{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1e: Spin-Bath model (pure dephasing)\n",
    "\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 overdamped Drude-Lorentz Spectral Density, commonly used with the HEOM. We show how to do the Matsubara and Pade analytical decompositions, as well as how to fit the latter with a finite set of approximate exponentials.  This differs from examble 1a in that we assume that the system and coupling parts of the Hamiltonian commute, hence giving an analytically solvable ''pure dephasing'' model. This is a useful example to look at when introducing other approximations  (e.g., fitting of correlation functions) to check for validity/convergence against the analytical results.  (Note that, generally, for the fitting examples, the pure dephasing model is the 'worst possible case'.  \n",
    "\n",
    "### Drude-Lorentz spectral density\n",
    "The Drude-Lorentz spectral density is:\n",
    "\n",
    "$$J(\\omega)=\\omega \\frac{2\\lambda\\gamma}{{\\gamma}^2 + \\omega^2}$$\n",
    "\n",
    "where $\\lambda$ scales the coupling strength, and $\\gamma$ is the cut-off frequency.\n",
    "We use the convention,\n",
    "\\begin{equation*}\n",
    "C(t) = \\int_0^{\\infty} d\\omega \\frac{J_D(\\omega)}{\\pi}[\\coth(\\beta\\omega) \\cos(\\omega \\tau) - i \\sin(\\omega \\tau)]\n",
    "\\end{equation*}\n",
    "\n",
    "With the HEOM we must use an exponential decomposition:\n",
    "\n",
    "\\begin{equation*}\n",
    "C(t)=\\sum_{k=0}^{k=\\infty} c_k e^{-\\nu_k t}\n",
    "\\end{equation*}\n",
    "\n",
    "The Matsubara decomposition of the Drude-Lorentz spectral density is given by:\n",
    "\n",
    "\\begin{equation*}\n",
    "    \\nu_k = \\begin{cases}\n",
    "               \\gamma               & k = 0\\\\\n",
    "               {2 \\pi k} / {\\beta \\hbar}  & k \\geq 1\\\\\n",
    "           \\end{cases}\n",
    "\\end{equation*}\n",
    "\n",
    "\\begin{equation*}\n",
    "    c_k = \\begin{cases}\n",
    "               \\lambda \\gamma (\\cot(\\beta \\gamma / 2) - i) / \\hbar               & k = 0\\\\\n",
    "               4 \\lambda \\gamma \\nu_k / \\{(nu_k^2 - \\gamma^2)\\beta \\hbar^2 \\}    & k \\geq 1\\\\\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": [],
   "source": [
    "import contextlib\n",
    "import time\n",
    "\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy.optimize import curve_fit\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from qutip import *\n",
    "from qutip.ipynbtools import HTMLProgressBar\n",
    "from qutip.nonmarkov.heom import HEOMSolver, BosonicBath, DrudeLorentzBath, DrudeLorentzPadeBath"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cot(x):\n",
    "    \"\"\" Vectorized cotangent of x. \"\"\"\n",
    "    return 1. / np.tan(x)\n",
    "\n",
    "def coth(x):\n",
    "    \"\"\" Vectorized hyperbolic cotangent of x. \"\"\"\n",
    "    return 1. / np.tanh(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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",
    "        if m_op is None:\n",
    "            t, exp = result\n",
    "        else:\n",
    "            t = result.times\n",
    "            exp = np.real(expect(result.states, m_op))\n",
    "        kw.setdefault(\"linewidth\", 2)\n",
    "        axes.plot(t, 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": 4,
   "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": "markdown",
   "metadata": {},
   "source": [
    "Here we set $H_{sys}=0$, which means the interaction Hamiltonian and the system Hamiltonian commute, and we can compare the numerical results to a known analytical one.  We could in principle keep $\\epsilon \\neq 0$, but it just introduces fast system oscillations, so it is more convenient to set it to zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defining the system Hamiltonian\n",
    "eps = 0.     # Energy of the 2-level system.\n",
    "Del = 0.     # Tunnelling term\n",
