{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Example 1c: Spin-Bath model (Underdamped Case)\n", "### Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The HEOM method solves the dynamics and steady state of a system and its environment, the latter of which is encoded in a set of auxiliary density matrices.\n", "\n", "In this example we show the evolution of a single two-level system in contact with a single Bosonic environment. The properties of the system are encoded in Hamiltonian, and a coupling operator which describes how it is coupled to the environment.\n", "\n", "The Bosonic environment is implicitly assumed to obey a particular Hamiltonian (see paper), the parameters of which are encoded in the spectral density, and subsequently the free-bath correlation functions.\n", "\n", "In the example below we show how to model the underdamped Brownian motion Spectral Density.\n", "\n", "Note that in the following, we set $\\hbar = k_\\mathrm{B} = 1$.\n", "\n", "### Brownian motion (underdamped) spectral density\n", "The underdamped spectral density is:\n", "\n", "$$J_U = \\frac{\\alpha^2 \\Gamma \\omega}{(\\omega_c^2 - \\omega^2)^2 + \\Gamma^2 \\omega^2)}.$$\n", "\n", "Here $\\alpha$ scales the coupling strength, $\\Gamma$ is the cut-off frequency, and $\\omega_c$ defines a resonance frequency. With the HEOM we must use an exponential decomposition:\n", "\n", "The Matsubara decomposition of this spectral density is, in real and imaginary parts:\n", "\n", "\n", "\n", "\\begin{equation*}\n", " c_k^R = \\begin{cases}\n", " \\alpha^2 \\coth(\\beta( \\Omega + i\\Gamma/2)/2)/4\\Omega & k = 0\\\\\n", " \\alpha^2 \\coth(\\beta( \\Omega - i\\Gamma/2)/2)/4\\Omega & k = 0\\\\\n", " -2\\alpha^2\\Gamma/\\beta \\frac{\\epsilon_k }{((\\Omega + i\\Gamma/2)^2 + \\epsilon_k^2)(\\Omega - i\\Gamma/2)^2 + \\epsilon_k^2)} & k \\geq 1\\\\\n", " \\end{cases}\n", "\\end{equation*}\n", "\n", "\\begin{equation*}\n", " \\nu_k^R = \\begin{cases}\n", " -i\\Omega + \\Gamma/2, i\\Omega +\\Gamma/2, & k = 0\\\\\n", " {2 \\pi k} / {\\beta } & k \\geq 1\\\\\n", " \\end{cases}\n", "\\end{equation*}\n", "\n", "\n", "\n", "\n", "\\begin{equation*}\n", " c_k^I = \\begin{cases}\n", " i\\alpha^2 /4\\Omega & k = 0\\\\\n", " -i\\alpha^2 /4\\Omega & k = 0\\\\\n", " \\end{cases}\n", "\\end{equation*}\n", "\n", "\\begin{equation*}\n", " \\nu_k^I = \\begin{cases}\n", " i\\Omega + \\Gamma/2, -i\\Omega + \\Gamma/2, & k = 0\\\\\n", " \\end{cases}\n", "\\end{equation*}\n", "\n", "Note that in the above, and the following, we set $\\hbar = k_\\mathrm{B} = 1$." ] }, { "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": [ "import contextlib\n", "import time\n", "\n", "import numpy as np\n", "\n", "from qutip import *\n", "from qutip.nonmarkov.heom import HEOMSolver, HSolverDL, BosonicBath, UnderDampedBath" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def cot(x):\n", " \"\"\" Vectorized cotangent of x. \"\"\"\n", " return 1. / np.tan(x)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def coth(x):\n", " \"\"\" Vectorized hyperbolic cotangent of x. \"\"\"\n", " return 1. / np.tanh(x)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def underdamped_matsubara_params(lam, gamma, T, nk):\n", " \"\"\" Calculation of the real and imaginary expansions of the underdamped correlation functions.\n", " \"\"\"\n", " Om = np.sqrt(w0**2 - (gamma / 2)**2)\n", " Gamma = gamma / 2.\n", " beta = 1. / T\n", "\n", " ckAR = [\n", " (lam**2 / (4*Om)) * coth(beta * (Om + 1.0j * Gamma) / 2),\n", " (lam**2 / (4*Om)) * coth(beta * (Om - 1.0j * Gamma) / 2),\n", " ]\n", " ckAR.extend(\n", " (-2 * lam**2 * gamma / beta) * (2 * np.pi * k / beta) / \n", " (((Om + 1.0j * Gamma)**2 + (2 * np.pi * k / beta)**2) *\n", " ((Om - 1.0j * Gamma)**2 + (2 * np.pi * k / beta)**2)) + 0.j\n", " for k in range(1, nk + 1)\n", " )\n", " vkAR = [\n", " -1.0j * Om + Gamma,\n", " 1.0j * Om + Gamma,\n", " ]\n", " vkAR.extend(\n", " 2 * np.pi * k * T + 0.j\n", " for k in range(1, nk + 1)\n", " )\n", "\n", " factor = 1. / 4\n", "\n", " ckAI = [\n", " -factor * lam**2 * 1.0j / Om,\n", " factor * lam**2 * 1.0j / Om,\n", " ]\n", " vkAI = [\n", " -(-1.0j * Om - Gamma),\n", " -(1.0j * Om - Gamma),\n", " ]\n", " \n", " return ckAR, vkAR, ckAI, vkAI" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def plot_result_expectations(plots, axes=None):\n", " \"\"\" Plot the expectation values of operators as functions of time.\n", " \n", " Each plot in plots consists of (solver_result, measurement_operation, color, label).\n", " \"\"\"\n", " if axes is None:\n", " fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8))\n", " fig_created = True\n", " else:\n", " fig = None\n", " fig_created = False\n", "\n", " # add kw arguments to each plot if missing\n", " plots = [p if len(p) == 5 else p + ({},) for p in plots]\n", " for result, m_op, color, label, kw in plots:\n", " exp = np.real(expect(result.states, m_op))\n", " kw.setdefault(\"linewidth\", 2)\n", " axes.plot(result.times, exp, color, label=label, **kw)\n", "\n", " if fig_created:\n", " axes.legend(loc=0, fontsize=12)\n", " axes.set_xlabel(\"t\", fontsize=28)\n", "\n", " return fig" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "@contextlib.contextmanager\n", "def timer(label):\n", " \"\"\" Simple utility for timing functions:\n", " \n", " with timer(\"name\"):\n", " ... code to time ...