{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tests for QuTiP's SME solver against analytical solution for oscillator squeezing\n", "\n", "Denis V. Vasilyev\n", "\n", "1 August, 16 August 2013\n", "\n", "Minor edits by Robert Johansson \n", "\n", "5 August, 6 August 2013\n", "\n", "Edits by Eric Giguere to fit Pull request #815 on Stochastic code\n", "\n", "March 2018\n", "\n", "We solve the stochastic master equation for an oscillator coupled to a 1D field as discussed in [1]. There is a deterministic differential equation for the variances of the oscillator quadratures $\\langle\\delta X^2\\rangle$ and $\\langle\\delta P^2\\rangle$. This allows for a direct comparison between the numerical solution and the exact solution for a single quantum trajectory.\n", "\n", "In this section we solve SME with a single Wiener increment: \n", "## $\\mathrm{d}\\rho = D[s]\\rho\\mathrm{d}t + H[s]\\rho \\mathrm{d}W + \\gamma D[a]\\rho\\mathrm{d}t$\n", "\n", "The steady state solution for the variance $V_{\\mathrm{c}} = \\langle X^2\\rangle - \\langle X\\rangle^2$ reads\n", "\n", "$V_{\\mathrm{c}} = \\frac1{4\\alpha^{2}}\\left[\\alpha\\beta - \\gamma + \\sqrt{(\\gamma-\\alpha\\beta )^{2} + 4\\gamma \\alpha^2}\\right]$\n", "\n", "where $\\alpha$ and $\\beta$ are parametrizing the interaction between light and the oscillator such that the jump operator is given by $s = \\frac{\\alpha+\\beta}2 a + \\frac{\\alpha-\\beta}2 a^{\\dagger}$\n", "\n", "[1] D. V. Vasilyev, C. a. Muschik, and K. Hammerer, Physical Review A 87, 053820 (2013). arXiv:1303.5888\n", "\n", "# Implementation of Milstein method for homodyne detection\n", "\n", "It is easy to implement the Milstein method [2] for a single Wiener increment using the given QuTiP infrastructure. For a stochastic differential equation $\\mathrm{d}\\rho = a(\\rho)\\mathrm{d}t + b(\\rho) \\mathrm{d}W\\quad$ the Milstein scheme gives:\n", "\n", "$\\Delta \\rho = a(\\rho_n) \\Delta t + b(\\rho_n) \\Delta W_n + \\frac{1}{2} b(\\rho_n) b'(\\rho_n) \\left( (\\Delta W_n)^2 - \\Delta t \\right)$\n", "\n", "The derivative can be calculated explicitly which is done below for a homodyne detection stochastic term.\n", "\n", "[2] G. N. Milstein, Teor. Veroyatnost. i Primenen. 19, 583–588 (1974)." ] }, { "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 inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from qutip import *\n", "from numpy import log2, cos, sin\n", "from scipy.integrate import odeint\n", "from qutip.cy.spmatfuncs import cy_expect_psi, spmv" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "th = 0.1 # Interaction parameter\n", "alpha = cos(th)\n", "beta = sin(th)\n", "gamma = 1\n", "\n", "# Exact steady state solution for Vc\n", "Vc = (alpha*beta - gamma + sqrt((gamma-alpha*beta)**2 + 4*gamma*alpha**2))/(4*alpha**2)\n", "\n", "#********* Model ************\n", "NN = 200\n", "tlist = linspace(0,5,NN)\n", "Nsub = 10\n", "N = 10\n", "Id = qeye(N)\n", "a = destroy(N)\n", "s = 0.5*((alpha+beta)*a + (alpha-beta)*a.dag())\n", "x = (a + a.dag())/sqrt(2)\n", "H = Id\n", "c_op = [sqrt(gamma)*a]\n", "sc_op = [s]\n", "e_op = [x, x*x]\n", "rho0 = fock_dm(N,0) #initial vacuum state" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Solution of the differential equation for the variance Vc\n", "y0 = 0.5\n", "def func(y, t):\n", " return -(gamma - alpha*beta)*y - 2*alpha*alpha*y*y + 0.5*gamma\n", "y = odeint(func, y0, tlist)\n", "\n", "# Righthand side for the Milstein method for a homodyne detection scheme\n", "def rhs_milstein(L, rho_t, t, A_ops, dt, dW, d1, d2, args):\n", " drho_t = spmv(L.data,\n", " L.indices,\n", " L.indptr, rho_t) * dt\n", " \n", " A = A_ops[0]\n", " M = A[0] + A[3]\n", " e1 = cy_expect_rho_vec(M, rho_t)\n", " d1_vec = spmv(A[7].data, A[7].indices, A[7].indptr, rho_t)\n", " \n", " d2_vec = spmv(M.data, M.indices, M.indptr, rho_t)\n", " d2_vec2 = spmv(M.data, M.indices, M.indptr, d2_vec)\n", " e2 = cy_expect_rho_vec(M, d2_vec)\n", " return rho_t + drho_t + d1_vec*dt + (d2_vec - e1*rho_t)*dW[0,0] + \\\n", " 0.5 * (d2_vec2 - 2*e1*d2_vec + (-e2 + 2*e1*e1)*rho_t)*(dW[0,0]*dW[0,0] - dt)\n", " \n", "#The rhs option of smesolve, " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total run time: 0.11s\n" ] } ], "source": [ "# Solution for the expectation values\n", "sol = smesolve(H, rho0, tlist, c_op, sc_op, e_op,\n", " nsubsteps=Nsub, method='homodyne', solver='euler', store_measurement=True)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "#sol_mil = smesolve(H, rho0, tlist, c_op, sc_op, e_op,\n", "# nsubsteps=Nsub, method='homodyne', rhs=rhs_milstein, noise=sol.noise)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total run time: 0.11s\n" ] } ], "source": [ "#Built-in Milstein with single jump operator\n", "sol_mil_native = smesolve(H, rho0, tlist, c_op, sc_op, e_op,\n", " nsubsteps=Nsub, method='homodyne', solver='milstein', noise=sol.noise)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Variance $V_{\\mathrm{c}}$ as a function of time" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = subplots()\n", "\n", "ax.plot(tlist,sol.expect[1] - abs(sol.expect[0])**2, label='Euler-Maruyama')\n", "#ax.plot(tlist,sol_mil.expect[1] - abs(sol_mil.expect[0])**2, label='Milstein')\n", "ax.plot(tlist,sol_mil_native.expect[1] - abs(sol_mil_native.expect[0])**2, label='built-in Milstein')\n", "ax.plot(tlist,Vc*ones(NN), label='exact steady state solution')\n", "ax.plot(tlist,y, label=\"exact solution\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Deviation from exact solution" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = subplots()\n", "\n", "ax.plot(tlist, y.T[0] - (sol.expect[1] - abs(sol.expect[0])**2), label='Euler-Maruyama')\n", "#ax.plot(tlist, y.T[0] - (sol_mil.expect[1] - abs(sol_mil.expect[0])**2), label='Milstein')\n", "ax.plot(tlist, y.T[0] - (sol_mil_native.expect[1] - abs(sol_mil_native.expect[0])**2), label='built-in Milstein')\n", "ax.legend();" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_expectation_values([sol,sol_mil_native]);\n", "ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Norm of the density matrix\n", "\n", "Here we calculate $|\\rho|-1$ which should be zero ideally." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total run time: 0.41s\n" ] } ], "source": [ "#Solution for the density matrix\n", "sol2 = smesolve(H, rho0, tlist, c_op, sc_op, [], solver=\"euler\",\n", " nsubsteps=Nsub, method='homodyne', noise=sol.noise, options=Odeoptions(average_states=False))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total run time: 0.44s\n" ] } ], "source": [ "sol2_mil = smesolve(H, rho0, tlist, c_op, sc_op, [], solver=\"milstein\",\n", " nsubsteps=Nsub, method='homodyne', noise=sol.noise,\n", " options=Odeoptions(average_states=False))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = subplots()\n", "\n", "ax.plot(tlist,array([sol2.states[0][n].norm() - 1 for n in range(NN)]), label='Euler-Maruyama')\n", "ax.plot(tlist,array([sol2_mil.states[0][n].norm() - 1 for n in range(NN)]), label='Milstein')\n", "ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Milstein method with multiple Wiener increments\n", "\n", "In this section we solve the following SME:\n", "## $\\mathrm{d}\\rho = D[s]\\rho\\mathrm{d}t + \\sqrt{1-\\epsilon}H[s]\\rho \\mathrm{d}W_1 + \\sqrt{\\epsilon}H[is]\\rho \\mathrm{d}W_2 + \\gamma D[a]\\rho\\mathrm{d}t$\n", "Analytical results can be found in [1].\n", "\n", "We follow [3] in implementation of the Milstein scheme.