    "Hsys = 0.5 * eps * sigmaz() + 0.5 * Del* sigmax()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# System-bath coupling (Drude-Lorentz spectral density)\n",
    "Q = sigmaz() # coupling operator\n",
    "\n",
    "# Bath properties:\n",
    "gamma = .5 # cut off frequency\n",
    "lam = .1 # coupling strength\n",
    "T = 0.5\n",
    "beta = 1./T\n",
    "\n",
    "#HEOM parameters\n",
    "NC = 6 # cut off parameter for the bath\n",
    "Nk = 3 # 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": 7,
   "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": [
    "To get a non-trivial result we prepare the initial state in a superposition, and see how the bath destroys the coherence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initial state of the system.\n",
    "psi = (basis(2, 0) + basis(2, 1)) / np.sqrt(2.)\n",
    "rho0 = psi * psi.dag()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Simulation 1: Matsubara decomposition, not using Ishizaki-Tanimura terminator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RHS construction time: 0.05000424385070801\n",
      "ODE solver time: 0.5485279560089111\n"
     ]
    }
   ],
   "source": [
    "options = Options(nsteps=15000, store_states=True, rtol=1e-14, atol=1e-14)\n",
    "\n",
    "with timer(\"RHS construction time\"):\n",
    "    bath = DrudeLorentzBath(Q, lam=lam, gamma=gamma, T=T, Nk=Nk)\n",
    "    HEOMMats = HEOMSolver(Hsys, bath, NC, options=options)\n",
    "\n",
    "with timer(\"ODE solver time\"):\n",
    "    resultMats = HEOMMats.run(rho0, tlist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Simulation 2: Matsubara decomposition (including terminator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RHS construction time: 0.04774665832519531\n",
      "ODE solver time: 0.5990228652954102\n"
     ]
    }
   ],
   "source": [
    "options = Options(nsteps=15000, store_states=True, rtol=1e-14, atol=1e-14)\n",
    "\n",
    "with timer(\"RHS construction time\"):\n",
    "    bath = DrudeLorentzBath(Q, lam=lam, gamma=gamma, T=T, Nk=Nk)\n",
    "    _, terminator = bath.terminator()\n",
    "    Ltot = liouvillian(Hsys) + terminator\n",
    "    HEOMMatsT = HEOMSolver(Ltot, bath, NC, options=options)\n",
    "\n",
    "with timer(\"ODE solver time\"):\n",
    "    resultMatsT = HEOMMatsT.run(rho0, tlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the results\n",
    "plot_result_expectations([\n",
    "    (resultMats, P11p, 'b', \"P11 Matsubara\"),\n",
    "    (resultMats, P12p, 'r', \"P12 Matsubara\"),\n",
    "    (resultMatsT, P11p, 'b--', \"P11 Matsubara and terminator\"),\n",
    "    (resultMatsT, P12p, 'r--', \"P12 Matsubara and terminator\"),\n",
    "]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As in example 1a, we can compare to Pade and Fitting approaches.\n",
    "\n",
    "#### Simulation 3: Pade decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RHS construction time: 0.06110191345214844\n",
      "ODE solver time: 0.9042110443115234\n"
     ]
    }
   ],
   "source": [
    "options = Options(nsteps=15000, store_states=True, rtol=1e-14, atol=1e-14)\n",
    "\n",
    "with timer(\"RHS construction time\"):\n",
    "    bath = DrudeLorentzPadeBath(Q, lam=lam, gamma=gamma, T=T, Nk=Nk)\n",
    "    HEOMPade = HEOMSolver(Hsys, bath, NC, options=options)\n",
    "\n",
    "with timer(\"ODE solver time\"):\n",
    "    resultPade = HEOMPade.run(rho0, tlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the results\n",
    "plot_result_expectations([\n",
    "    (resultMatsT, P11p, 'b', \"P11 Matsubara (+term)\"),\n",
    "    (resultMatsT, P12p, 'r', \"P12 Matsubara (+term)\"),\n",
    "    (resultPade, P11p, 'b--', \"P11 Pade\"),\n",
    "    (resultPade, P12p, 'r--', \"P12 Pade\"),\n",
    "]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Simulation 4: Fitting approach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "tlist2 = np.linspace(0, 2, 10000)\n",
    "lmaxmats = 15000\n",
    "\n",
    "def c(t, anamax):\n",