\n", " \"\"\"\n", " start = time.time()\n", " yield\n", " end = time.time()\n", " print(f\"{label}: {end - start}\")" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Defining the system Hamiltonian\n", "eps = .5 # Energy of the 2-level system.\n", "Del = 1.0 # Tunnelling term\n", "Hsys = 0.5 * eps * sigmaz() + 0.5 * Del* sigmax()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# Initial state of the system.\n", "rho0 = basis(2,0) * basis(2,0).dag() " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# System-bath coupling (underdamed spectral density)\n", "Q = sigmaz() # coupling operator\n", "\n", "# Bath properties:\n", "gamma = .1 # cut off frequency\n", "lam = .5 # coupling strength\n", "w0 = 1. # resonance frequency\n", "T = 1.\n", "beta = 1./T\n", "\n", "# HEOM parameters\n", "NC = 10 # cut off parameter for the bath\n", "Nk = 2 # number of exponents to retain in the Matsubara expansion of the correlation function\n", "\n", "# Times to solve for\n", "tlist = np.linspace(0, 50, 1000)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "# Define some operators with which we will measure the system\n", "# 1,1 element of density matrix - corresonding to groundstate\n", "P11p = basis(2,0) * basis(2,0).dag()\n", "P22p = basis(2,1) * basis(2,1).dag()\n", "# 1,2 element of density matrix - corresonding to coherence\n", "P12p = basis(2,0) * basis(2,1).dag()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### First let us look at what the underdamped spectral density looks like:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_spectral_density():\n", " \"\"\" Plot the underdamped spectral density \"\"\"\n", " w = np.linspace(0, 5, 1000)\n", " J = lam**2 * gamma * w / ((w0**2 - w**2)**2 + (gamma**2) * (w**2))\n", " \n", " fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8))\n", " axes.plot(w, J, 'r', linewidth=2)\n", " axes.set_xlabel(r'$\\omega$', fontsize=28)\n", " axes.set_ylabel(r'J', fontsize=28)\n", "\n", "plot_spectral_density()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The correlation functions are now very oscillatory, because of the Lorentzian peak in the spectral density." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### So next, let us plot the correlation functions themselves:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def Mk(t, k, gamma, w0, beta):\n", " \"\"\" Calculate the Matsubara terms for a given t and k. \"\"\"\n", " Om = np.sqrt(w0**2 - (gamma / 2)**2)\n", " Gamma = gamma / 2.\n", " ek = 2 * pi * k / beta\n", " \n", " return (\n", " (-2 * lam**2 * gamma / beta) * ek * exp(-ek * abs(t))\n", " / (((Om + 1.0j * Gamma)**2 + ek**2) * ((Om - 1.0j * Gamma)**2 + ek**2))\n", " )\n", "\n", "\n", "def c(t, Nk, lam, gamma, w0, beta):\n", " \"\"\" Calculate the correlation function for a vector of times, t. \"\"\"\n", " Om = np.sqrt(w0**2 - (gamma / 2)**2)\n", " Gamma = gamma / 2.\n", " \n", " Cr = (\n", " coth(beta * (Om + 1.0j * Gamma) / 2) * np.exp(1.0j * Om * t)\n", " + coth(beta * (Om - 1.0j * Gamma) / 2) * np.exp(-1.0j * Om * t)\n", " )\n", "\n", " Ci = np.exp(-1.0j * Om *t) - np.exp(1.0j * Om * t)\n", " \n", " return (\n", " (lam**2 / (4 * Om)) * np.exp(-Gamma * np.abs(t)) * (Cr + Ci) +\n", " np.sum([Mk(t, k, gamma=gamma, w0=w0, beta=beta) for k in range(1, Nk + 1)], 0)\n", " )\n", "\n", "\n", "def plot_correlation_function():\n", " \"\"\" Plot the underdamped correlation function. \"\"\"\n", " Nk = 3\n", " t = np.linspace(0, 20, 1000)\n", " corr = c(t, Nk=3, lam=lam, gamma=gamma, w0=w0, beta=beta)\n", "\n", " fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8))\n", " axes.plot(t, np.real(corr), '-', color=\"black\", label=\"Re[C(t)]\")\n", " axes.plot(t, np.imag(corr), '-', color=\"red\", label=\"Im[C(t)]\")\n", " axes.set_xlabel(r't', fontsize=28)\n", " axes.set_ylabel(r'C', fontsize=28)\n", " axes.legend(loc=0, fontsize=12)\n", "\n", "\n", "plot_correlation_function()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is useful to look at what the Matsubara contributions do to this spectral density. We see that they modify the real part around $t=0$:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_matsubara_correlation_function_contributions():\n", " \"\"\" Plot the underdamped correlation function. \"\"\"\n", " t = np.linspace(0, 20, 1000)\n", "\n", " M_Nk3 = np.sum([Mk(t, k, gamma=gamma, w0=w0, beta=beta) for k in range(1, 2 + 1)], 0)\n", " M_Nk5 = np.sum([Mk(t, k, gamma=gamma, w0=w0, beta=beta) for k in range(1, 100 + 1)], 0)\n", " \n", " fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8))\n", " axes.plot(t, np.real(M_Nk3), '-', color=\"black\", label=\"Re[M(t)] Nk=2\")\n", " axes.plot(t, np.real(M_Nk5), '--', color=\"red\", label=\"Re[M(t)] Nk=100\")\n", " axes.set_xlabel(r't', fontsize=28)\n", " axes.set_ylabel(r'M', fontsize=28)\n", " axes.legend(loc=0, fontsize=12)\n", "\n", "\n", "plot_matsubara_correlation_function_contributions()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solving for the dynamics as a function of time:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we calculate the exponents using the Matsubara decompositions. Here we split them into real and imaginary parts.