\n", "\n", "Stochastic equation is defined as\n", "\n", "$dX^i = a^i(X)dt + \\sum_{j=1}^M b^{i,j}(X)dW^j$\n", "\n", "It is convenient to define a differential operator as follows\n", "\n", "$L^j = \\sum_{k=1}^N b^{k,j}\\frac{\\partial}{\\partial x^k}$\n", "\n", "Then the numerical scheme is\n", "\n", "##$Y^i_{n+1} = Y^i_n + a^i\\Delta t + \\sum_{j=1}^M b^{i,j}(X)\\Delta W^j_n + \\sum_{j_1,j_2=1}^M L^{j_1}b^{i,j_2} I_n(j_1,j_2)$\n", "\n", "where $I_n(j_1,j_2) = \\int_{t_n}^{t_{n+1}}\\int_{t_n}^{s_1}dW_{s_2}^{j_1}dW_{s_1}^{j_2}$\n", "\n", "## Commutative noise\n", "\n", "An impotant case is the commutative noise which means $L^{j_1}b^{k,j_2} = L^{j_2}b^{k,j_1}$. For the homodyne detection it means that the jump operators for different stochastic terms commute. In this case we have\n", "\n", "$I_n(j_1,j_2) = I_n(j_2,j_1) = \\frac12\\Delta W^{j_1}_n \\Delta W^{j_2}_n$\n", "\n", "Evaluation of the derivatives $L^j$ for homodyne scheme provides us with the numerical scheme implemented below. We also have used the assumption of the commutative noise. The smesolve routine has to be modified. It should provide all the A_ops to the rhs function.\n", "\n", "[1] D. V. Vasilyev, C. a. Muschik, and K. Hammerer, Physical Review A 87, 053820 (2013). arXiv:1303.5888\n", "\n", "[3] S. Cyganowski, L. Gruene, and P. E. Kloeden, MAPLE for Stochastic Differential Equations." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "th = 0.1\n", "alpha = cos(th)\n", "beta = sin(th)\n", "gamma = 1\n", "eps = 0.3\n", "\n", "VcEps = ((1-2*eps)*alpha*beta - gamma + \\\n", " sqrt((gamma-alpha*beta)**2 + 4*gamma*alpha*((1-eps)*alpha + eps*beta)))/(4*(1-eps)*alpha**2)\n", "UcEps = (-(1-2*eps)*alpha*beta - gamma + \\\n", " sqrt((gamma-alpha*beta)**2 + 4*eps*beta*gamma*(beta-alpha)))/(4*eps*beta**2)\n", "\n", "NN = 200\n", "tlist = linspace(0,3,NN)\n", "Nsub = 20\n", "N = 10\n", "Id = qeye(N)\n", "a = destroy(N)\n", "s = 0.5*((alpha+beta)*a + (alpha-beta)*a.dag())\n", "x = (a + a.dag())/sqrt(2)\n", "H = Id\n", "c_op = [sqrt(gamma)*a]\n", "sc_op = [sqrt(1-eps)*s, sqrt(eps)*1j*s]\n", "e_op = [x, x*x]\n", "rho0 = fock_dm(N,0)\n", "y0 = 0.5" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def func(y, t):\n", " return -(gamma - (1-2*eps)*alpha*beta)*y - 2*(1-eps)*alpha*alpha*y*y + 0.5*(gamma + eps*beta*beta)\n", "y = odeint(func, y0, tlist)\n", "\n", "def funcZ(z, t):\n", " return -(gamma + (1-2*eps)*alpha*beta)*z - 2*eps*beta*beta*z*z + 0.5*(gamma + (1-eps)*alpha*alpha)\n", "z = odeint(funcZ, y0, tlist)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total run time: 3.90s\n" ] } ], "source": [ "#Built-in taylor for multiple stochastic increments\n", "sol_taylor = smesolve(H, rho0, tlist, c_op, sc_op, e_op,\n", " nsubsteps=Nsub, method='homodyne', solver='taylor1.5', \n", " options=Odeoptions(store_states=True, average_states=False))" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total run time: 0.61s\n" ] } ], "source": [ "sol = smesolve(H, rho0, tlist, c_op, sc_op, e_op, solver=\"euler\", noise=sol_taylor.noise,\n", " nsubsteps=Nsub, method='homodyne', store_measurement=True,\n", " options=Odeoptions(store_states=True, average_states=False))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total run time: 0.85s\n" ] } ], "source": [ "#Built-in Milstein for multiple stochastic increments\n", "sol_mil = smesolve(H, rho0, tlist, c_op, sc_op, e_op, solver=\"milstein\",\n", " nsubsteps=Nsub, method='homodyne', noise=sol_taylor.noise,\n", " options=Odeoptions(store_states=True, average_states=False))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Variance $V_{\\mathrm{c}}$ as a function of time" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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hRDNWa9LXWtuA6cDXwB5gqdY6WSk1VymVWEv31wFvpVQyFR8eC7XWuy436IvVp0MA2vc03mWtSN4pL2UWQrRcdRrT11qv0lp301p31lo/V7nuKa31ihraDqu8ykdrXai1vl1rHam17qW1frF+w6+7tj0jAfhh/VZXhSDEBWVnZxMbG0tsbCxt2rShffv2zuXy8vI678dms+Hv73/Rx58yZQohISHExsaet83q1avx8/NzxvXcc89d9HGEazXrMgxVdY++mh83rMZxzOLqUISoUVBQkPMp2Tlz5lQrlnYl2Ww2TCYT99xzDw8//DD33XffBdsPHz6cTz/99IrHJa6MZl2GoaqIEG+KPA/jnd+JvByZ0BVNy4033ki/fv2IjIxkwYIFALz11lvVPhT+/e9/88QTT1Tr53A4eOyxx4iKiiI6OtpZKnn16tUMGzaMMWPGOEs9DB06lMDAwAY6I+EqLeZKv52/JydNDtpoE2u/XcFNd/zW1SGJRuz5rc+z93T93nPQI7AHTyY8eUl933vvPQIDAykuLiYuLo6xY8cyfvx4+vTpw7x58zCZTCxcuJD33nuvWr