoNdT+TaColmIkWB4n71Ghft7rvcNnA6POitISYFHHqlwvxrfQRsqjW+QlQWTJ5tlV1zBr3EJZe7qbEBFKqLnqXyOpiGnqG7LItURzmFHtQr3d6JqDV7pca1ZOHs2bNpU4b41voE2VBrf4JVXYO/es9uhoQXXUZWSNBVBqiOcCLETKzoPnG+hSAg9BMCm3AYoDz2C5nS5gr01G5wVOBzGcgYdrh4QWGqoRGSQiOwQkd0iMqWQ/feIyJ8isklEfhaRplboqfEyx47B9Okm0XsdLiPuvd3l7lIP//kmTW3J1LRlkuYIZ7e9lsf6zQkJ48mLxpmFS5bAV1957Bwa67DMUIlICDALuAxoC4wSkbb5mm0Euiil2gNfAM9UrpYab5IXwff+pTfB6bMGJSWiKi/1HFWhvvV6Kl9EkRBmeFObc+vj8PDjZ/G5F8DFF5uF992na1YFAFZ6VBcAu5VSfymlsoFPAFORIaXUUqVU3tjNGqBxJeuo8TLnHt/PdYnfmWQv97iW5CoxFerXvTx9iC5P7xOcY0sm1naGdBXGTnttz59AhIHnDMUubo+1PXvgpZc8fy5NpWKloWoEuCfnOuiUFcUtwHeF7RCR8SKyXkTWH9NhqX7F1KXvEqrcDMm55/J+58sr3G8WYZxwVCFUFHVtaRXuT1NRFAlhhwHYnON5byqPnXXiCtaseuIJOHzYK+fTVA5WGqrCFk8UOvMpItcDXYBCZ9eVUrOVUl2UUl3q1KnjQRU13qT33t/p/9d6k+zf8VeT417FtQLkZanQw3/W09iWQi1bBhkqjJ127/5GX+h1HSkRbrkDU1NhwgQdWOHHWGmoDgJN3LYbA4fyNxKRi4GHgCFKKT3YHCjk5vLQkndMot+atOOHlhd67BQ6oMJXcJubyqmP3cuPnVNR1Xmh12iz8Ouv4f33vXpejfew0lCtA1qKSDMRCQeuBb52byAiHYE3MYzUUQt01HiLt96i9fF9rk0HwvT+40DKn6UgP0cc0diVUEsyCCfXY/1qykYj22nq2DI4o0LZ4Y25qUL4oNNg6N7dLJw0yUh4rPE7LDNUSqlcYCLwA7AN+EwptVVEHheRIc5mzwLRwOcikigiXxfRncaf2Lu3wOLeL9v1Z0v9cz16mlxCOOYsT19fF1O0iLPe1Jbc+tgpW5aR8mK3hcDcuVDFrWrw6dNwyy16CNAPsXQdlVLqW6VUK6VUC6XUk07ZI0qpr53/v1gpVU8pleD8G1J8jxqfx+GAsWONwohO0sMiebbPDV45Xd7wX4ghyAIAABUFSURBVOOQFK/0rymehrbT1LWlk6lC2Z5byfPHrVrBjBlm2U8/wZtvVq4emgqjM1NoKpeXX4YVK0yiJ/qP40g17wwJ7XfmkmsWcopQ7F45h6Yozmah2JJbj9xK8qZMTJwI/fqZZffdZ4Sta/wGbag0lcf27UatKTeWNevMvA6Xeu2Up1QU/9ijCRc7LUJOeO08moI0sKVSLySdTBXCtty6lX7+uCmLiJv6Hb1a3wDRbqVE0tPhppvArl9c/AVtqDSVQ24u3HijqSBiSkRVHrjsDo8GUBTGdrvxkGwTehRdTLHyyPOmtlrlTTk5WL0ePP+8WbhypV4I7EdoQ6WpHJ5+GtatM4keuWSC14b83Nlnr0GGCqOmLVMHVVQS9Wyp1A9JI0uFsC23ntXqwLhxMGiQWTZ1KmzbZo0+mjKhDZXG+yQmGsXs3PiuVQ++atuvUk7vwMYO50S+4VVpvI27N5VjoTflQgTefhtquNW/ysoyvPxcvXTB19GGSuNd8h4GOTku0fGo6jx06X+8PuTnzo7c2jiUcI4tmaq6RL1XaWhLoWFIqtObqvy5qcKIm7KIuFcSubPXLeYd69cXjAzU+BzaUGm8y2OPwebNJtHUSydyMqp6papxhnD22mtiEzgvROeD9BZRZNM33Kgrtjm3PtmEWqyRma/a9oNhw8zCxx4zvH6Nz6INlcZ7rFljzE25Mf/8i/ixlefSJJWFvKCK80KP64zqXsCGg4vC9xApufxtj2FLbn2rVSqICLz+OrjnBM3NhZEj4YSOCvVVtKHSeIeMDBgzxljgm0ejRjx28b8tU+mooyonHFFESi5xISct0yNQ6Rp2kLoh6aQ5wlme3QxVaN5pH6BuXXjjDbNs92646ipdu8pH0YZK4x0eeAB27jTL3nmH05HRhbevFMQ1Z6KDKjxLs5CTtA09il0JS7Obk4VnMuB7g7gpi4hbG8En7Qead6xcaUQH6hRLPoc2VBrPM3s2vPqqSfRhwmXELbU+uuoveyyZKoQ6tgxqi65T5Qmqyxl6hiUBsC6nCceVlS8jpefhgbdB375m4YcfwvTp1iikKRJtqDSe5X//g9tuM4n2V6/HUxfdbJFCZuzY2JVrrN1qE6qDKipKKHb6h+8hTBz8lRvLNi/XmvIkOSFhJHT4N3/VbGje8eij8PHH1iilKRRtqDSeY906uOYa87xUlSrcMWQyGeFVij6uktlur4tSxnBVJDklH6ApAkWPsH3UsGWS7Ijkl5ymFF4P1XdJrhLDzSMe5VRkNfOOm26CVausUUpTAG2oNJ5hzx4YPNgIonBiFxvjLruPPxqeZ6FiBUlTERxw1CBEFK1Cj1utjt/SOuQYLUJPkqNsLMluYWmapIqQFNuI8cMegvDws8LsbBg6VCev9RG0odJUnOPH4bLL4Jh5KO3RSyawuGU3i5Qqnm3OTBWtQ44iOv9fmakjaVwQZhQh/CUnjhTlOx5zeVjXpB28Y644zYkTxsvXqVPWKKVxoQ2VpmJkZMAVV8CuXSbxa91H8GHHf1mkVMkccsSQ7Iikqi2Hc2zJVqvjV0SQQ7/wvwgRxZ+5ddlrj7VaJY8Qt6UmL/YcZRbu2GEsEM7OtkYpDaANlaYi2O0werSxsNed0aN5ts+N1uhUasRVyE+HqpeeSHK4OGI30bZsjjqqsi6nsdUqeZQXe17Hgvw5KJctg/HjzXOvmkpFGypN+VAK7rwTFi40y/v3h3ffRYnvf7V222uTo2w0CEmlhpyxWh2fp6ZkcEXENura0kl3hLEsuwWOQHuEiPDAZXeytnFbs3zuXLj6ajijvydWEGDfMk2lMXMmzJpllsXHw5dfmielfZgcQthtrwVor6okzrGdYnDEdpcn9U1WG9KVf9znspIdGsa/r3qIpBoNzDvmzzdexI7pZQ2VjTZUmrKhFDz1FEyebJY3agTffgvVKzfZbEXJy1TRIuQEVUXPQxRE0T70MAMijLVSu3Nj+T7rPM4QmEYqj1NR1blp5DSOROebf1uzBi68sGDWFY1XERVg6UK6dOmi1q9fb7UagUleCe/PPzeJT4dHMfL6Z9hRJ84avSpI//DdNA1J5oi9Kt9ln4fS728AhOCgZ1gSLUJPohRsyG3E5tz6+NtaqYrQ8PRRfl3xHGzdat4RGwtffw09e1qjmBcQkQ1KqS5W61EY+hepKR379hk/ynxGirAw/j3sIb81UgC/ZDclXYVRLySdzs6Cf8FOFbK5LGK7a53Uz9nnsjm3AcFkpAAOxdSFX36BAQPMO06eNGSffWaNYkGGNlSaklm+HLp0gT/+MMtjY+H771ndtIM1enmILMJYlt0ch4L4sH9oHOTh6rUknSsit1HHlkGqI5xFWa054KhR8oGBSvXqxrD2mDFmeVaWkYnlmWd0Ilsvow2VpmiUMmr3XHyxsajXnfh4I2VS//7W6OZhjjqq8XtuIwB6h+8NyvmqMHLpFHqQf0Vsp6rk8I89mm+y2nBKRVmtmqXETVlE3CM/EVdvBM/3Gl2wwQMPwO23m6pYazyLNlSawsnOhgkTjB9gbr6s51ddBb/+Cs2bW6Obl9icW5+D9hgixU7fsD1IkBRXFBy0+f/27j46qvJO4Pj3N5OQQBIIksREgQAWAd2uFRGFWOu2tVa0pe3Wl25Ppad6PJ7iOXV3/6jb0je3rS/07LHW3Vp37R71cFwrXS3byhF2bdfTFtCsBwjyIqBJGkwAA3krL8nM/PaP5waGySSZwMy9dya/zzn33Jm5T+785pmZ/OY+97nPEz3E50t3cFlxB0Wi7I5V80r/xaGersN3IjzW8AX+7qa/ZSCSMlzUE0/Ahz7krrkyWWedKcwQV618msd/9QhXHtg5dOP3vgerVjHrG+v9D8wHJQywvHQnZTJA00AtjbHCuqD1TMrMSBeLituYEnETBnbEy3ljYHreTNURlCUt2/jZiz9k8sk/D934xS/C6tVQVzd0W4iFuTOFJSpzWnc3rF7N8Yd/xMRYykyn5eXcff3XAptG3k81kV5unLCHiMDGkx+grQDPz1RJH1cWt1EbdXNydSdKaByYTmuikvHWYeJszT3cwr+v/S7Te9JcVzV5MjzwAKxcCUVF/gd3FsKcqKzpz7iTwo8+ChddBD/4wdAkNWcObNo0LpIUFPb5qilynOuK9/Op0t3URvs4oUVs6p/JiycvpTUxFUtSmdtbXc+nVjzKLz748aEbe3rgvvtg4UKbLiQL7IhqPEsk3ARx3/oWNDenLfL7+su4d/nX6Zo42d/YAqdcP2Ev06M9eX99VYQE9dGjzI8ePnUEFVPhrdj5NMXqGMjT6TnC5Iq2nfzjxp9yyaF30xdYsQK+/32YHt6m5DAfUVmiGo9UYcMG11sptcu553BZJT9u+Bueu+wG4qknjseJfD9fVSEnmBd9n7lF71MqrkPMgEbYH5/G9lhdwQ6BFJRoIs7+GS2wapU7okoVibjpcO68E26+GYrD1VHFEpWPLFGNoLUV1q6F55+H119PW6RvwkR+tvhzPHXlZ0I1K29Qks9Xbeqfye54NWFuHhOUGZEu5hcd5sLo6X+WnYmJ7IlV8058mh1B5VDzQzdBR4cbYuzZZ4cvWFMDd9zhktb8+f4FOAJLVD6yRJWiudklpxdeGDY5AfRHilhz+Y08vuQ2OssKr/PAufiLonauLD4AwMF4OX8cqKcrRBMFCkptpJf66FHqo0eZ5B09xVR4N34ee2LVHNYywpxgC0XzQzedvvPaa64zxY4dI/9RQ4NLWLfcAuXB9ba0ROWjcZ+oVN0khi+95JJTBnWxbsG1/OjDX6J1an51p/WPMjt6lMXFrUySGAnv/M7WWF1g068LCeoivcyKHqU+2nWqaQ+gK1HKnlg1++LT6Cc/epwVqqJ4jFubNvLDjt8P28x+unCR63zR0HB6qa31J1AsUflqXCWq48fdYJlbt7ovwdatsH17+vbxNF6bdTmPfGQFO2o/kONAC8MEYiwsPsD86GFEoDcxgc0DM33rvl5EnDrvyGlmtIsSiZ/a1p0ooTk+lZb4VDp1Enb0FC7NDy6DN990092vWZPxd5Q5c04nrSVLXM/csrKcxGiJykcFk6hU3Ye5owPa2916cGlpcQlp9+4xzzraeOECXp53DevnLaV9cnWOgi9sVdLH0gktTIu4SfSa45Vs6Z/JsSxPfVFEnJpIH7WRXuoivVRFjhGR09/Xo4mJNMcraY6fR5eWYskpPzR/+6/c3