\n", "\n", "The HEOM code will optimize these, and reduce the number of exponents when real and imaginary parts have the same exponent. This is clearly the case for the first term in the vkAI and vkAR lists." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "ckAR, vkAR, ckAI, vkAI = underdamped_matsubara_params(lam=lam, gamma=gamma, T=T, nk=Nk)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Having created the lists which specify the bath correlation functions, we create a `BosonicBath` from them and pass the bath to the `HEOMSolver` class.\n", "\n", "The solver constructs the \"right hand side\" (RHS) determinining how the system and auxiliary density operators evolve in time. This can then be used to solve for dynamics or steady-state.\n", "\n", "Below we create the bath and solver and then solve for the dynamics by calling `.run(rho0, tlist)`." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RHS construction time: 0.2594919204711914\n", "ODE solver time: 4.743985891342163\n" ] } ], "source": [ "options = Options(nsteps=15000, store_states=True, rtol=1e-14, atol=1e-14)\n", "\n", "with timer(\"RHS construction time\"):\n", " bath = BosonicBath(Q, ckAR, vkAR, ckAI, vkAI)\n", " HEOMMats = HEOMSolver(Hsys, bath, NC, options=options)\n", " \n", "with timer(\"ODE solver time\"):\n", " resultMats = HEOMMats.run(rho0, tlist)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_result_expectations([\n", " (resultMats, P11p, 'b', \"P11 Mats\"),\n", " (resultMats, P12p, 'r', \"P12 Mats\"),\n", "]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In practice, one would not perform this laborious expansion for the underdamped correlation function, because\n", "QuTiP already has a class, `UnderDampedBath`, that can construct this bath for you. Nevertheless, knowing how\n", "to perform this expansion will allow you to construct your own baths for other spectral densities.\n", "\n", "Below we show how to use this built-in functionality:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RHS construction time: 0.31698179244995117\n", "ODE solver time: 4.749270677566528\n" ] } ], "source": [ "# Compare to built-in under-damped bath:\n", "\n", "with timer(\"RHS construction time\"):\n", " bath = UnderDampedBath(Q, lam=lam, gamma=gamma, w0=w0, T=T, Nk=Nk)\n", " HEOM_udbath = HEOMSolver(Hsys, bath, NC, options=options)\n", "\n", "with timer(\"ODE solver time\"):\n", " result_udbath = HEOM_udbath.run(rho0, tlist) #normal 115" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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TaNWrV0dCQgJmzy7pitMV43WBDQB/+YssDxxwbzmIyHM1aNAACQkJ2L59OwCgV69eGDhwICIiIq5Zt1OnTnjssccQGhqKKlWq4JlnnsGePXtwtoQJH5YsWYLu3buXqzwzZ87ETTfdhNGjRyMkJASNGzfGkiVLrK8fOnQI3bt3R1BQEHr37o3U1NRC71+3bh26du2K4OBgtG/fHitXrrS+FhcXh+effx7dunVDjRo1rrkyVUBAAOLi4rBw4UKsXbvWelnKDRs24MYbb0RwcDDq16+PkSNHIisry/o+pRRmzJiBZs2aISgoCBMmTMCBAwdw4403ombNmhg4cKB1/ZUrV6Jhw4aYMmUKwsLCEB0djblz51q3lZmZidGjRyMqKgp169bFsGHDcPXqVevr06ZNQ/369REREYFPP/20xOPo4+ODBx98EOfOncOpU6cAAAcOHEDPnj1Ru3ZthIWF4aGHHsKFCxcAAA8//DCOHj2KO++8E4GBgYWmHJ07dy6ioqIQFhaGV155pdB+4uLirMfJKF4Z2E2ayJKBTUQlSU5OxuLFi9GhQ4dyv3f16tWoV68eateuXezrf/75J1q0aFHu7a5fvx4tWrRAamoqxowZg8cee8xa233wwQcRExOD1NRUTJgwAbNmzbK+LyUlBX379sU///lPnDt3DtOnT8eAAQNge0XEzz//HB999BHS0tJKvAZ3VFQUYmNjsWbNGgByWdC33noLqampWLt2LX766SfMmDGj0HuWLl2KTZs2Yd26dZg6dSoSExMxd+5cJCcnY/v27fjyyy+t6548eRKpqalISUnBrFmzkJiYaD21MHbsWOzduxdbtmzB/v37kZKSgokTJ1r3MX36dKxYsQL79u0rtfk6NzcXs2fPRuPGja1XQtNaY9y4cTh+/Dh27dqF5ORkvPTSS9bjEhUVZW15GTNmjHVbv/76K/bs2YOffvoJEydOxC6b3sytWrXC1q1bSyxHRXhlYDduLMsjR9xbDiICoJRrbnbq378/goODcdNNN6F79+4YP358uT7OsWPHMGLECLz55pslrnPhwgUEBQWVa7uAXPd66NCh8PX1xaOPPooTJ07g1KlTOHr0KDZu3IhJkyahWrVquOWWW3DnnXda3zdnzhz06dMHffr0gY+PD3r37o3Y2FgsXrzYus7gwYPRpk0b+Pn5oUqVKiWWISIiAufOnQMAxMTEoEuXLvDz80N0dDQef/zxa84Njx07FjVr1kSbNm3Qtm1bxMfHo0mTJqhVqxYSEhKwefPmQutbPkP37t3Rt29fzJ8/H1prfPzxx3jrrbcQGhqKoKAgjB8/HvPmzQMg/QuGDBmCtm3bIiAgwBq2tqZPn47g4GAEBARg1KhRmDRpEnx9fQEATZs2Re/evVGtWjWEh4fj2Weftesc94svvgh/f3+0b98e7du3LxTQQUFBuHjxYpnbKA9D5hI3m8hIWaakuLccROR5FixYgF69elXovWfOnEF8fDyeeOIJPPBAyZdYCAkJQVpamvWxn598FWdnZ1vvWx7bhme9evWs92vUqAEAuHz5MlJTUxESEoKAgADr640aNUJycjIA4MiRI/jqq6+waNGiQtvu0aOH9XGk5YuxDCkpKejatSsA6Wz37LPPIikpCenp6cjJyUFMTEyh9W2v5+3v73/N45MnTxY6LkU/w/Hjx3HmzBmkp6cX2rbW2noO+vjx44VeK66FYPTo0Zg8eTK01tixYwfi4+MRGhqKhIQEnD59Gk899RTWrFmDtLQ05OXlISQkpMxjUfTfw9JBEQDS0tJQq1atMrdRHl5Zw27YUJacZ57IA2jtmpuTnT9/HvHx8bjrrrvw/PPPl7puu3btsHfvXuvj+vXro0qVKjh8+HCh9Q4dOlRi87St+vXr4/z587hy5Yr1uaNHj1rvR0ZG4uGHH8aFCxestytXrhTqQKfsaIVITk7Gpk2bcPPNNwMAhg8fjpYtW2Lfvn24dOkSpkyZ4lCHtOI+Q0REBMLCwuDv748dO3ZYy3/x4kVrQNavX9/646ToZy9KKYW2bduiW7du1nPM48aNg1IK27Ztw6VLlzBnzpxCn8OeY1PUrl270L59+3K/rzReGdgNGsiSgU1E9srNzUVGRgZycnKQl5eHjIwMZGdnAwAuXbqE2267Dd26dcNrr71W5rb69OlTqMnV19cXAwYMwPPPP4+zZ88iOzsbX375JXbu3ImEhIQyt9eoUSPExsbixRdfRFZWFn799ddCtelBgwZh0aJFWLZsmfVzrFy50u6rY6Wnp2PVqlXo168fOnXqhD59+gCQWmTNmjURGBiI3bt344MPPrBre6WxfIY1a9bg+++/x7333gsfHx8MHToUzzzzjHWoVEpKCpYtWwYAGDhwIGbOnImdO3ciPT0dL7/8cqn72L17N3799Ve0yZ9JKy0tDYGBgQgODkZKSgqmTZtWaP26dete0xGvLKtWrbLr3648vDKwLZ08T5wAShj3TkRUyOeffw5/f38MHz4ca9asgb+/P4YOHQoA+Pbbb7Fx40Z89tlnCAwMtN5Kqul17NgRtWrVwvr1663PzZgxA6GhoWjXrh3q1KmD9957Dz/88EOhJuTSfPHFF1i/fj1CQ0Px8ssv45FHHrG+FhkZie+++w5TpkxBeHg4IiMjMW3aNOvwrZKMHDkSQUFBqFu3LkaNGoUBAwZg6dKl8PGR6Jg+fTq++OILBAUFYejQobjvvvvsKmtJ6tWrh5CQEEREROChhx7Chx9+iJYtWwIAXn/9dTRt2hRdunRBzZo10atXL2uHtISEBIwaNQo9e/ZE06ZN0bNnz2u2PXXqVAQGBiIgIADx8fEYMmQIHn/8cQDyI+GPP/5ArVq10LdvX9xzzz2F3jtu3DhMnjwZwcHBmD59epmfIyMjA4sXL8ajjz7q0PEoSnnyeLrY2FidlJTklG3XqwecOgUkJxc0kROR8+3atQutWrVydzHcbvny5ZgxYwYWLFjg7qJ4hJUrV2LQoEGV4prY7777LpKTkwsNASuqpP8HSqlNWuvY4t7jlZ3OAAnpU6ek4xkDm4hcLT4+HvHx8e4uBjnBk08+6ZTtemWTOMCOZ0REZC4MbAY2EZHbxcXFVYrmcGdiYPPvg4iITMBrA9sytIuTpxC5nid3diVytor+/TOwGdhELuXr62sdv0zkjYrOaGcvrw1sy4xy+RdrISIXCQ4OxqlTp8ocA0xUGeXl5eHUqVMVmrbUa4d1WeYisJnGlohcICwsDMeOHbNOekHkbQICAhAWFlbu93ltYIeEAH5+wMWLQEYGUL26u0tE5B18fHwQFRXl7mIQmY7XNon7+AB16sj9/KlpiYiIPJbXBjZQ0CzO89hEROTpGNhgYBMRkedjYIMdz4iIyPN5dWBzaBcREZmFVwc2m8SJiMgsGNhgYBMRkedjYIOBTUREno+BDXY6IyIiz8fABmvYRETk+bw6sENDZcazCxcAXjyIiIg8mVcHtq+vhDYAnD3r3rIQERGVxqsDGwDCw2WZmurechAREZXG6wPbcoWzM2fcWw4iIqLSMLDzA5s1bCIi8mQMbAY2ERGZgNcHNs9hExGRGXh9YPMcNhERmQEDm03iRERkAl4f2GwSJyIiM/D6wGaTOBERmQEDm03iRERkAl4f2LZN4lq7tyxEREQl8frArlEDqF4dyMgArlxxd2mIiIiK5/WBrRSbxYmIyPN5fWAD7ClORESej4EN9hQnIiLPx8AGm8SJiMjzMbDBJnEiIvJ8hgS2Uup2pdQepdR+pdRzxbxeSym1SCm1VSm1Qyk1xIj9GoVN4kRE5OkcDmyllC+A9wEkAGgN4AGlVOsiq40AsFNr3R5AHIA3lFJVHd23UdgkTkREns6IGnYnAPu11ge11lkA5gHoV2QdDSBIKaUABAI4ByDHgH0bwhLYZ8+6txxEREQlMSKwGwBItnl8LP85W+8BaAXgOIA/ATyttc4zYN+GqF1blqxhExGRpzIisFUxzxWd5PM2AFsARAC4HsB7SqmaxW5MqUSlVJJSKumMi04qs4ZNRESezojAPgYg0uZxQ0hN2tYQAN9osR/AIQAti9uY1vojrXWs1jo23NJ928lYwyYiIk9nRGBvBNBMKdU4vyPZ/QAWFlnnKIBbAUApVRdACwAHDdi3ISyBffYsLwBCRESeyc/RDWitc5RSIwEsA+AL4FOt9Q6l1LD81z8EMAnATKXUn5Am9LFaa4+pz1avDgQEyMU/0tKAmsU21hMREbmPw4ENAFrrxQAWF3nuQ5v7xwHEG7EvZ6ldWwI7NZWBTUREnoczneVjxzMiIvJkDOx87HhGRESejIGdjzVsIiLyZAzsfKxhExGRJ2Ng52MNm4iIPBkDOx9r2ERE5MkY2PlYwyYiIk/GwM7HGjYREXkyBnY+1rCJiMiTMbDzsYZNRESejIGdjxcAISIiT8bAzlejhlwEJDMTSE93d2mIiIgKY2DnU4rN4kRE5LkY2DbY8YyIiDwVA9sGa9hEROSpGNg2WMMmIiJPxcC2wRo2ERF5Kga2DdawiYjIUzGwbbCGTUREnoqBbYM1bCIi8lQMbBusYRMRkadiYNuwnZ6UiIjIkzCwbViaxFnDJiIiT8PAtsEaNhEReSoGto2gIKBKFbn4x9Wr7i4NERFRAQa2DdsLgLCWTUREnoSBXQSHdhERkSdiYBfBoV1EROSJGNhFsIZNRESeiIFdBGvYRETkiRjYRbCGTUREnoiBXQRr2ERE5IkY2EWwhk1ERJ6IgV0Ea9hEROSJGNhFcOIUIiLyRAzsIngBECIi8kQM7CJYwyYiIk/EwC6iVi3A1xdISwOystxdGiIiIsHALsLHBwgNlfusZRMRkadgYBeDQ7uIiMjTMLCLwaFdRETkaRjYxWANm4iIPA0DuxisYRMRkadhYBeDNWwiIvI0DOxisIZNRESehoFdDE6eQkREnoaBXQxOT0pERJ6GgV0M1rCJiMjTMLCLwRo2ERF5GgZ2MVjDJiIiT8PALkZICKAUcOECkJPj7tIQERExsIvl6yuhDQDnzrm3LERERAADu0ScPIWIiDwJA7sEnDyFiIg8CQO7BKxhExGRJzEksJVStyul9iil9iulnithnTil1Bal1A6l1Coj9utMrGETEZEn8XN0A0opXwDvA+gN4BiAjUqphVrrnTbrBAOYAeB2rfVRpVQdR/frbKxhExGRJzGiht0JwH6t9UGtdRaAeQD6FVnnQQDfaK2PAoDW+rQB+3Uq1rCJiMiTGBHYDQAk2zw+lv+creYAQpRSK5VSm5RSj5S0MaVUolIqSSmVdObMGQOKVzHePnnKiRPAoUOA1u4uCRERAcYEtirmuaJf834AYgD0BXAbgAlKqebFbUxr/ZHWOlZrHRseHm5A8SrGW6cnTU8HHnwQiIgAmjQBbr4ZOHLE3aUiIiIjAvsYgEibxw0BHC9mnaVa6yta61QAqwG0N2DfTuONNWytgYEDgS+/BKpUAQICgN9+A3r14gQyRETuZkRgbwTQTCnVWClVFcD9ABYWWec7ADcrpfyUUjUAdAawy4B9O4031rA/+QT44QcgNBTYsgU4ehTo0AHYvx8YNcrdpSMi8m4OB7bWOgfASADLICE8X2u9Qyk1TCk1LH+dXQCWAtgGYAOAT7TW2x3dtzN5Ww376lXghRfk/nvvAa1bS3D/979A9erA558DGza4t4xERN5MaQ/uVRQbG6uTkpLcsu/sbKBqVbkISHa2zC9emX3wAfDEE1Kj3rRJPrfFc88Br78O9OkjNXAiInIOpdQmrXVsca9xprMSVKkC1Kol53UvXHB3aZzv449l+Y9/FA5rABg9GvD3BxYvluZxIiJyPQZ2Kbxl8pTNm+UWEgLcffe1r4eFSWc0oCDYiYjItRjYpfCWyVNmzpTlQw/J+eriDBsmy88+A7KyXFIsIiKywcAuhTfUsLUGvv1W7g8aVPJ6nTsDbdsCZ84AP/7omrIREVEBBnYpvKGGvXUrkJwM1KsH3HBDyespVdAs/tVXrikbEREVYGCXwhuGdi1aJMs77wR8yvhruPdeWS5YwGZxIiJXY2CXwhsmT7EE9l13lb1uy5bSLH7hAvDzz04tFhERFcHALkVlr2GfPy9jrqtUAXr0sO89/fvLcvFipxWLiIiKwcAuhaWG7caLhjnV6tVAXp50KAsIsO89CQmyXLLEeeUiIqJrMbBLUa+eLE+dcm85nOWXX2Rpb+0akHAPCZEJVDiJChGR6zCwS1G3rixPnnRvOZylIoHt6wvEx8t91rKJiFyHgV0K2xq2B0+5XiHnzgHbtgHVqgE33li+995+uywZ2ERErsPALkVgIFCjhlzJKi3N3aUx1vr1soyNLXl2s5JYAnvlSiAz09BiERFRCRjYpVCqoJZd2ZrFLYHdpUv531uvHtCmjfyQ4SU3iYhcg4Fdhsoa2OvWybJz54q933Le23IenIiInIuBXYbK2FM8L8+xGjYAxMXJcuVKI0pERERlYWCXoTLWsPfuldnKIiKAhg0rto3u3WX5++9ARoZhRSMiohIwsMtQGQPbUrvu3FnO01dEWBjQrp10OrM0rxMRkfMwsMtQGcdiWwK2os3hFpbz2GwWJyJyPgZ2GSpjDfuPP2RZ2uU07WE5j82OZ0REzsfALkNl63SWlwds3y7327VzbFvdu0uT+rp1MsSLiIich4FdhspWwz54EEhPlw5nlquRVVRIiIR+VlbBeXEiInIOBnYZLOewT52S2qnZbdsmS0dr1xaW3uKrVhmzPSIiKh4DuwzVqklNMidH5t82uz//lOV11xmzPQY2EZFrMLDtUJmaxY2uYd9yiyzXruW84kREzsTAtkNlGtpldGCHhcm84hkZQFKSMdskIqJrMbDtEBEhy+PH3VsOR125Ahw4APj5AS1bGrddSy2bzeJERM7DwLaDZfrOY8fcWw5H7dgh1/Vu2RKoWtW47fI8NhGR8zGw7VBZAtvoDmcWlsD+7TcgO9vYbRMRkWBg26FBA1mmpLi3HI4y+vy1Rb16QPPm0uRumUWNiIiMxcC2A2vYZWOzOBGRczGw7VAZAltr59WwgYLAXr3a+G0TERED2y516wK+vsDp0+Yda3zyJHD2LBAcXPFrYJfG0lN8zRogN9f47RMReTsGth18fc0/tMtSu77uuopfA7s0kZFA48bApUvA1q3Gb5+IyNsxsO1k6Xhm1mZxZzaHW/A8NhGR8zCw7WT289jO7HBmwcAmInIeBradzB7Yrqxhr1lTOa5sRkTkSRjYdoqMlOXRo+4tR0VkZwO7dsn9tm2dt5/oaPlhc+6czKpGRETG8XN3AcwiOlqWhw65tRgVsncvkJUlncKCgpy3H6Wklj13rjSLO7P53Z0uXAC+/lp+lPj7A926AfHxMkc7EZGz8CvGTo0by9KMgW05f+3M5nAL28AeOdL5+3MlrYEZM4AJE4Dz5wu/1ro18P77QFycW4pGRF6AgW0nS2AfPixf3M4YGuUstkO6nM12AhWzHafS5OYCw4YBn3wij2+5BejTB0hLkx8oO3cCt94KvPUW8NRT7i0rEVVOPIdtp+BguaWnywQqZuKKDmcWzZrJ3OKnTwO7dzt/f66gNTBqlIS1vz8wbx6wciUwdiwwebJ8znHjpKPd008D06e7u8REVBkxsMvBrM3irhjSZaEU0KOH3F+xwvn7c4X//Ad47z25JOnixcB99xVuOahWDZgyBfj0U3n8