+PP/6YPXv28PPPP5OZmUl8fDxDhgwBICkpiZSUFDp06HBRsWzYsIGYmBjat2/PSy+9RK9evS7pnIRrtJgrfaNBcdyvH+WGEvbvadCHgoW4bC+//DIxMTEMHDiQ9PR0Dh48iK+vL0OGDOHLL78kOTkZo9F4zqP5GzZsYMKECRiNRtq0acPVV1/trG8zcODAi0748fHxpKam8vPPP/Pggw9y66231ts5iobRYq70Adq1akVh5g94ZUZgtVoxm6U0g6jZpV6RXwmrV69m/fr1bN68GU9PT66++mpKSyuqnUybNo358+cTHh7O3XfffVH7tVgufn7Lz8/P+f2NN97Igw8+6Hxpi2gaWsyVPkCnYAvZ5lw8bL78uE6ezhVNQ15eHoGBgXh6epKcnMy2bduc2wYNGsTBgwf5+OOPGTdu3Dl9Bw8ezOLFi3E4HJw6dYqNGzcSF1drTa7zOnnypPP7zZs3YzKZJOE3MS0q6UcEW9hg64Rd2di5TV6YLpqGG264geLiYnr16sWf//xn+vfvX237bbfdxpAhQ6pdhVfd1qNHD3r37s21117L/PnzadWqVY3Huf322xk8eDApKSmEhoby7rvvAvD66687J48XL15MZGQksbGxPProoyxZsqR+T1ZccbWWVm5o9V1auarNh7IZ/9Zm7nccwVgewO/n34HB0KI+98QFNNXSyqNHj2b27NkMHTrU1aGIBnKlSys3G52CK8Yw3YJzsJS24pef1rk4IiEuXXZ2Nl27diUgIEASvqizFjWRG+LjTligJ0e8wukGbNrwEzFxw10dlhCXJCgoiP3797s6DNHEtKgrfaUU10e1ZeVxfwosR8g9GuTqkIQQokG1qKQPcH10W2wOjSnoBD5FHUg7KC93EEK0HC0u6fcO9aO9vycZ3hVX+Wu+Xe3iiIQQouG0uKSvlGJ0VBuWn2xHkccpTh72cnVIQgjRYFpc0ge4ukswVofCGJKGJa8Tx48ecHVIQgBgNBqdZYtjY2OZN29eve17586drFq1qs7tc3Nz+de//lVvx3/33XeZPn36Ze2jrudwsed6KcLDw8nKyrpgm3fffZfjx487l6dNm0ZKSsoVjas2LTLpx4UHYFBgbNsKAwa+/fLs97kL4Rqenp7s3LnT+TVr1qx627erk359aExJvy7OTvoLFixweYG6Fpn0fTzMRLbz48eybhS5Z3D8oIerQxLivPLy8ujevTv79u0DYMKECfznP/8B4MEHHyQuLo7IyEiefvppZ59t27Zx1VVXERMTQ0JCAnl5eTz11FMsWbKE2NjYc56kTU5OJiEhgdjYWHr37s3+/fuZNWsWBw8eJDY21lmy+cUXXyQ+Pp7evXtXO97NN9/sLP381ltvOdcvXLiQbt26kZCQwMaNGwEoKCggIqKi/hVAfn5+teUzPv74Y6KiooiJiWHIkCGUl5efcw5bt25l4MCB9OnTh6uuuop9+/bV2K6oqIh77rmHhIQE+vTpw2efnVuG5cSJEwwZMoTY2FiioqL44YeKt+wtWrSI6OhooqKiePLJc2sypaamEhUV5Vx+6aWXmDNnDsuWLSMpKYlJkyYRGxtLSUkJw4YNcxa8O99+vb29+dOf/kRMTAwDBgzg1KlTNf9iXCqtda1fwGhgH3AAmHWBdmMBDcRVWdcb2AQkA78AHhc6Vr9+/XRDmPt5su76p1X61b8/r1+9/1t97Mj+BjmuaLxSUlKc35947jmdOvnOev068dxztcZgMBh0TEyM82vx4sVaa62/+eYbPWDAAL1o0SI9atQoZ/vs7GyttdY2m00PHTpU//zzz7qsrExHRETorVu3aq21zsvL01arVS9cuFA//PDDNR53+vTp+oMPPtBaa11WVqaLi4v14cOHdWRkpLPN119/re+9917tcDi03W7XN9xwg163bl21OIqLi3VkZKTOysrSx48f12FhYTojI0OXlZXpq666ynn8qVOn6uXLl2uttX7zzTf1Y489dk5MUVFROj09XWutdU5OjtZan3MOZ85Na62//fZbfeutt9bYbvbs2fr999937qtr1666sLCw2vFeeukl/eyzzzp/nvn5+frYsWPOc7BarXr48OHOuDt27KgzMzPP+Tm9+OKL+umnn9Zaaz106FC9bds257YzyxfaL6BXrFihtdb6iSee0M8888w5P5uqv6tnAEm6Dvm81it9pZSRinfdXgf0AiYopc75+0Qp5QPMBLZUWWcCPgAe0FpHAsMA69l9XaF/RCDlNgehPcMwYGD1V67/U1CIs4d3zhRRGzFiBNHR0Tz88MPOOjgAS5cupW/fvvTp04fk5GRSUlLYt28fbdu2JT4+HgBfX19Mpgs/hzlw4ED+9re/8fzzz5OWloanp+c5bb755hu++eYb+vTpQ9++fdm7d6/z4bBXX33VeWV69OhR9u/fz5YtWxg2bBghISG4ublVKwg3bdo0Fi5cCFT8NVBThdBBgwYxdepU/vOf/2C322uMOy8vj9tvv52oqCgeffRRkpOTa2z3zTffMG/ePGJjYxk2bBilpaUcOXKkWpv4+HgWLlzInDlz+OWXX/Dx8WHbtm3OczCZTEyaNIn169df8GdZFxfar5ubG2PGjAGgX79+pKamXvbxqqrLE7kJwAGt9SEApdRi4Cbg7NmIZ4Dngaqv7hkJ7NJa/wygtc6+7IjrSUJEIEpBmkcfyt13kn/A3dUhiUakzR//6OoQqnE4HOzZswcvLy9ycnIIDQ3l8OHDvPTSS2zbto2AgACmTp3qLLl8sSZOnEj//v1ZuXIl119/PW+++SadOnWq1kZrzezZs7n//vurrV+7di2rV69m06ZNeHl5OZPqhQwaNIjU1FTWrl2L3W6vNjxyxhtvvMGWLVtYuXIl/fr1Y/v27ee0+ctf/sLw4cNZvnw5qampDBs2rMbjaa355JNP6N69+3ljGjJkCOvXr2flypVMnTqVxx57rMYidmczmUw4HA7n8qX+NzjDbDajlAIqJvZtNttl7e9sdRnTbw8crbKcXrnOSSnVFwjTWp89I9oN0Eqpr5VSPyml/lDTAZRS9ymlkpRSSZmZDfMqQ38vN2JC/VmzPwvPtkfwlrt4RCP28ssv07NnTz766CPuvvturFYr+fn5WCwW/Pz8OHXqFF9++SUA3bt358SJE84SzAUFBdhsNnx8fCgoKKhx/4cOHaJTp07MmDGDm266iV27dp3TftSoUbzzzjsUFhYCcOzYMTIyMsjLyyMgIAAvLy/27t3L5s2bAejfvz/r1q0jOzsbq9XKxx9/XO2Yd911FxMnTjzvewAOHjxI//79mTt3LiEhIRw9evScmPLy8mjfviIdnakKCtQY+2uvvXZmyJkdO3acc7y0tDRat27Nvffey7Rp0/jpp59ISEhg3bp1ZGVlYbfbWbRo0Tl1jlq3bk1GRgbZ2dmUlZXxxRdfnDeOM+qy3yvlsidylVIGYD7weA2bTcDVwKTKf29RSl1zdiOt9Vta6zitdVxISMjlhlRnIyNb83N6HpF9O2HAyLcyxCNcrKSkpNotm7NmzWLfvn0sWLCAf/zjHwwePJghQ4bw7LPPEhMTQ58+fejRowcTJ05k0KBBQMXwwJIlS/jd735HTEwMI0aMoLS0lOHDh5OSklLjRO7SpUuJiooiNjaW3bt3c9dddxEUFMSgQYOIioriiSeeYOTIkUycOJGBAwcSHR3NbbfdRkFBAaNHj8Zms9GzZ09mzZrFgAEDAGjbti1z5sxh4MCBDBo06JyqkJMmTSInJ4cJEybU+LN44oknnBOdZyalzz6HP/zhD8yePZs+ffpUuyI+u91f/vIXrFYrvXv3JjIykr/85S/nHG/t2rXOn+mSJUuYOXMmbdu2Zd68eQwfPpyYmBj69evHTTfdVK2f2WzmqaeeIiEhgREjRtCjRw/ntqlTp/LAAw84J3LPqMt+r