FZPPeXG0Ryr6mqYNQtmz3br5KWmxo1NeBbXblmiGu7JRT4J/BiIAv+mqg+lbC8BngGuADqB21S1eaR9LrrkEm185pmhGzJ5naqny6VbDy6JxJlL8mPxuBvza3CJxc68PzAAx465KTP6+tw69faRIy45nTgxesyjSCA0Tl/A+nkNrL+4gY7JVee8T+POCy2IHmRh8XsUS4IBjbArVkOnTqIrMZEeLRnj7LdKCXGqIn+mNtJLbbSXKjkzMSUUOnUSrfGpNMen0qOl2X9hxlezjhzg1qaNLNv9B2Z1tWdvx+XlUFk5dKmogJISKC1168GltBRZudIS1ZAnFokCbwPXA23AG8AXVHVnUpmvAn+pqveIyO3AZ1X1tpH2u0hEC+B46pz0lJTRVHsRG+YuYf3FSzlUMS3okApWmfRzVXEr9dEzR1xPKPRqCd06ka5EKd1aSq+WUEKMMulnkgwMWRdJYsg+OrWMjng5HYkKDibKGbBzTgWruu8IVxzYxaK2ndwVaXdNhanjbOaQgCWqIU8ssgT4rqre4N3/BwBVfTCpzCtemU0iUgR0ANU6QtDjLVG1VNayq2Y2O2vmnFofmFwNYs1AfqqL9HBBpIfKyAkq5TjlcpLIGN+Cfo3SpaV0xCvoSFRwKFFuXcnHsZKBk1zWsZdFbTu54sAu5r7fygU9hynS3AyWHOZEFeTPswuBPyXdbwOuGq6MqsZEpBuYBpwx54SI3A3c7d09KTBKf9BQqCLldZyVrg63vL3p3CNKLztx5l6gcbZkVszqMrsKPs63gRdGLZU18/x7qrEJMlGl+72ZeqSUSRlU9UngSQARaQzrr4JkFmd25UOc+RAjWJzZlk9xBh3DcIIcvKwNmJF0fzqQOg/4qTJe098U4Igv0RljjAmFIBPVG8BcEZktIhOA24F1KWXWAYPzP38eeHWk81PGGGMKT2BNf945p3uBV3Dd03+uqm+JyANAo6quA54CnhWRfbgjqdsz2PWTOQs6uyzO7MqHOPMhRrA4s83iPEcFd8GvMcaYwpKfE+wYY4wZNyxRGWOMCbW8T1QislpEdovIdhF5UUTSjhAqIp8UkT0isk9E7g8gzltE5C0RSYjIsF1VRaRZRJpEZGsQ3UXHEGfQ9XmeiGwUkb3eeuow5eJeXW4VkdTOOrmKbcS6EZESEXne275FRGb5EVeaOEaL88sicjip/u4KIMafi8ghEUl7baQ4j3mvYbuILPQ7Ri+O0eK8TkS6k+ry237H6MUxQ0R+KyK7vO/519KUCUWdnkFV83oBPgEUebcfBh5OUyYK7AfmABOAbcAlPse5AHdB3e+ARSOUawaqAqzPUeMMSX0+Atzv3b4/3fvubevzOa5R6wb4KvCEd/t24PkA3udM4vwy8LjfsaXEcC2wENgxzPZlwHrcNZdXA1tCGud1wK+DrEsvjjpgoXe7AndNcer7Hoo6TV7y/ohKVTeo6uCAWJtx12OlWgzsU9V3VLUf+A9guV8xAqjqLlXd4+dzno0M4wy8Pr3ne9q7/TTwGZ+ffziZ1E1y7GuBj4n4PuZVGN7DUanqa4x87eRy4Bl1NgOVIuL7xGoZxBkKqtquqm96t3uBXbgRgJKFok6T5X2iSvEV3C+BVOmGa0p9c8JCgQ0i8n/e0FBhFIb6PF9V28F9+YCaYcqVikijiGwWET+SWSZ1c8bQYMDg0GB+yvQ9/Guv+WetiMxIsz1oYfgsZmqJiGwTkfUicmnQwXhNzpcDW1I2ha5O82IoZhH5byDdVJffVNVfeWW+CcSANel2keaxrPfLzyTODDSo6nsiUgNsFJHd3q+1rMlCnIHX5xh2M9OrzznAqyLSpKr7sxNhWlkbGizHMonhv4DnVPWkiNyDOwr8aM4jG5sw1GUm3gTqVbVPRJYBLwFzgwpGRMqBXwL3qWrqLI6hq9O8SFSq+vGRtovICuBm4GPqNbKmyGS4pnM2WpwZ7uM9b31IRF7ENdFkNVFlIc7A61NEDopInaq2e80Sh4bZx2B9viMiv8P9gsxlohrL0GBtAQ4NNmqcqtqZdPdfceeAw8aXz+K5Sk4GqvqyiPyLiFSpqu+D6opIMS5JrVHV/0xTJHR1mvdNf+ImX/w68GlVPTZMsUyGawqciJSJSMXgbVxHkTCOBB+G+kweXmsFMORIUESmipt8ExGpAhqAnanlsixfhgYbNc6U8xKfxp3PCJt1wB1eT7Wrge7BJuEwEZHawfOQIrIY97+3c+S/ykkcghvxZ5eq/tMwxcJXp0H35jjXBdiHa0/d6i2DvakuAF5OKrcM18NlP66Jy+84P4v7pXISOAi8khonrgfWNm95K6xxhqQ+pwH/A+z11ud5jy/CzRYNsBRo8uqzCbjTp9iG1A3wAO7HFEApbvaGfcDrwBy/6y/DOB/0PofbgN8C8wOI8TmgHRjwPpd3AvcA93jbBfhn7zU0MUKP2oDjvDepLjcDSwOK8xpcM972pP+Zy8JYp8mLDaFkjDEm1PK+6c8YY0xhs0RljDEm1CxRGWOMCTVLVMYYY0LNEpUxxphQs0RljDEm1CxRGWOMCTVLVMYYY0LNEpUxOSQiHxERFZEbkx6b7U2y91iQsRmTL2xkCmNyTEReBUpVdamITAH+CLwLLFfVeLDRGRN+lqiMyTER+TBuBPwbgL8HzgeuUdW+QAMzJk9YojLGByKyETdIbhdwlaq2BRySMXnDzlEZ4499wCTgO5akjBkbO6IyJsdE5G7gJ7j5nE6o6tUBh2RMXrFEZUwOicj1wG+Au3BzP20Clqnq+kADMyaPWKIyJkdE5FLgD8DjqrrKe2wjMEVVFwcanDF5xBKVMTkgIjXAFqARuFUHp04VuRb4X+BmVf1NgCEakzcsURljjAk16/VnjDEm1CxRGWOMCTVLVMYYY0LNEpUxxphQs0RljDEm1CxRGWOMCTVLVMYYY0LNEpUxxphQ+3+RwOtlEQt6+QAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%pylab inline\n", "import math, random, pylab\n", "\n", "# Define the anharmonic (quartic) potential\n", "def V_anharmonic(x, gamma, kappa):\n", " V = x**2 / 2 + gamma * x**3 + kappa * x**4\n", " return V\n", "\n", "def rho_free(x, y, beta): # free off-diagonal density matrix\n", " return math.exp(-(x - y) ** 2 / (2.0 * beta)) \n", "\n", "def read_file(filename):\n", " list_x = []\n", " list_y = []\n", " with open(filename) as f:\n", " for line in f:\n", " x, y = line.split()\n", " list_x.append(float(x))\n", " list_y.append(float(y))\n", " f.close()\n", " return list_x, list_y\n", "\n", "beta = 4.0\n", "g = 1.0 #-cubic and quartic coefficients\n", "\n", "T = 1 / beta\n", "N = 16 # number of imaginary times slices\n", "dtau = beta / N\n", "delta = 1.0 # maximum displacement on one slice\n", "n_steps = 1000000 # number of Monte Carlo steps\n", "x = [0.0] * N # initial path\n", "hist_data = []\n", "for step in range(n_steps):\n", " k = random.randint(0, N - 1) # random slice\n", " knext, kprev = (k + 1) % N, (k - 1) % N # next/previous slices\n", " x_new = x[k] + random.uniform(-delta, delta) # new position at slice k\n", " old_weight = (rho_free(x[knext], x[k], dtau) *\n", " rho_free(x[k], x[kprev], dtau) *\n", " math.exp(-dtau * V_anharmonic(x[k], -g, g)))\n", " new_weight = (rho_free(x[knext], x_new, dtau) *\n", " rho_free(x_new, x[kprev], dtau) *\n", " math.exp(-dtau * V_anharmonic(x_new ,-g, g)))\n", " if random.uniform(0.0, 1.0) < new_weight / old_weight:\n", " x[k] = x_new\n", " if step % 10 == 0:\n", " hist_data.append(x[0])\n", " \n", "# Figure output:\n", "list_x, list_y = read_file('data_anharm_matrixsquaring_beta' + str(beta) + '.dat')\n", "v = [V_anharmonic(a, -g, g) for a in list_x]\n", "pylab.plot(list_x, v, c='gray', linewidth=2.0, label='Anharmonic potential')\n", "pylab.plot(list_x, list_y, c='red', linewidth=4.0, label='path integral Monte Carlo')\n", "pylab.hist(hist_data, 100, normed = 'True', label='matrix squaring') #histogram of the sample\n", "pylab.ylim(0,1)\n", "pylab.xlim(-2,2)\n", "pylab.title('Position distribution at $T=%.2f$, $\\gamma_{cubic}=%.2f$, $\\gamma_{quartic}=%.2f$' % (T,-g,g), fontsize = 13)\n", "pylab.xlim(-2.0, 2.0) #restrict the range over which the histogram is shown\n", "pylab.xlabel('$x$', fontsize = 15)\n", "pylab.ylabel('$\\pi(x)$', fontsize = 15)\n", "pylab.legend()\n", "pylab.savefig('plot_T_%.2f_anharm_g_%.1f_prob_path_int.png' % (T,g))\n", "pylab.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 2 }