j38AX37pnrISUeXFwC4HMwb2hQvSs716daBpU9fs8/bbZbl0qWv250x790qtGZAadmnnqIcMAd5+W+4/9hiwebOzS0dE3oSBXQ5mDOzt22XZurXrejHHx8ty5Urg6lXX7NMZcnOBhx+W0yAPPij3y/LUUxLcV68CAwbIVK1EREZgYJeDGQPbleevLerVAzp0kNAy89W7/vMfYMMGGVv+/vv2vUcp4IMP5PMfOiTnvomIjMDALocmTWR58KB7y1EerhzSZSshQZZmbRY/dw4YP17uv/GGdDi0V7VqwJw5chris8+Ab75xShGJyMswsMuheXNZ7tnj3nKUhyuHdNmynMdevFh6WZvNpElyOdK4OODee8v//tatgddfl/uJicCJE4YWj4i8EAO7HKKjpfaUkiLjbz2d1u6rYd94IxAaKp22du507b4dlZwsE6QAMq66omPJR46U8/lnzwJDh5rzhwsReQ4Gdjn4+hbUss0wxvjIEflhUaeO3FzJzw/o31/uf/21a/ftqFdekalc77sPuP76im/Hx0eGegUHAz/8IOfEiYgqioFdTi1bytIMge2ODme2BgyQpZkC++BBCVYfH+CllxzfXoMGBR3WnnnGXB0WicizMLDLqVUrWVqufuXJXDlhSnFuvRWoVUt+OOzb554ylNfLLwM5OTKEy/LjzFEPPCDnwS9fBh59VIaLERGVFwO7nFjDtl+1asCdd8r9+fPdU4by2L1benf7+QEvvGDcdpWSc+J168q1wi2TqxARlQcDu5wsNWwzBLa7OpzZeuABWc6a5fmdriZOlPnA//a3giF8RgkLK7hwyPjxvF44EZWfIYGtlLpdKbVHKbVfKfVcKevdoJTKVUr91Yj9ukPz5nJ+c+9ez57FKyNDyujjU/Ajwx3i44GICGkS/+0395WjLLt2yUU9qlQBnn/eOfu44w7g//6voEObGUYaEJHncDiwlVK+AN4HkACgNYAHlFKtS1jvdQDLHN2nO9WoIQGYm1vQ5OyJdu2SMjZvLleYchc/PzlvCxTUMD3RpEnSAvDYY0BUlPP28+abclplxw45T56X57x9eZLMTGD5cukj0L8/0LmzXNmtdWvghhukg+JzzwH/+x/HrBOVxIjZpTsB2K+1PggASql5APoBKDr69kkAXwO4wYB9utUNN8gX7saN8sXjidw1YUpxHnsMeO01uYLVq68C9eu7u0SF7dxZULu2zG7mLEFBwHffyd/Nd9/JZTlfe82x64YfPgz8/DOwaRNw7JjU4AMD5YdB585Ar14y65o7bNsmY9m/+ab0edWTkgo/btJEJq3p0UNuDRo4tZhEpmBEYDcAkGzz+BiAQjGmlGoA4G4APVEJAjs2Fpg589ovGU/i7g5ntv7yF+Duu+VL+9135VKUnsRSu/6//wMiI52/v+bNgf/+F+jTB5g6VX4oTJpUvtDOygK+/Rb48EO5yEppAgOB++8H/v5343q+l+XQIem4N3duQd+F66+X8O3USVoxateWHvlpabL+7t3A2rVyO3hQbpZLljZvXhDecXHSgY/I2yjtYE8gpdS9AG7TWv9f/uOHAXTSWj9ps85XAN7QWq9TSs0E8L3W+n8lbC8RQCIAREVFxRw5csSh8jnD+vVAly7SnOepnYd69QJ++klqcXfd5e7SyJdw164yzOvAAfmy9gQ7dwJt20rT/YEDrglsi/nz5Spgublyha/33y/79MXhw8BHH8lY8dOn5bmAAOkr0K2bXKCmenW5rOqff0oz9B9/FLx/4EBp5TC6U53F6dPA5MnyQyI7W36MDBsGjBgBtGhh3zZyc4GtW4FffpGWg9WrZUicrdat5cdos2bygzAsDAgJAWrWlH4bRW++vgX3/fxkMptq1Qz/+IbS2rGWFzInpdQmrXVssa8ZENg3AnhJa31b/uNxAKC1ftVmnUMALH96YQDSASRqrReUtu3Y2Fid5IHV2IwMadrMzZVmvsBAd5eoMK1lZrPUVPmCb9TI3SUS8fHAihVyfWlPGdo0cCDw1VfA8OEF05G60jffAIMGSQfGxo0l7AYMKBwmFy/KnOwzZ8rxs/yXbdtWyv3QQ/JDqCS7d0uz9KxZci65alW5DOjzz5fvoialSUuTi6S88YaEq1LyuV5+ueAqdxWVnS3N/ZYA/+03Yzp8BgZK0EdFSQ2+eXPpnxIbK1eccyatZSbCLVvkx8mhQzIlbnKyTGV79ap8z/j4SL+ZGjWA8HDpwBkRIacIoqLkFhkpy6AgY8qWmwucPy8XwDl7Vv5tc3Lk+Zwc+fsJDJRbUJC0dtSsyR8XRnF2YPsB2AvgVgApADYCeFBrXWzds6wati1PDWxA/lNv2iQ1mN693V2awo4fl//QwcHyn85T/iNt3SqXnfT1lWPn7uZ6S62/enXpxd6woXvKsW2bhK7l2uUBAXJsAgOlA9bOnQWd06pWlUlYhg2TGnV5/m2TkyWkP/9cHteuLbO5Pf641IQrIjMT+Pe/5YfGmTPyXN++ctrDWf++mZnSarB3r/y7HTokf+fnz0u45OVJIOblScjk5RW+n50tLRA5OSXvo0EDICZG/p937CjN+RERFfu/lJsrFwz64w+5bd4sQX3hQsU+f0mCgwtC3BLktWrJ33f16nJMMjLklp4uYXzmTOHb2bNSrvLGgr+/9E2x/UFhe2vYUJ43olUjK0v+nS9fLlha7l+9WvDvbLu0/TxKFfw72i4r+lxkJNC9u+Ofq6B8Tgzs/B30AfA2AF8An2qtX1FKDQMArfWHRdadiUoQ2GPGANOmAWPHSqchT7JkiZwf7d697PObrjZihNRkW7eWPgDu6sGuNXDTTcDvv0uITZ7snnJY5OTI+doZM+SHjS0/P+k89uCDci46NNSxfSUlAc8+K5O4ANJUPXWqTHJjbyBlZUmNf8oUqSkCcsGX118Hbr7ZsfK5gtbSOnbmjLRC7d0rofrnn/JjsrgOcrVrA+3bS0fORo0kiOrVkzCsWlXC4sIF+eFw6JCcYtm9W/4909Ov3V5YmPyAvf56qd1HRsotPFxq1NWrS+BcvSqBdPq0/Bg/flw6FyYnA0ePFtwyMow5NkpJ+IeGymcOCpIfdH5+8mM7Kwu4ckXKdPEicPKkPLZHWJgct9q15Yep5ebnJ8FquWVnSwBfunTtLSvLmM9plP79pT+JUZwe2M7iyYG9fDlw223yC3zjxrLXP3pUmiU3bJA/1sceA/r1c07ZXn1Vejs/9RTwr385Zx8VdeWK1Fj27pXP/9VXFa/dOeLrr4G//lVOHezfb1xzohFOnZJheVevyhdc69bypWYkrYEFC+SH5/798lzbtnK6YsAAOR9cnCNHgNmzgY8/lsAApHxTpkhfCU9pzXFEXp6EbVKS/N+2NFufO1fxbUZFSY29Y0cJ6Q4dpEZq1PHSWk6BHT1aEOTJyRKqV6/KzcenoLbt7y+BHB4u/wfCw+UWFiZh7etbvv2npUlrkOUHRUqK/KhISSm4nThRequGvXx95f9rUFBBs7xl6e8vr1v6LNj2XbAcJ0vk2S4deS4mRn4AG4WB7QTp6fIHn5Ulf5gRESWvu3ixTJRRtOPMU0/JuVyjv+Tuv196IX/6qXRm8jTbtwO33CI1kdtukyba8HDX7T8tDWjTpuAymsOHu27fniYrS47B1KkF45/9/KQnd7t28uMyL0++cDduLDyHfps2wIQJ8sOnvF/wZqO1/D/fulU6mlrC6PRpaaLPypKwqFWroGn6L38BmjaVWrkr/749VW6uHK+UFGmJuHxZfsBfuSKvWYLW11f+BmvWvPYWFCQ/OCrDD8OSlBbY0Fp77C0mJkZ7srvvlt9cb79d8jpLlmhdtaqsd/fdWi9frvX06QXPvf668eVq2VK2vWmT8ds2yrp1WteuLeWsVUvr8eO13rhR64wM5+97xAjZb2ys1tnZzt+fGWRmaj17ttY9e2rt62upS1x78/fX+oEHtF66VOvcXHeXmqjyAZCkS8hE1rAdMH++1Jw7dJDzXkV/9f34o0xHmZkJPPmkNE9b1lmwQMYm+/lJJ5S2bY0pU3q6/ApVSn7BumvCDHskJ8upgRUrCp7z9ZXzg0VvrVrJhDWO1uR+/lmuIubn5xkd3zzR+fPSHLxzp5wz1FpakNq0kea/qlXdXUKiyos1bCdJT9c6PFxqHitWFH7tl1+kNgJoPWyY1nl5177/8cfl9b59jSvT+vWyzbZtjdums61erfXQoVo3b661j0/JtbvQUK0feUTrX38t/niWJSVF6zp1ZFsvvGD85yAichRKqWHzal0O8PeXTjoAMGpUQS/NRYtkaMvVqzJ71vvvF3/OZeJEqQ3/8INxvbktPYzbtzdme65w880yGciePXI+a/duYOlSGS40frz0jm7aVDr9zJ4tvbs7dpRz3/b2GD1/HkhIkHNoPXsae/lMIiJXYGA7aNQoGZKxY4eMi733Xun9nJ4uzb3//ndBD8Wi6tQBRo+W+1OnGlOeLVtkef31xmzP1apXl2FGt90GJCYCr7wi01vu2ydBPm6c9GTdsgV45BGZsWvaNBleUpKjR2VKy23bZNvz5lX+TlJEVPkwsB0UECBXGGrQQCZF+N//JAwmTZKhLyWFtcWIERJSS5YYc41tyyn/Dh0c35anadFChg8lJ8vUnK1bS4/TMWNk/Oqzz8p5V0u3jNOngenTpbVh61appa9YwR67RGRO7HRmkHPnZPB8ero0vTZtav97H39cmoSfeEKazysqK0ua2LOyZNhEadNVVgZ5ecCyZRLKP/9c8Ly/v/wIOn++4Lk77pDm9JLGFxMReQKOw/Zwf/4pvZWDg2UsbEV7diclSU/qli0Lj5f1Bn/8Ib3wly+XmZcAmQbx1lulFSMhoXKP3SSiyqG0wDbi8prkoOuuk+EymzYBCxfKBSkqYsMGWXbqZFzZzKJjR7m4hdYynC09XZq+yzolQURkFvw68xCDB8ty5syKb8MyReoNpr/ieMUpVXAFIYY1EVUm/ErzEA88IHNqL1smc/FWhDfXsImIKjsGtoeoXVuulpSXB3zxRfnff+mSnLeuUsVcY7CJiMg+DGwP8vDDspwzp/zvTUqS87ft2xtzzVkiIvIsDGwP0qePXAFs61bpOV4eq1fL8qabjC8XERG5HwPbg1StWtBDvLy1bEtg33KLsWUiIiLPwMD2MIMGyXLuXLlGrD0yM4G1a+X+zTc7p1xEROReDGwP07Ur0LixTLm5apV970lKkguPtGkj82wTEVHlw8D2MEoV1LI//9y+9/zyiyzZHE5EVHkxsD2QJbC//lpm7CrLDz/I8rbbnFcmIiJyLwa2B2reXCY/SUuTqUpLc+YMsH69dFi79VbXlI+IiFyPge2h7B2TvWSJjL+OiwMCA51eLCIichMGtoe67z7Azw9YulSu61wSSw38jjtcUy4iInIPBraHCg8Hbr9dhnZ99lnx61y4AHz/vXRU69/flaUjIiJXY2B7sJEjZfmvf8lY66K++kqej4sDIiNdWjQiInIxBrYHi48H2rUDTpy4doiX1sA778h9y6U5iYio8mJgezClgLFj5f4LL0ivcYuFC4Ht24GICOD++91TPiIich0Gtoe7/34Z4nXihDSRaw2cPw+MGiWvjx0rQ7qIiKhy83N3Aah0Pj7AJ58AnTsDs2cDp04Bx44Bhw8D118PPPGEu0tIRESuwBq2CVx3HTB/PhAQACxbBuzYIfONL1woQ7+IiKjy49e9SdxxB7BzJ/Dtt4C/v0xfWqOGu0tFRESuwsA2kago4Omn3V0KIiJyBzaJExERmQADm4iIyAQY2ERERCbAwCYiIjIBBjYREZEJMLCJiIhMgIFNRERkAgxsIiIiE2BgExERmQADm4iIyAQY2ERERCbAwCYiIjIBBjYREZEJMLCJiIhMgIFNRERkAgxsIiIiE2BgExERmQADm4iIyAQY2ERERCbAwCYiIjIBBjYREZEJMLCJiIhMwJDAVkrdrpTao5Tar5R6rpjXH1JKbcu//a6Uam/EfomIiLyFw4GtlPIF8D6ABACtATyglGpdZLVDALprrdsBmATgI0f3S0RE5E2MqGF3ArBfa31Qa50FYB6AfrYraK1/11qfz3+4DkBDA/ZLRETkNYwI7AYAkm0eH8t/riSPAVhiwH6JiIi8hp8B21DFPKeLXVGpHpDAvqnEjSmVCCARAKKiogwoHhERkfkZUcM+BiDS5nFDAMeLrqSUagfgEwD9tNZnS9qY1vojrXWs1jo2PDzcgOIRERGZnxGBvRFAM6VUY6VUVQD3A1hou4JSKgrANwAe1lrvNWCfREREXsXhJnGtdY5SaiSAZQB8AXyqtd6hlBqW//qHAF4AUBvADKUUAORorWMd3TcREZG3UFoXe7rZI8TGxuqkpCR3F4OIiMgllFKbSqrQcqYzIiIiE2BgExERmQADm4iIyAQY2ERERCbAwCYiIjIBBjYREZEJMLCJiIhMgIFNRERkAgxsIiIiE2BgExERmQADm4iIyAQY2ERERCbAwCYiIjIBBjYREZEJMLCJiIhMgIFNRERkAgxsIiIiE2BgExERmQADm4iIyAQY2ERERCbAwCYiIjIBBjYREZEJMLCJiIhMgIFNRERkAgxsIiIiE2BgExERmQADm4iIyAQY2ERERCbAwCYiIjIBBjYREZEJMLCLyssDdu8G0tPdXRIiIiIrBratc+eAzp2BVq2A6Ghg3Tp3l4iIiAgAA7uwQYOApCS5f+YMcN99QFqae8tEREQEBnaBn34CliwBatYEDh4EYmKAo0eBN990d8mIiIgY2FbTp8tyzBigcWNg2jR5/OGHQFaW+8pFREQEBrZITgaWLQOqVgWGDZPn4uKANm2AkyeBxYvdWjwiIiIGNgDMnw9oDfTrB9SuLc8pJee0AeCbb9xXNiIiIjCwxfLlsrz77sLP33OPLBcuBLKzXVsmIiIiGwzsq1eB1avlfq9ehV9r3hxo0QK4eBHYuNH1ZSMiIsrHwP71VyAjA+jYEQgPv/b1Hj1kuXKlS4tFRERki4FtaQ6Pjy/+dUtg//KLa8pDRERUDAZ2WYHdvbssf/uNw7uIiMhtvDuwT5wAtm0DatQAunYtfp26dYHWreVc94YNri0fERFRPu8O7BUrZBkXB1SrVvJ6N90ky/XrnV4kIiKi4nh3YJfVHG5xww2yZE9xIiJyE+8N7Ly8ghp2WYHdqZMs2SRORERu4r2BvW0bcPo00LAh0LJl6eu2bg34+wOHDgGpqa4pHxERkQ3vDWzb5nClSl/Xz0/GaQMFl98kIiJyIQZ2Wc3hFjyPTUREbuSdgX3lCrBmjdSsb73VvvdYathbtzqvXERERCXwzsD++WeZBCU2FggLs+897drJcts255WLiIioBN4Z2N9/L8s777T/PS1byrns/fulhk5ERORC3hfYWgM//CD3+/a1/33VqgGtWsn7t293TtmIiIhK4H2BvWULkJICREQAHTqU771sFiciIjfxvsCeM0eW/fqVPZyrKAY2ERG5iSGBrZS6XSm1Rym1Xyn1XDGvK6XUO/mvb1NKdTRiv+WWlVUQ2IMHl//97dvLkj3FiYjIxRwObKWUL4D3ASQAaA3gAaVU6yKrJQBoln9LBPCBo/utkH//W2Y3u+66gnHV5WFbw9ba2LIRERGVwogadicA+7XWB7XWWQDmAehXZJ1+AGZrsQ5AsFKqvgH7ts/Zs8CHHwIvvCCPJ00qf3M4ANSrJ8PALl4EkpONLSMREVEpjAjsBgBs0+tY/nPlXcd5UlKA4cOBCxeAu+8G7rqrYttRCmjbVu7v3GlY8YiIiMpiRGAXV1Ut2l5szzqyolKJSqkkpVTSmTNnHC4cAAnZRx4BPvoI+O9/K1a7tmid39rPwCYiIhfyM2AbxwBE2jxuCOB4BdYBAGitPwLwEQDExsYac6LYxweYNcuQTaFVK1kysImIyIWMqGFvBNBMKdVYKVUVwP0AFhZZZyGAR/J7i3cBcFFrfcKAfbuepYa9a5d7y0FERF7F4Rq21jpHKTUSwDIAvgA+1VrvUEoNy3/9QwCLAfQBsB9AOoAhju7XbWybxLV2rHmdiIjITkY0iUNrvRgSyrbPfWhzXwMYYcS+3K5uXSAkBDh/Hjh5Eqjvus7uRETkvbxvpjNHKVVwHpvN4kRE5CIM7IpgT3EiInIxBnZFMLCJiMjFGNgVwSZxIiJyMQZ2RbCGTURELsbArojISCAwUC4kkprq7tIQEZEXYGBXBHuKExGRizGwK4qBTURELsTAriiexyYiIhdiYFcUA5uIiFyIgV1RvAgIERG5EAO7oqKjgerVgWPHgEuX3F0aIiKq5BjYFeXrC7RoIfdZyyYiIidjYDuC57GJiMhFGNiO4HlsIiJyEQa2I1jDJiIiF2FgO8IyeQoDm4iInIyB7YimTQE/P+DwYeDKFXeXhoiIKjEGtiOqVAGaNwe0BvbscXdpiIioEmNgO4rnsYmIyAUY2I7iRUCIiMgFGNiOYg2biIhcgIHtKAY2ERG5AAPbUc2bAz4+wP79QGamu0tDRESVFAPbUdWrA3/5C5CXB+zd6+7SEBFRJcXANgInUCEiIidjYBuBc4oTEZGTMbCNwI5nJVu7FvjrX4EGDYBGjYBHHuFxIiKqAAa2ERjY19IaePFFoFs34OuvgePHgaNHgc8/B9q3Bz780N0lJCIyFQa2EVq2lOXevUB2tnvL4gm0BkaNAiZOlB70zz0H7NsH7NgBDB0K5OQAw4cD77/v7pISEZkGA9sIAQHS3JudDRw44O7SuN977wHvvANUqwZ88w3w6qtyoZTWrYGPPgI++EDWGzkSWLLEvWUlIjIJBrZR2PFMbNwIPPOM3J85E7jrrmvXGTZMat+AnNM+ftxlxSMiMisGtlF4HhvIyAAefRTIzZUm8fvvL3nd558HevcGUlOBp592WRGJiMyKgW0UBrZ0Mtu1S87pT5lS+ro+PsAnnwA1agD/+x+wdKlrykhEZFIMbKN4++Qpe/YAb74JKAV89hng71/2e6KigJdekvsjRwJZWU4tIhGRmTGwjWIJ7N27pUnY2fLygHnzgIceknHOb78NXLzo/P2W5O9/l97ff/sb0KWL/e8bNUpq5AcOSI2biIiKpbTW7i5DiWJjY3VSUpK7i2G/hg2BlBSpbTZv7rz9XLokIb1iReHnw8OBOXOA+Hjn7bs4S5cCCQlAUJAM36pbt3zv/+YbYMAAoF49uYhKQIBzyklE5OGUUpu01rHFvcYatpHat5fltm3O20duLnDvvRLWdeoA//qX9Mbu1g04c0aC05U11ezsgl7hEyaUP6wB4O67gZgY4ORJGRJGRETXYGAbqV07WW7d6rx9vPEGsHy51KbXrgWeekp6Zq9eLYGZlwckJkpN2xVmzJDTAE2bSlkqQqmCTmqvvy4tCEREVAgD20iWGrazAjslpaCT1uzZQJMmBa/5+MjY5ldflZnGBg8GfvzROeWwSE0tKM8bb8hEKRXVuzdw883A+fMFE6sQEZEVA9tIzm4SnzoVuHoVuOce4Pbbi1/nueeAMWOk6XzgQOfOvDZhAnDhAtCrF3DnnY5tSykZmw1Ib/OrVx0uHhFRZcLANlKzZlLLPHJEgsxIJ0/KtJ5AQa22JK++Ctxxh9RW+/UD0tKMLQsAbN4M/PvfgK+vnEdXyvFtxsfLuezTp4FPP3V8e0RElQgD20h+fkDbtnLf6Fr2hx/KTGL9+wPXXVf6uj4+cg67ZUu54MYjj8i5baNoDTz5ZMHSMmmMo5QCxo+X+1OnVq4LqWgNHDoEfPEF8NprwOTJ0jnwzz+N/bchokqLgW00ZzSL5+QA//mP3Le3Y1etWsB338lywQJg0iTjyvPFF8Bvv0kv9bJq++XVv7+MaT96FJg719htu0NmpvzY6tBB+hw89BAwbpycThg6VDoqNmokAX7unLtLS0QejIFtNGf0FF+6FDh2THpix8XZ/77mzWVyFR8fCdZvv3W8LGfPyiQpgNQUa9VyfJu2fHwk0Czbd8UkNM6ycKG0PgwfLn8PwcFyrv8f/5C+BvffDzRoIP+2EybIKZUZM1jjJqLiaa099hYTE6NN55dftAa0vuEG47Z5772yzddeq9j7p06V9wcEaL1tm2Nleegh2dbNN2udm+vYtkqSlaV1dLTsZ/585+zDmdLStP7b36T8gNatWmn9xRdaZ2Rcu25urtbLl2vdo0fB+vHxWp886fpyE5HbAUjSJWSi20O5tJspA/vsWTms/v5a5+Q4vr2rV7UODJRtHjpUsW3k5Wn9wAOyjcaNtT59umLb+d//Cj7bvn0V24a9ZsyQfV1/vZTfLPbv17plSyl7tWpav/WW1tnZZb8vL0/rr77SunZteW+9elqvX+/04hKRZyktsNkkbrTQULmoxdWrMkWpo376Cbh8Wc6BRkdXbBtKSQenjh2l41N8vPQgL4/du4EhQ+T+a69J87wzDRkiU5Vu2QL88INz92WUX38FOneWY9WmDbBpk8yV7udX9nuVkulmt24FuneXUQE9egDff+/0YhOROTCwnSE2fxrYjRsd39aCBbLs39+x7dSoIcHXvLmEYEKC/UPPUlNl/2lpMrb7yScdK4s9qlcHxo6V+y+9JI3FnmzuXODWW+Ucf0KCzELXpk35t9OggUw7O3gwkJ4uw/J4URQiAgPbOSyB7eiFS3Jzpac34HhgA1Jj/fFH6ZW8fj1w441lT6xy+rTUyPfskSFr//mPMWOu7fH441LmTZs8t5attfygGDRILg86cqR0NgsKqvg2q1SRcegvvCAd0IYOBaZNM6zIRGRODGxnuOEGWTpaw167Vi7o0aRJ2WOv7RUZKfOOX3edNN127Ah8/LEMHStq5Ur58bF5s/RgXr4cCAw0phz28Pf37Fp2Rgbw8MPAyy9L7/Z33gHefde+JvCyKCXbff99eTxmjIxR97RjQEQuw8B2BksNe8sWqXVVlG1zuJG12qgoOd/av79caCMxEWjRQsLxP/+R2lzPnnIONTlZauKrVgH16xtXBnvZ1rI96XzuqVNyfObOlcuBLlzonFMFTzwBfP65zCj36qvAiBEc9kXkrUrqjeYJN1P2Erdo1kx6+27aVLH35+Vp3aSJbGP1amPLZruPL74o2E/RW40aWk+cWPxwJFd66y0pT+vW9vW4drbNm7WOjJQyRUVpvXWr8/f53XfS6xyQoXVZWc7fJxG5HNhL3A0cPY+9fTtw8KBcRrNrV+PKZUsp4IEH5Pz0ihUyYcmjj0pN8dNP5epgEyY4dhUuIwwfLqcFdu50bwcsraXJu3PngpaHDRsKJstxprvuApYskVMSc+cCAwbwAilEXsahk21KqVAA/wUQDeAwgIFa6/NF1okEMBtAPQB5AD7SWv/Lkf2awg03AF9+KeexExPL/37LrGR33SXNoc7k5ydX3OrVy7n7qahq1WRu8b/+VTpiPfCA8TOslSU5WZqnLc3yjz8OvP229GZ3lR49ZJhfQgKwaJEsFy4EatZ0XRnc6fJlmbI2JUWGvWVkyHzzWssscqGhMl1us2bec0zIqzjaO+Y5AD9prV9TSj2X/3hskXVyAPxda/2HUioIwCal1Aqt9U4H9+3ZOneW5e+/V+z9Rg3nqizuuUeul71mjXRAe+st1+w3K0s6k730EnDlivxQ+OQT+fHgDp06SafB3r2lX8Gtt0rNOyzMPeVxlsxMGZO+caO0YmzcKJ0k7e10V6+eXPymY0f5v9i5s/TdcNUIByInUNqBXqdKqT0A4rTWJ5RS9QGs1Fq3KOM93wF4T2u9oqztx8bG6iRHh0a5S1aWfLlnZMjQqPBw+9975IhMkhIQIGOgXVmL82R//CGBlZcnFx+58Ubn7evSJbmc6dtvS40OkGbot96SnvbudvCghPbBg3KxlK+/lqWjzp2TcNy+XU5BnDwpHeyuXJHXfXyAkBD5e65TR05VNG0qt7/8pWKjCLKzJYw3bZJ9b9woHTaLXq2tShX5f9GggXSArFFDngOAixel7MePA/v2yf+7ourWleDu0kWWN9zg2PA7IidQSm3SWscW95qjNey6WusTAJAf2nXKKEg0gA4A1ju4X89XtaoEyi+/SI/su++2/72W2nVCAsPaVseOcuGM116TmdA2b5ahX0Y6eVJq1DNmSAgAMv582jTg9tuN3ZcjmjSR1ob4eLmEaseO0grw9NPl+5u5elX+Pn/8UW6bNzs2dCw8XMb5R0cXhGtgoPz49PWV/aWlyQVPjhwB9u+XS4xmZhbejlLyA6RTJwnWTp2kr4A9/Sny8qTpfOdOqZ2vXy/LU6fkFMLChQX7aNOmIMA7dJCJhcwY4pmZ8vdquWVlyY+ZqlVlWaOGnDIICmIrg4mVWcNWSv0IOf9c1PMAZmmtg23WPa+1DilhO4EAVgF4RWv9TSn7SwSQCABRUVExR44cKeszeK6XXpKxtKNGla8Jt0cPGQM9Z45cjpEKZGRIOO3aJZOVzJ5tzBfQvn3A9OnArFkF4XHLLTL+uU8fz/2Su3QJeOYZ6SQISO1/xAj5u2nY8Nr1MzOlBvvLL3L7/ffCYVm1qgRk+/YSZpGRUpO2fNHn5Mi0tqmpUps9cEBu+/fLsqLDGJs0kcC0hHNMjLHnobWWMq5fL7d166QWX9z8AxERMsyxYUNpWq9XT36IWH54WG7+/vIjxM/v2mXR53x85IeE5aZ1wf3MTDk/b3tLS5N/2wsXCgfxxYvFP1dci0Jx/PwkuEND5TRKnToFrSXF3a9d2/l9aKiQ0mrYLmkSV0pVAfA9gGVa6zft3b6pm8QB4Oef5Rxjx47S3GePs2flP4uPjzSlhxT7+8e7bd8utaIrV4A335TAqqgNG6RD2zffyJeoUjId6Nixsg+zWLZMflzYXoc9OlqaqWvWlGNlqdHaXrJUKQlKS6fDbt2kNlYReXnSQnH4sNyOHJFQv3JFbrm5su2AAKl5N2okt3btpNOYq129Ki0K69ZJiO/YIT/cHJk7wV38/OQUXHCwLKtWlVMK2dnyeS5flh9allMb9lKqINhDQqS2bntTSrZv2Y/tzbJ/y2tFH2st5bS0AliW1avLjyHLsuh9e1/z9S15/0VvOTmlP87Lk+/k4m7t2gF/+5th/5TODOxpAM7adDoL1VqPKbKOAjALwDmt9ajybN/0gZ2eLv+BcnPl/Jo9PZtnzpTm3t69ZWYxKt5XX8m85oDM1PZ//2f/e/PypLf39OnSrAzIF8UjjwCjR0tnJTPKzZUOaJ99Jn87ly9fu46Pj3y+Hj1kcpzu3aUWRSI3V35o7NsHnDghP0BOnJAWBcsPjytX5NhmZMj6ubnyBW9Z2t63LPPyCmraShV82SslzfxBQVKDt9wCAuT7wnKzBHFJz/n729cKlJkp30Vnz8pnOnNGKganTxd//9w5Zx9x87v7bvnBbxBnBnZtAPMBRAE4CuBerfU5pVQEgE+01n2UUjcBWAPgT8iwLgAYr7VeXNb2TR/YgNRYfv9dAqJv37LXv+MOmTd7xgwZf0wle/NN4O9/l/tjxwITJ8qv9JJcuSJjmN94A9i7V56rVUuGaD39tDSFVha5uXLa4PhxaV4NDJSm3ebNjT/vT5VXdraE++nTUkMvWvO0rSXb1pZta8wl3VeqcM08O1t+UGRmSutHRoYsi94v7TXb+7m51+67tJufX8mPfXwKn8awvTVpIsNvDeK0wHa2ShHYL7wATJok5xXfe6/0dS9ckKan3Fz5oq1b1yVFNLX335ewzc2VmuNzz8l/HsuphIsXpRa9YAEwf76EFyBDfJ55BnjsMXN2MiKiSomB7U4bNkgP1EaN5FrUpTVbzZoll1Xs0UPOf5N9Vq2SK1rt21fwXFiYhHjR637feCPw1FMyjtqIi3QQERnImcO6qCyxsVJrPnJEOrW0bVvyul99JUvLuVmyT/fuMjRozhz50bNhg5yfA+T8YIcO0ifgwQfNe36aiLweA9vZfHxkWNDMmTKdZEmBfe6cdBTy8ZFZvah8qlWT5u3HHpNzYefOSWtGeLjnDskiIioHXvzDFSyTpsyZU/KkFLNnS9D06iU1cqq4KlXk/H+dOgxrIqo0GNiukJAgNb2dO4u/epfWMg0mID2WiYiIimBgu0KVKjIrFyBjZItatUqG4NSrB9x5p2vLRkREpsDAdhXLTDgzZ8qcxrYmTpTl8OEFFzMgIiKywcB2lbZtZXzw1asyv7jFN9/InM61aslwIyIiomIwsF1p8mQZ+/vBB1LTTkoCEhPltVdecc98ykREZAoMbFe67jpgyhS5P2SIXJno7FmZspTTkBIRUSkY2K72j38A774L1K8vV5UZMQL43/9k/DUREVEJODWpu1gmkue1ZomIKF9pU5OyWucuSjGsiYjIbgxsIiIiE2BgExERmQADm4iIyAQY2ERERCbAwCYiIjIBBjYREZEJMLCJiIhMgIFNRERkAgxsIiIiE2BgExERmQADm4iIyAQY2ERERCbAwCYiIjIBBjYREZEJMLCJiIhMgIFNRERkAgxsIiIiE1Baa3eXoURKqTMAjhi4yTAAqQZuzxvxGDqOx9BxPIbG4HF0nNHHsJHWOry4Fzw6sI2mlErSWse6uxxmxmPoOB5Dx/EYGoPH0XGuPIZsEiciIjIBBjYREZEJeFtgf+TuAlQCPIaO4zF0HI+hMXgcHeeyY+hV57CJiIjMyttq2ERERKbkFYGtlLpdKbVHKbVfKfWcu8tjFkqpT5VSp5VS222eC1VKrVBK7ctfhrizjJ5OKRWplPpFKbVLKbVDKfV0/vM8jnZSSlVXSm1QSm3NP4Yv5z/PY1hOSilfpdRmpdT3+Y95DMtBKXVYKfWnUmqLUiop/zmXHcNKH9hKKV8A7wNIANAawANKqdbuLZVpzARwe5HnngPwk9a6GYCf8h9TyXIA/F1r3QpAFwAj8v/+eBztlwmgp9a6PYDrAdyulOoCHsOKeBrALpvHPIbl10Nrfb3NUC6XHcNKH9gAOgHYr7U+qLXOAjAPQD83l8kUtNarAZwr8nQ/ALPy788C0N+VZTIbrfUJrfUf+ffTIF+WDcDjaDctLuc/rJJ/0+AxLBelVEMAfQF8YvM0j6HjXHYMvSGwGwBItnl8LP85qpi6WusTgIQRgDpuLo9pKKWiAXQAsB48juWS35S7BcBpACu01jyG5fc2gDEA8mye4zEsHw1guVJqk1IqMf85lx1DP2dt2IOoYp5j13hyKaVUIICvAYzSWl9Sqrg/SyqJ1joXwPVKqWAA3yql2rq5SKailLoDwGmt9SalVJybi2Nm3bTWx5VSdQCsUErtduXOvaGGfQxApM3jhgCOu6kslcEppVR9AMhfnnZzeTyeUqoKJKznaq2/yX+ax7ECtNYXAKyE9K3gMbRfNwB3KaUOQ04L9lRKzQGPYblorY/nL08D+BZyytVlx9AbAnsjgGZKqcZKqaoA7gew0M1lMrOFAB7Nv/8ogO/cWBaPp6Qq/R8Au7TWb9q8xONoJ6VUeH7NGkopfwC9AOwGj6HdtNbjtNYNtdbRkO/An7XWg8BjaDelVIBSKshyH0A8gO1w4TH0iolTlFJ9IOdvfAF8qrV+xb0lMgel1JcA4iBXozkF4EUACwDMBxAF4CiAe7XWRTumUT6l1E0A1gD4EwXnDsdDzmPzONpBKdUO0pnHF1LJmK+1nqiUqg0ew3LLbxIfrbW+g8fQfkqpJpBaNSCnk7/QWr/iymPoFYFNRERkdt7QJE5ERGR6DGwiIiITYGATERGZAAObiIjIBBjYREREJsDAJiIiMgEGNhERkQkwsIkIAKCUGqyU0vm3aHeXh4gKY2ATERGZAAObiIjIBBjYREREJsC5xIm8XP7FIH6xY9UeWuuVTi0MEZWINWwiIiITYA2byMvlX9u3MYB+ACbnP30bgONFVj2ktb7iyrIRUQE/dxeAiNwrP4S3K6VibZ7eq7U+7KYiEVEx2CRORERkAgxsIiIiE2BgExERmQADm4iIyAQY2ERERCbAwCYiIjIBBjYRWXBSBiIPxsAmIosMm/vV3FYKIioWA5uILE7Y3P+L20pBRMXiTGdEZLEZUsuuDmCSUiobwBEAefmvp2itr7qrcETejnOJE5GVUup1AGNKeJlX6yJyIzaJE5Gt5wAMBbAGwDkAue4tDhFZsIZNRERkAqxhExERmQADm4iIyAQY2ERERCbAwCYiIjIBBjYREZEJMLCJiIhMgIFNRERkAgxsIiIiE2BgExERmQADm4iIyAQY2ERERCbAwCYiIjKB/wdO6hlxb6XgvAAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_result_expectations([\n", " (result_udbath, P11p, 