5RaSysrpQYCc7TWoyqXZwNorf9euewHHAQKK7u0AU4DiUAX4Dqt9ZTKtn8BSrXWL57veFeytPLZDmQUcu38dfx1TA9OLduK3a2Q2S/c2yDHFo1PUy2t3FQtW7aMzz77jPfff9/VoTQ5V7q08jagq1IqQinlBowHVpzZqLXO01oHa63DtdbhwGYgUWudBHwNRCulvCondYdy7lyAy3Rp5U2nYAur92Xh3f4IPvkRHD7wi6vDEqLZ+93vfsesWbNqvOIWV1atSV9rbQOmU5HA9wBLtdbJSqm5SqnEWvrmUDH0sw3YCfxUw7i/S42IbM2mg9n0H9wXhYFvV33r6pCEaPZee+01Dhw4QLdu3VwdSotTp3r6WutVwKqz1j11nrbDzlr+gIrbNhulMdHteHPdIX41dKfA8h2kNtycghBCNLQW+URuVVHtfekUYuHTHcdoFZ6FT3F7dmz93tVhCSHEFdHik75Siptj27Pl8Gn6DR2GAzs/rDn3di4hhGgOWnzSB0iMaQfAj6cDKfI7QNmxDtjr+YEIIYRoDCTpA+HBFuI6BrBk2xE6di/DqzyI9d8td3VYogVqTKWVL8Tb27vWNq+88grFxcXO5euvv57c3Nx6Ob64dJL0K00e0JHU7GJCYn6D1VDG9i1Ha+8kRD1rTKWVL9fZSX/VqlX4+/s32PFFzSTpV7ouug2BFjeWJpdTHrQX46luFOTnuDosIVxWWhlg/vz5REVFERUVxSuvvHJObGvXrnUWBwOYPn067777Lq+++irHjx9n+PDhDB8+HKj+0pGa9puamkrPnj259957iYyMZOTIkdWeYhX1o063bLYE7iYjd8SF8db6gyT28yNttRerPl3EuLsecnVowgV+WPorWUcLa294EYLDvBl8x4XvSz9ThuGM2bNnM27cOP75z38ydepUZs6cSU5ODvfeW/Hk+HPPPUdgYCB2u51rrrmGXbt20aNHD8aNG8eSJUuIj48nPz8fLy8v5s6dS1JSEv/85z/POe4bb7zBzJkzmTRpEuXl5djtdrZv387ChQvZsmULWmv69+/P0KFD6dOnT63nOmPGDObPn8+aNWsIDg6utu18+w0ICGD//v0sWrSI//znP9xxxx188sknTJ48uS4/XlFHkvSrSIxpxxvrDlIUNpRit584lGx0dUiihTkzvHO2ESNG8PHHH/Pwww/z888/O9cvXbqUt956C5vNxokTJ0hJSUEpdU5p5doMHDiQ5557jvT0dG699Va6du3Khg0buOWWW7BYLADceuut/PDDD3VK+hdyvv0mJiYSERHh/NC7EmWFhST9anq29aGNrwdr9+cSHXYYx8G+7N+7na49+rk6NNHAarsib2iuKK1cF/VdVtjd/X8lzo1GowzvXAEypl+FUorhPUL4YX8Ww0cOBODblWtdG5QQuKa08uDBg/n0008pLi6mqKiI5cuXM3jw4Gr9OnbsSEpKCmVlZeTm5vLdd985t53veHXZr7hy5Er/LMO7t2LR1qPkWHpS6PsJhiNh2G02jLW8eUiI+nD2mP7o0aO5++67WbBgAVu3bsXHx8dZWvmvf/2rs7RyWFhYjaWVS0pK8PT0ZPULfGzOAAAgAElEQVTq1QwfPtz59qgzcwVnLF26lPfffx+z2UybNm344x//SGBgIFOnTiUhIQGoeNvV2UM7YWFh3HHHHURFRREREVFt+3333cfo0aNp164da9asca7v27dvjfuVoZyGUWtp5YbWkKWVa1JUZqPP3G8Z2y+U2LzvyNrSm+43ZXLtdeNq7yyaNCmtLJqKK11auUWxuJu4LS6URVuP4NnjGsqNxfy06aSrwxJCiHohSb8GT9/Yi74d/PnDqnTsrfbgntmDUyfSXB2WEEJcNkn6NXA3GXltYl9sdo1u549Jm1nxiZRlaAka23CnEGe73N9RSfrn0d7fk8SYdiw8Gkq+9yFyDrTBbpcibM2Zh4cH2dnZkvhFo6W1Jjs7Gw8Pj0veR51uSVFKjQb+DzACC7TWNVaBUkqNBZYB8ZWvSzyzvgMVr0mco7V+6ZKjbWDTBnfivzuO4d4uA/dfO/HdV8sYecN4V4clrpDQ0FDS09PJzMx0dShCnJeHhwehoaGX3L/WpK+UMgKvAyOAdGCbUmqF1jrlrHY+wExgSw27mQ98eclRukivdr5c3SWYL072YIyxiB2bMhl5g6ujEleK2WwmIiLC1WEIcUXVZXgnATigtT6ktS4HFgM31dDuGeB5oNojeUqpm4HDQPJlxuoS0wZHcKjQHVur3Xhl9+DI4b2uDkkIIS5ZXZJ+e6BqneH0ynVOSqm+QNjZLz1XSnkDTwJ/vcw4XWZotxC6tfbmoIcfBm1k5acNV5pWCCHq22VP5CqlDFQM3zxew+Y5wMta6wuWK1RK3aeUSlJKJTW28VSlFNMGd+LrnI7k+/5K4eGOlJVJPRAhRNNUl6R/DAirshxaue4MHyAKWKuUSgUGACuUUnFAf+CFyvWPAH9USk0/+wBa67e01nFa67iQkJBLOpEr6ZY+7YkItpDrk4FXeQCff/K+q0MSQohLUpekvw3oqpSKUEq5AeOBFWc2aq3ztNbBWutwrXU4sBlI1Fonaa0HV1n/CvA3rfW5xbwbObPRwB9Gdee/hdEUuWdyYIfU4RFCNE21Jn2ttQ2YDnwN7AGWaq2TlVJzlVKJVzrAxmJ0VBsiO7Qi3z8Fn4JwNq1fWXsnIYRoZOp0yaq1XgWsOmvdU+dpO+w86+dcZGyNilKKyQM6Mm9ZZyYZSvhh9QEGDnF1VEIIcXHkidyLcF1UG4rNrSgK2oVHZk+5fVMI0eRI0r8IFncT10W1ZZfBgkEbWPGJDPEIIZoWSfoXaWy/9mwt60y+/17KUrtSkJ/j6pCEEKLOJOlfpAERQbT396QoqAQPmzfLPvp/rg5JCCHqTJL+RTIYFGP7tmdRdg8KLKlk7mlLeVmZq8MSQog6kaR/CW7tG4oDAx4ds7CUBfPZsnddHZIQQtSJJP1LEB5sISE8kIXZvSj0OMXB7Z44HA5XhyWEELWSpH+JXro9hq5tAsnwTsGnOJRvVi52dUhCCFErSfqXqEOQF0vuH0iKTwIl5jx2brhgTTkhhGgUJOlfBqNBMSahJ9m+O/DJ68L67z91dUhCCHFBkvQv09i+oXzt6E6pqYAfvznp6nCEEOKCJOlfpjZ+HsR270aO/w58cruxce2K2jsJIYSLSNKvB78f2Z1vHF0pMxXyw9fHau8ghBAuIkm/HvRq58uE4fFk+W3HJ6e7lF0WQjRakvTrycPDu3AkJJYyYxFrv0xzdThCCFEjSfr1xM1k4MW7R5MTsB3fnB6slTt5hBCNkCT9etTWz5OBN9xccSfPlxlorV0dkhBCVFOnpK+UGq2U2qeUOqCUmnWBdmOVUrrypegopUYopbYrpX6p/Pc39RV4Y3XdgBgKQnbgV9CFVSs+dHU4QghRTa1JXyllBF4HrgN6AROUUr1qaOcDzAS2VFmdBdyotY4GpgDv10fQjZlSitG330mx22l2rbPhsNtdHZIQQjjV5Uo/ATigtT6ktS4HFgM31dDuGeB5oPTMCq31Dq318crFZMBTKeV+mTE3egN6daakdTK+xR1YuvhtV4cjhBBOdUn67YGjVZbTK9c5KaX6AmFa6wvdqzgW+Elr3SKKz986+X4KPE6Sts1H6u0LIRqNy57IVUoZgPnA4xdoE0nFXwH3n2f7fUqpJKVUUmZm5uWG1ChEdWyDvX0q3qWtefftf7s6HCGEAOqW9I8BYVWWQyvXneEDRAFrlVKpwABgRZXJ3FBgOXCX1vpgTQfQWr+ltY7TWseFhIRc/Fk0UnfePZ1cywEKUiLIzjxeewchhLjC6pL0twFdlVIRSik3YDzgLDCjtc7TWgdrrcO11uHAZiBRa52klPIHVgKztNYbr0D8jVqHYF/MXe142