    "    \"\"\"Calculates real and imag. parts of the correlation function using anamax Matsubara terms\"\"\"\n",
    "\n",
    "    result = complex(lam * gamma * (-1.0j + cot(gamma * beta / 2.)) * np.exp(-gamma * t))\n",
    "\n",
    "    for k in range(1, anamax):\n",
    "        vk = 2 * np.pi * k * T\n",
    "        result += ((4 * lam * gamma * T * vk / (vk**2 - gamma**2)) * np.exp(- vk * t))\n",
    "\n",
    "    return np.real(result), np.imag(result)\n",
    "\n",
    "corr_ana = [c(t, lmaxmats) for t in tlist2]\n",
    "corrRana, corrIana = zip(*corr_ana) # real and imag parts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def wrapper_fit_func(x, N, *args):\n",
    "    a, b = list(args[0][:N]), list(args[0][N:2*N])\n",
    "    return fit_func(x, a, b, N)\n",
    "\n",
    "# actual fitting function\n",
    "def fit_func(x, a, b, N):\n",
    "    tot = 0\n",
    "    for i in range(N):\n",
    "        tot += a[i]*np.exp(b[i]*x)\n",
    "    return tot\n",
    "\n",
    "def fitter(ans, tlist, k):\n",
    "    # the actual computing of fit\n",
    "    popt = []\n",
    "    pcov = [] \n",
    "    # tries to fit for k exponents\n",
    "    for i in range(k):\n",
    "        params_0 = [0]*(2*(i+1))\n",
    "        upper_a = abs(max(ans, key = abs))*10\n",
    "        #sets initial guess\n",
    "        guess = []\n",
    "        aguess = [ans[0]]*(i+1)#[max(ans)]*(i+1)\n",
    "        bguess = [0]*(i+1)\n",
    "        guess.extend(aguess)\n",
    "        guess.extend(bguess)\n",
    "        # sets bounds\n",
    "        # a's = anything , b's negative\n",
    "        # sets lower bound\n",
    "        b_lower = []\n",
    "        alower = [-upper_a]*(i+1)\n",
    "        blower = [-np.inf]*(i+1)\n",
    "        b_lower.extend(alower)\n",
    "        b_lower.extend(blower)\n",
    "        # sets higher bound\n",
    "        b_higher = []\n",
    "        ahigher = [upper_a]*(i+1)\n",
    "        bhigher = [0]*(i+1)\n",
    "        b_higher.extend(ahigher)\n",
    "        b_higher.extend(bhigher)\n",
    "        param_bounds = (b_lower, b_higher)\n",
    "        p1, p2 = curve_fit(lambda x, *params_0: wrapper_fit_func(x, i+1, \\\n",
    "            params_0), tlist, ans, p0=guess, sigma=[0.01 for t in tlist], bounds = param_bounds,maxfev = 1e8)\n",
    "        popt.append(p1)\n",
    "        pcov.append(p2)\n",
    "    return popt\n",
    "\n",
    "# function that evaluates values with fitted params at given inputs\n",
    "def checker(tlist, vals):\n",
    "    y = []\n",
    "    for i in tlist:\n",
    "        y.append(wrapper_fit_func(i, int(len(vals)/2), vals))\n",
    "    return y\n",
    "\n",
    "# Fits of the real part with up to 4 exponents\n",
    "k = 4\n",
    "popt1 = fitter(corrRana, tlist2, k)\n",
    "for i in range(k):\n",
    "    y = checker(tlist2, popt1[i])\n",
    "    plt.plot(tlist2, corrRana, tlist2, y)\n",
    "    plt.show()\n",
    "\n",
    "# Fit of the imag. part with 1 exponent\n",
    "k1 = 1\n",
    "popt2 = fitter(corrIana, tlist2, k1)\n",
    "for i in range(k1):\n",
    "    y = checker(tlist2, popt2[i])\n",
    "    plt.plot(tlist2, corrIana, tlist2, y)\n",
    "    plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set the exponential coefficients from the fit parameters\n",
    "\n",
    "ckAR1 = list(popt1[k-1])[:len(list(popt1[k-1]))//2]\n",
    "ckAR = [complex(x) for x in ckAR1]\n",
    "\n",
    "vkAR1 = list(popt1[k-1])[len(list(popt1[k-1]))//2:]\n",
    "vkAR = [complex(-x) for x in vkAR1]\n",
    "\n",
    "ckAI1 = list(popt2[k1-1])[:len(list(popt2[k1-1]))//2]\n",
    "ckAI = [complex(x) for x in ckAI1]\n",
    "\n",
    "vkAI1 = list(popt2[k1-1])[len(list(popt2[k1-1]))//2:]\n",
    "vkAI = [complex(-x) for x in vkAI1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Overwrite imaginary fit with analytical value just in case\n",
    "\n",
    "ckAI = [complex(lam * gamma * (-1.0))]\n",
    "vkAI = [complex(gamma)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RHS construction time: 0.270967960357666\n",