'b', \"P11 (UnderDampedBath)\"),\n", " (result_udbath, P12p, 'r', \"P12 (UnderDampedBath)\"),\n", "]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### We can compare these results to those of the Bloch-Redfield solver in QuTiP:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ODE solver time: 2.6972014904022217\n" ] } ], "source": [ "UD = (\n", " f\" 2* {lam}**2 * {gamma} / ( {w0}**4 * {beta}) if (w==0) else\"\n", " f\" 2* ({lam}**2 * {gamma} * w / (({w0}**2 - w**2)**2 + {gamma}**2 * w**2)) * ((1 / (exp(w * {beta}) - 1)) + 1)\"\n", ")\n", "\n", "options = Options(nsteps=15000, store_states=True, rtol=1e-12, atol=1e-12)\n", "\n", "with timer(\"ODE solver time\"):\n", " resultBR = brmesolve(Hsys, rho0, tlist, a_ops=[[sigmaz(), UD]], options=options)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_result_expectations([\n", " (resultMats, P11p, 'b', \"P11 Mats\"),\n", " (resultMats, P12p, 'r', \"P12 Mats\"),\n", " (resultBR, P11p, 'g--', \"P11 Bloch Redfield\"),\n", " (resultBR, P12p, 'g--', \"P12 Bloch Redfield\"),\n", "]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lastly, let us calculate the analytical steady-state result and compare all of the results:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The thermal state of a reaction coordinate (treating the environment as a single damped mode) should, at high temperatures and small gamma, tell us the steady-state:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "dot_energy, dot_state = Hsys.eigenstates()\n", "deltaE = dot_energy[1] - dot_energy[0]\n", "\n", "gamma2 = gamma\n", "wa = w0 # reaction coordinate frequency\n", "g = lam / np.sqrt(2 * wa) # coupling\n", "\n", "NRC = 10\n", "\n", "Hsys_exp = tensor(qeye(NRC), Hsys)\n", "Q_exp = tensor(qeye(NRC), Q)\n", "a = tensor(destroy(NRC), qeye(2))\n", "\n", "H0 = wa * a.dag() * a + Hsys_exp\n", "# interaction\n", "H1 = (g * (a.dag() + a) * Q_exp)\n", "\n", "H = H0 + H1\n", "\n", "energies, states = H.eigenstates()\n", "rhoss = 0 * states[0] * states[0].dag()\n", "for kk, energ in enumerate(energies):\n", " rhoss += (states[kk] * states[kk].dag() * exp(-beta * energies[kk])) \n", "rhoss = rhoss / rhoss.norm()\n", "\n", "P12RC = tensor(qeye(NRC), basis(2,0) * basis(2,1).dag())\n", "P12RC = expect(rhoss, P12RC)\n", "\n", "P11RC = tensor(qeye(NRC), basis(2,0) * basis(2,0).dag())\n", "P11RC = expect(rhoss, P11RC)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "# XXX: Decide what to do with this cell\n", "\n", "matplotlib.rcParams['figure.figsize'] = (7, 5)\n", "matplotlib.rcParams['axes.titlesize'] = 25\n", "matplotlib.rcParams['axes.labelsize'] = 30\n", "matplotlib.rcParams['xtick.labelsize'] = 28\n", "matplotlib.rcParams['ytick.labelsize'] = 28\n", "matplotlib.rcParams['legend.fontsize'] = 28\n", "matplotlib.rcParams['axes.grid'] = False\n", "matplotlib.rcParams['savefig.bbox'] = 'tight'\n", "matplotlib.rcParams['lines.markersize'] = 5\n", "matplotlib.rcParams['font.family'] = 'STIXgeneral' \n", "matplotlib.rcParams['mathtext.fontset'] = 'stix'\n", "matplotlib.rcParams[\"font.serif\"] = \"STIX\"\n", "matplotlib.rcParams['text.usetex'] = False" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# XXX: Decide what to do with this cell\n", "\n", "fig, axes = plt.subplots(1, 1, sharex=True, figsize=(12, 7))\n", "\n", "plt.yticks([P11RC, 0.6, 1.0], [0.38, 0.6, 1])\n", "\n", "plot_result_expectations([\n", " (resultBR, P11p, 'y-.', \"Bloch-Redfield\"),\n", " (resultMats, P11p, 'b', \"Matsubara $N_k=3$\"),\n", "], axes=axes)\n", "axes.plot(tlist, [P11RC for t in tlist], color='black', linestyle=\"-.\",linewidth=2, label=\"Thermal state\")\n", "\n", "axes.set_xlabel(r'$t \\Delta$',fontsize=30)\n", "axes.set_ylabel(r'$\\rho_{11}$',fontsize=30)\n", "\n", "axes.locator_params(axis='y', nbins=4)\n", "axes.locator_params(axis='x', nbins=4)\n", "\n", "axes.legend(loc=0)\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"figures/fig3.pdf\")" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
SoftwareVersion
QuTiP4.7.0.dev0+c898b89
Numpy1.21.2
SciPy1.7.1
matplotlib3.4.3
Cython0.29.23
Number of CPUs4
BLAS InfoINTEL MKL
IPython7.27.0
Python3.9.7 (default, Sep 16 2021, 13:09:58) \n", "[GCC 7.5.0]
OSposix [linux]
Thu Jan 06 22:34:19 2022 CET
" ], "text/plain": [ "" ] }, "execution_count": 25, "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": { "anaconda-cloud": {}, "jupytext": { "formats": "ipynb,md:myst" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 1 }