Hx49z8fuTocIYSoPelrrW3AdOBrYA+wVGudrJSaq5RKrKX7dKAL8JRSamflV6vLjroJmXbnb8ny3475aG/2pWxzdThCiBZONbYHiOLi4nRSUpKrw6hXf3/vE7y2WCgJ/JVZz85wdThCiGZIKbVdax1XWzt5IrcBjL9hNBn+W/DJiuL7rz92dThCiBZMkn4DiAi2kB1xFcVup9n2VTllZcWuDkkI0UJJ0m8gd1/TlzTfXXiXtOX9BW+6OhwhRAslSb+B9O8UREnnGzjts4eClG4cObzX1SEJIVogSfoNaPYNkSS5WzE6zCxe+LWrwxFCtECS9BtQl1beDBt6PRkBm7BkRPPtyiWuDkkI0cJI0m9gM6/pyqnwgRS5Z7LjGyjMz3V1SEKIFkSSfgMzGBTPTxrGkcD9WMpCePvfUoVTCNFwJOm7QKDFjZtuv5dM/yQMh3uzbp28SF0I0TAk6bvIiF6t8YvvR7mpiI2fZbIzNcPVIQkhWgBJ+i706NhrCIo5hF9xBxa//SYHMgpdHZIQopmTpO9id90zk4LA3bTL6s8Tr/6Hhz7cTk5RuavDEkI0U5L0XcxgNDLlgVFYjcUkFAXxQ/IRZizegd3RuArhCSGaB0n6jUDbDt3pMjgD35JQJnvu5Yf9WTzzRQoOSfxCiHomSb+RuGncfRS32oXXsTge6HiEd39M5cEPt1NSbnd1aEKIZkSSfiNy98O3UuqWi2FvELOHh/BNyil++942SfxCiHpTp6SvlBqtlNqnlDqglJp1gXZjlVL6zPtxK9fNruy3Tyk1qj6Cbq6CW3eg//V2PMsCydu4mZdui2bzoWymf/QTje1lN0KIpqnWpK+UMgKvA9cBvYAJSqleNbTzAWYCW6qs60XFO3UjgdHAvyr3J85jyOjxGDsnYcmIovznFcy6rgff7c1g3a+Zrg5NCNEM1OVKPwE4oLU+pLUuBxYDN9XQ7hngeaC0yrqbgMVa6zKt9WHgQOX+xAXcO2Mm+T4HOZXUiQTPNDoEejHvy71yR48Q4rLVJem3B45WWU6vXOeklOoLhGmtz64nUGtfcS6zuyfjpvXFYbDx9UcneGRwCHtPFvDOhsOuDk0I0cRd9kSuUsoAzAcev4x93KeUSlJKJWVmyjAGQKfu/eh1bTZeJa05uGoNo3q2Yt5Xe/nxQJarQxNCNGF1SfrHgLAqy6GV687wAaKAtUqpVGAAsKJyMre2vgBord/SWsdpreNCQkIu7gyasdE3342xaxJemZH0L9pMRLCFaf8viUVbj8jErhDiktQl6W8DuiqlIpRSblRMzK44s1Frnae1DtZah2utw4HNQKLWOqmy3XillLtSKgLoCmyt97Noxu6f8Rh5AckU/dKD3/c4TZ8O/sz+7y+8vuaAq0MTQjRBtSZ9rbUNmA58DewBlmqtk5VSc5VSibX0TQaWAinAV8DDWmu56fwiGM1uTHt4BMVu2ez+Ep4Z7sWY3m15ZfV+fknPc3V4QogmRjW2YYK4uDidlJTk6jAanZ82fsH6D40Uex1nyhNjuPXtX/DzNLNyxmDMRnnGToiWTim1XWsdV1s7yRZNRN9BY+g06Ah+hRF88M/F/PXGnvx6qpAPN6e5OjQhRBMiSb8JSZx0P+Zu2/HOjObgV0u4qnMQr3y3n7xiq6tDE0I0EZL0m5hpMx+juPUOOBjLtewgr8TKv9bJpK4Qom4k6TcxBqOR3/3ht+T5/krhT52Z3Pow729K47S8eEUIUQeS9JsgD4s/v50xnBL3LAL2h9PZkcLbGw65OiwhRBMgSb+Jah3anbG/7YQ22BiS35E1P66XsX0hRK0k6TdhXaIHcM1ET0x2d4bm+rFg1RpXhySEaOQk6TdxsQNHEXdTEe5WX6wbMkg9IkXZhBDnJ0m/GRg8chytBx3Gq6wVi/5vLTlZx10dkhCikZKk30xMmPQQpyO24V0Uyr+f/4KcbEn8QohzSdJvRn477VF+Dd6MT0En3pi3ipzMo7V3EkK0KJL0m5GwQC86DR3HnqBNeBd05I1537L1lz1ShlkI4SRJv5mZeU1XrrvjtxwJ3YalOJTv3tnKhPmf8N2eU64OTQjRCEjSb2YMBsWNMe148c9/pPWQQ3iVtiEmvYRnP/gvH2054urwhBAuJkm/GRs34QF6XZ+FZ1kwowsD+GDFf+WKX4gWTpJ+Mzfixkkk3G7DbPfimrwIPvz4A3KkTo8QLZYk/RbgquE3Muq3AdiNZcScjOSVf70mk7tCtFB1SvpKqdFKqX1KqQNKqVk1bH9AKfWLUmqnUmqDUqpX5XqzUuq9ym17lFKz6/sERN1E9hnMhJk9KfI4SfDBGF54cZ6rQxJCuECtSV8pZQReB64DegETziT1Kj7SWkdrrWOBF4D5letvB9y11tFAP+B+pVR4PcUuLlJYp2ge/NMI8n334X2oP888/QIFxcWuDksI0YDqcqWfABzQWh/SWpcDi4GbqjbQWudXWbQAZ8YONGBRSpkAT6AcqNpWNLCAoPbMeGoq+SFbCTwVx/89/T5Hj6W6OiwhRAOpS9JvD1R9tDO9cl01SqmHlVIHqbjSn1G5ehlQBJwAjgAvaa1PX1bE4rL5eFuYPfdJdLdN+BSGs+j5bSRt+d7VYQkhGkC9TeRqrV/XWncGngT+XLk6AbAD7YAI4HGlVKez+yql7lNKJSmlkjIzM+srJHEhSjH9sT9B319R2sDG98p5+fVXXB2VEOIKq0vSPwaEVVkOrVx3PouBmyu/nwh8pbW2aq0zgI1A3NkdtNZvaa3jtNZxISEhdYtc1IsZ06YTPsaXIs903H7pzd+enk9BQY6rwxJCXCF1SfrbgK5KqQillBswHlhRtYFSqmuVxRuA/ZXfHwF+U9nGAgwA9l5u0KL+KKW4fdQIpj91G6eDN+J3KpZ/PbWKXT/94OrQhBBXQK1JX2ttA6YDXwN7gKVa62Sl1FylVGJls+lKqWSl1E7gMWBK5frXAW+lVDIVHx4Ltda76v0sxGXz9fNn6mOP82ubdZisFtYsKOK9t1/H4XC4OjQhRD1Sje0hnbi4OJ2UlOTqMFqsH/ZnMvfdpQwrN+Bf0J38oD3cef8oQjt0cXVoQogLUEpt11qfM3x+NnkiV1QzuGsIUxPHsMInjBNBa/A63YWlL6SwbNE7rg5NCFEP5Epf1EhrzbpfM3l38ft0ywvEr7gjuYHJTHn4BkLbn3MDlhDCxep6pS9JX1xQRn4p3+06yP7VS/E/NQirsZRWcceYdNf9GAzyh6IQjYUkfVGvym0O/vLq6/ile+FXHEGezyFunNiT6D6DXB2aEAIZ0xf1zM1kYM70h+gybgjZ7dbiUdyatW8V8+oLr5Cbl+3q8IQQdSRX+uKildsc/PHtpfgcTiM4N55icy7t4zMZN/G3GE0mV4cnRIskV/riinEzGXj+3nH0HjeJA+02YzPnkfNjV1588iPWfLvc1eEJIS5Akr64JEaD4pY+oUx/cAaLLEFkhq7FaPUi5RM//v6nf7E9aa2rQxRC1ECSvrgsnUO8efa2OD4oHsCHXiVktlqHZ05HNi2w8fxfXmPP7m2uDlEIUYWM6Yt6kVlQxmc7j7H18GmyjiQTVZxKYG4CRoeZvOBfsHYLZ9SgwQzsFATA7mP59Gjrg9ko1x1C1Ae5ZVO41IGMQv68YDHdCk8QlJOAQRvI8NvNyRA/Cnx7svnQaeLDA3h9Ul9a+Xi4OlwhmjxJ+sLlTuaVsnDjYYb4nyDp+63o470xOzzI9tmL6mTio2NhKIPi2p6tmXVdD9r5e7o6ZCGaLEn6otHJOJLCx4s/pfRIJB42H/IsRyltc5rlBZ3p0S6YJfcNxGBQrg5TiCZJkr5otAqzj7N88Qcc398e79K2lJoKOeWbgm/vOHp27cHgbsEy5CPERZKkLxo9R1kR3614h6SfHHjnRAKQ5buHVEsZU8dNYniPti6OUIimQ5K+aFKSt67kq693wKloPGw+FJtzKQw8wJARA7nm6sGuDk+IRk+SvmiSSnNPsvLTD9mX4oZPfg8MGMmzpJHlcwJztwHMuW0onm5GV4cpRKNTr0lfKTUa+D/ACCzQWs87a/sDwMOAHSgE7tNap1Ru6w28CfgCDiBea116vmNJ0hdnJP+0lhWr1qCyuuJT2g6HspPjsx+vduV0GXANHt7BXNuzNaYq9/ofyixk+Y5jpGUXE2hx486BHekc4u3CsxCiYdRb0ldKGYFfgRFAOhXvup1wJqlXtvHVWudXfp8IPKS1Hq2UMgE/AXdqrX9WSgUBuVpr+/mOJ0lfnM1hLWf7umWs/zEVe1YXLOXBFR8Alv2UBeQz8NrRHC3xYd2vGWw+dBqTQdHO35OT+aVY7Q7+OaEvN/SW+QHRvNU16delJGICcEBrfahyx4uBmwBn0j+T8CtZgDOfJCOBXVrrnyvbSQ1ecdEMZjfir51I/LXgsJbx1cpFpPxyAo/MLgQd7cHhhVnkWpKIsGTSL6oHUxKvo5WvB5kFZUx7bxtPfbabqzoHEWBxc/WpCOFydbnSvw0YrbWeVrl8J9Bfaz39rHYPA48BbsBvtNb7lVKPAP2AVkAIsFhr/UINx7gPuA+gQ4cO/dLS0i77xETz57BZ+XrVUvbuSqMsOxSfklAAit2zMYak0yUykDaRQ5n4bgqjo9rwyrjYakNBQjQn9Tm8U6ekX6X9RGCU1nqKUur3VIz1xwPFwHfAn7XW353veDK8Iy6J1hzctZb1G7dw8qg3XnldMDncsCsbBZYj5LqfxBrgz5P33EnbQD9XRytEvavP4Z1jQFiV5dDKdeezGPh35ffpwHqtdVZlUKuAvlQkfyHqj1J0jhlO55jhABTnnuLH7z9nz94sTFlt6Jg9AJVtYMmfN1Lim4Z/6xK6RYaTcNW1+Hj7ujh4IRpOXa70TVRM5F5DRbLfBkzUWidXadNVa72/8vsbgae11nFKqQAqEvzVQDnwFfCy1nrl+Y4nV/riSshIS2bl19+QergUz5IO+JRWTOw6lJ0iyzHMAafxb+PBtdf8ho7hPVwcrRAXr96u9LXWNqXUdOBrKm7ZfEdrnayUmgskaa1XANOVUtcCViAHmFLZN0cpNZ+KDwoNrLpQwhfiSmnVMZK774vk56O5PPDBdryKDnG15RjmEoUqboNnei9Kj7rxxbbjFLvtxu59Cr9WVjp2bk1sv6to166jq09BiHohD2eJFud0UTnPf7mX/RkFlFgdtPF1J64NeGXt5Mihk6hibzxK22Epa+XsU+yWg8P7JL7BJbQL9ad7r9507dFX3gksGg15IleIS3Qgo5Anl/1M9tFkbgkrwLPMRm62OxS0qfZBYDWUUeqZgdEnF/8gB+3DgujeK5rwTtHyYSAanCR9IS5DqdXOn5bv5pOf0okJ8+flO2IA+HTjDtqVHcSam012pp3SfF9MJa3xtP7vjiCboZwSjyzwzMXTt4zAEHfad2hH5+7RhLXvjMFgoNRq590fU1n/aybXRbXh+ui2BHm7A2C1OziQUUiPNj4oJaWmRd1I0heiHnyx6zh/Wr6bMpsdh4ZymwOA0ABPbunTHj9PM95uBjoaTpJ1dA9ZJ0+Tl+OgrNALVRKIZ1kwBv2/WkHlxmJK3LOwmvIoNxViN9nJdBg4pb3JdQ8jrG07DmQUkVlQxnO3RDGpv8wliLqRpC9EPTmZV8pTn+3G3WzkD6O6s+NoLku2HWHjgXMfMA/wMvPH63tya99QFPDT/jR2/LSJI4cPYS0qw93hiZvdH1O5Hx5lgZh09aeEy4zFlLrlYHPLw2ooIiTIgL+/B9l2hdXDnxsGx9OtYyfMRnMDnb1oKiTpC3GFFZRaAcguLCf5eD75pVaWbU9ne1oOfp5mvNyMnMirqC3YKcTChPgO3B4Xir9XRaJ32KycOLKHtIN7OXHiFKeziynMN1Be4gVlfpjL/XC3W845rl3ZKHXLw2rOx2EuRLmV4OOt8PE24evnhZ+/L0EhrQhqE0arVh3wdPe66HPLL7VSarUT4OUmL69vIiTpC+ECDofmq+STrNmbQW6JlRui2zK4a7BzvP5i7Eg7zcqtKRRnHSTKz4q9uJBDx/KxlyrMDk8Mdm/MVl/MNl/c7DUndgcOykxFWE1F2E2F4FaCya0Ms5sdDw/w9DRi8TJj8fbCx9cHLx9/vksr54NdJRTaLYQGeLP4vgG09vWgxGrH16Nx/YWRU1TO6j2nuDGmHR7mplty2+HQ/Jyei1KK2DD/S9qHJH0hmiG7Q/Pm+oMkH8tnZGRrBnQK4mBGIa98uYtTxw8TpHIJUCVYsOGBxl2bMDrcMGtPlM0Tk82Cye6N2e5Zba6hJuWGUqymYmzGEuzGUuyGUsxmOyazHaPZjsmkKcdGuXYQFmzBy9MNT4sHFi8LFosFb28ffHz88PMPxmIJxOhmgVompstsdvacKCCnuJw+Yf7Ov4pq8uPBLB5dspNT+WX0DvVjTmIkYQFeBFncmtS7lj/dcYxnV6aQVVjOb3q04p2p8Ze0H0n6QrQweSVWjp4uxs/TTF6JlfScYo7lltK3gz99OgRwMq+URVuPsHjbEU7lleGGlSCVR6ChiBBzGWZ7KT4GB50DPHHTirJSKC1VlJYYMWp3lN0dg8Mdo8Mdo90ds6Pu7zG2Kxt2Qzl2gxWHwYpWVrTBijbYUAYbGG1oZcOqrdi1Da3sYHDg5WHAYNSYTAa8PE0E+LjhZjZxrKCMnccK8fRwo0e7QDal5lNgN1CuzViVG16eXvj6+BDROgAfizenChQTr+pMv44BV/C/wMUpKrPxj29+5Z2Nh+nXMYC7BnZkaLeQC37QXYgkfSFEjax2B2v2ZnCqoAxvdyOHM4s4XVyOl5uJKVeF097fs1p7h0NjMCh2H8tj/FubaeXjzqioNljLbfRt68GvaUf5cvs+vFQprdwc+Lk5KCwqoYOfB228PSgotpGdZ8Vq0xi0AYM2YlImDA4zSptQDhM4KpYNDjNGXfGvyWFGUT/zCRoHdmXHYbDhUBUfKg5lRxsqP2CUHa0cUO1Lg3KgnP86UAYNSqOURhmq/gsGg8ZgoPJ7UIaKfw0GhVJgR1Nud2A2GSkss3OyoJQym4M2/l50ae2D0Wigbds2DBp+yyWdY4tM+if/9jfK9uyt54iEEGfYtcagFFUHTzSQnlOM2WiglY8HSkFadhEn80oxGw3YHBqTQdHWzwM3s5G84nIKy2yUWh2cyT9KKUIDPGnn7+nctwOwabBpRZkdckpsZBXbMBiM+Hqa8fRwQ2uwY8COAYdWODDgUAYcGLBjxIEBrYzYMWB1VLRTBhMYTWiM2DGCMqKVCa0MgEIrAxpj5bKhxmWUEU1FZtcYK/+tWI+69LkFd9sOpi14/JL61meVTSGEAMBYw5i8AsICqk8kdwyy4O/pxqmCisQfFuiFuXKcPbjyZTaair86rHYHJoMBd1P1q3oD4KbATWm8DBBgNhLuY0QpUGig7KJi18CJvBKOni6p+LBRYNYVHzitfd0psznwMBsJtrjh5W5yfvhkF5VzIKMQD7MBb3cTNocmr9iKj6eJHm18OfsnogGNwupwkFNs5VhuKXatCfL2wOJuxurQuJsUZpMRR+U1twOF1uAR3uaizulSNKuk3+aPf3R1CEKIRiwcaJ9dzLd7TlFUZuOWPu356+fJrN6TQccgL47nlmC1ayxuRvp3CsLTbGTlLyfoe60/C+9OwM+z4u6lDzan8cSnuxncNRiDUkxICCPEx523NxwmNswfheL/vttPYZmNiGAL/5zYh8h2jeM9Ds1qeEcIIS5FcbkNLzcTOUXlrPs1k+1pOazZl8HJvFIeHNaZ6b/pgrvpf8M2WmseX/ozPx7MxmhQHMstAcDH3URBmQ2A4d1DeHBYF+I6BjTI3UQtckxfCCHqi9YVE69Vk31NbHYHH2xO43SxlfuHdCItu5iichtxHf9/e3cXIlUdxnH8+3NdKzIyMsjytfBmezcwQwqhAivQIC+2oNogohex7oqIsi69MCglkRQsKg2L2EQJISG6aG1XNDUr1yIyBFcrTXrdero4/13HcWfnPzu7c+Y/83xg4Zw5/2GfZ/+7z545L8+5qKa9k/yYvnPOVUFS2YIPML5lHB3zZw2ut11W309i8/urnXOuiUQVfUkLJX0jqVfSs0Nsf0zSXkm7JX0mqa1o+3RJp8KD0p1zzuWkbNGX1AKsBu4E2oD7ios68I6ZXWNm1wMrgJVF21cC20YhXuecc1WI2dOfC/Sa2Xdm9jewEVhcOMDMThasnk92qSoAku4Bvgf245xzLlcxRf9y4MeC9cPhtTNIelLSIbI9/WXhtYnAM8BL1YfqnHOuWqN2ItfMVpvZlWRF/vnw8nLgFTM7Ndx7JT0qqVtSd19f32iF5JxzrkjMJZs/AdMK1qeG10rZCLwelm8ClkhaAUwC/pP0p5mtKnyDma0F1kJ2nX5k7M455yoUU/S/AGZLmkVW7NuB+wsHSJptZgfD6t3AQQAzu6VgzHLgVHHBd845Vztli76Z9UtaCnwMtADrzWy/pJeBbjPrBJZKuh34B/gFeGikAfX09ByT9MNI3w9MBo5V8f560Sh5gOdSjxolD/BcBsyIGVR3bRiqJak75lbketcoec7OFKEAAANcSURBVIDnUo8aJQ/wXCrld+Q651wT8aLvnHNNpBGL/tq8AxgljZIHeC71qFHyAM+lIg13TN8551xpjbin75xzroQki35E189zJG0K27skzax9lHEicumQ1Bc6mO6W9EgecZYjab2ko5L2ldguSa+GPL+UNKfWMcaKyGWBpBMFc/JCrWOMIWmapB2SvpK0X9JTQ4xJYl4ic0llXs6VtFPSnpDLWW1qxrSGmVlSX2T3ChwCrgAmAHuAtqIxTwBrwnI7sCnvuKvIpQNYlXesEbncCswB9pXYfhdZp1UB84CuvGOuIpcFwJa844zIYwowJyxfAHw7xO9XEvMSmUsq8yJgYlhuBbqAeUVjxqyGpbinX7brZ1jfEJY3A7epls8tixeTSxLM7FPg52GGLAbetMznwCRJU2oTXWUickmCmR0xs11h+TfgAGc3S0xiXiJzSUL4WQ/0I2sNX8UnV8eshqVY9GO6fg6OMbN+4ARwcU2iq0xUB1Pg3vDRe7OkaUNsT0Fsrqm4OXw83ybpqryDKSccHriBbK+yUHLzMkwukMi8SGqRtBs4Cmw3s5LzMto1LMWi32w+Amaa2bXAdk7/93f52QXMMLPrgNeAD3OOZ1ihxfn7wNN25rMvklMml2Tmxcz+teyhU1OBuZKurtX3TrHox3T9HBwjaTxwIXC8JtFVpmwuZnbczP4Kq28AN9YottFWabfWumVmJwc+npvZVqBV0uScwxqSpFayIvm2mX0wxJBk5qVcLinNywAz+xXYASws2jRmNSzFoj/Y9VPSBLKTHJ1FYzo53fRtCfCJhTMidaZsLkXHVxeRHctMUSfwYLhaZB5wwsyO5B3USEi6dOD4qqS5ZH9HdbdTEWJcBxwws+JHmA5IYl5ickloXi6RNCksnwfcAXxdNGzMalhMa+W6YnFdP9cBb0nqJTsh155fxKVF5rJM0iKgnyyXjtwCHoakd8munpgs6TDwItkJKsxsDbCV7EqRXuB34OF8Ii0vIpclwOOS+oE/gPY63amYDzwA7A3HjwGeA6ZDcvMSk0sq8zIF2KDs+ePjgPfMbEutapjfkeucc00kxcM7zjnnRsiLvnPONREv+s4510S86DvnXBPxou+cc03Ei75zzjURL/rOOddEvOg751wT+R/DG+4j2NkF+gAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = subplots()\n", "\n", "ax.plot(tlist,sol.expect[1]-sol.expect[0]*sol.expect[0].conj(), label='Euler-Maruyama')\n", "ax.plot(tlist,sol_mil.expect[1]-sol_mil.expect[0]*sol_mil.expect[0].conj(), label='Milstein expl.')\n", "ax.plot(tlist,sol_taylor.expect[1]-sol_taylor.expect[0]*sol_taylor.expect[0].conj(), label='Taylor1.5')\n", "ax.plot(tlist,VcEps*ones(NN), label='Exact steady state solution')\n", "ax.plot(tlist,y, label='Exact solution')\n", "\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Deviation from exact solution" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = subplots()\n", "\n", "ax.plot(tlist, y.T[0] - (sol.expect[1] - abs(sol.expect[0])**2), label='Euler-Maruyama')\n", "ax.plot(tlist, y.T[0] - (sol_mil.expect[1] - abs(sol_mil.expect[0])**2), label='Milstein expl.')\n", "ax.plot(tlist, y.T[0] - (sol_taylor.expect[1] - abs(sol_taylor.expect[0])**2), label='Taylor1.5')\n", "\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Norm of the density matrix\n", "\n", "Here we calculate $|\\rho|-1$ which should be zero ideally." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = subplots()\n", "\n", "ax.plot(tlist,array([sol.states[0][n].norm() - 1 for n in range(NN)]), label='Euler-Maruyama')\n", "ax.plot(tlist,array([sol_mil.states[0][n].norm() - 1 for n in range(NN)]), label='Milstein')\n", "ax.plot(tlist,array([sol_taylor.states[0][n].norm() - 1 for n in range(NN)]), label='Taylor1.5')\n", "\n", "ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Software versions" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
SoftwareVersion
QuTiP4.4.0.dev0+76c6ebda
Numpy1.16.0
SciPy1.2.0
matplotlib3.0.2
Cython0.29.3
Number of CPUs1
BLAS InfoOPENBLAS
IPython7.2.0
Python3.6.7 (default, Oct 22 2018, 11:32:17) \n", "[GCC 8.2.0]
OSposix [linux]
Wed Jan 30 12:25:30 2019 JST
" ], "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qutip.ipynbtools import version_table\n", "\n", "version_table()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 1 }