      "ODE solver time: 35.03621983528137\n"
     ]
    }
   ],
   "source": [
    "options = Options(nsteps=15000, store_states=True, rtol=1e-14, atol=1e-14)\n",
    "NC = 8\n",
    "\n",
    "with timer(\"RHS construction time\"):\n",
    "    bath = BosonicBath(Q, ckAR, vkAR, ckAI, vkAI)\n",
    "    HEOMFit = HEOMSolver(Hsys, bath, NC, options=options)\n",
    "    \n",
    "with timer(\"ODE solver time\"):\n",
    "    resultFit = HEOMFit.run(rho0, tlist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analytic calculations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pure_dephasing_evolution_analytical(tlist, wq, ck, vk):\n",
    "    \"\"\"\n",
    "    Computes the propagating function appearing in the pure dephasing model.\n",
    "        \n",
    "    Parameters\n",
    "    ----------\n",
    "    t: float\n",
    "        A float specifying the time at which to calculate the integral.\n",
    "    \n",
    "    wq: float\n",
    "        The qubit frequency in the Hamiltonian.\n",
    "\n",
    "    ck: ndarray\n",
    "        The list of coefficients in the correlation function.\n",
    "        \n",
    "    vk: ndarray\n",
    "        The list of frequencies in the correlation function.\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    integral: float\n",
    "        The value of the integral function at time t.\n",
    "    \"\"\"\n",
    "    evolution = np.array([np.exp(-1j*wq*t - correlation_integral(t, ck, vk)) for t in tlist])\n",
    "    return evolution\n",
    "\n",
    "def correlation_integral(t, ck, vk):\n",
    "    \"\"\"\n",
    "    Computes the integral sum function appearing in the pure dephasing model.\n",
    "    \n",
    "    If the correlation function is a sum of exponentials then this sum\n",
    "    is given by:\n",
    "    \n",
    "    .. math:\n",
    "        \n",
    "        \\int_0^{t}d\\tau D(\\tau) = \\sum_k\\frac{c_k}{\\mu_k^2}e^{\\mu_k t}\n",
    "        + \\frac{\\bar c_k}{\\bar \\mu_k^2}e^{\\bar \\mu_k t}\n",
    "        - \\frac{\\bar \\mu_k c_k + \\mu_k \\bar c_k}{\\mu_k \\bar \\mu_k} t\n",
    "        + \\frac{\\bar \\mu_k^2 c_k + \\mu_k^2 \\bar c_k}{\\mu_k^2 \\bar \\mu_k^2}\n",
    "        \n",
    "    Parameters\n",
    "    ----------\n",
    "    t: float\n",
    "        A float specifying the time at which to calculate the integral.\n",
    "    \n",
    "    ck: ndarray\n",
    "        The list of coefficients in the correlation function.\n",
    "        \n",
    "    vk: ndarray\n",
    "        The list of frequencies in the correlation function.\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    integral: float\n",
    "        The value of the integral function at time t.\n",
    "    \"\"\"\n",
    "    t1 = np.sum(np.multiply(np.divide(ck, vk**2), np.exp(vk*t) - 1))\n",
    "    \n",
    "    t2 = np.sum(np.multiply(np.divide(np.conjugate(ck), np.conjugate(vk)**2),\n",
    "                            np.exp(np.conjugate(vk)*t) - 1))\n",
    "    t3 = np.sum((np.divide(ck, vk) + np.divide(np.conjugate(ck), np.conjugate(vk)))*t)\n",
    "\n",
    "    return 2*(t1+t2-t3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the pure dephasing analytics, we just sum up as many matsubara terms as we can"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "lmaxmats2 =  15000\n",
    "\n",
    "vk = [complex(-gamma)]\n",
    "vk.extend([complex(-2. * np.pi * k * T) for k in range(1, lmaxmats2)])\n",
    "\n",
    "ck = [complex(lam * gamma * (-1.0j + cot(gamma * beta / 2.)))]\n",
    "ck.extend([complex(4 * lam * gamma * T * (-v) / (v**2 - gamma**2)) for v in vk[1:]])\n",
    "\n",
    "P12_ana = 0.5 * pure_dephasing_evolution_analytical(tlist, 0, np.asarray(ck), np.asarray(vk))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, we can just do the integral of the propagator directly, without using the correlation functions at all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_5094/4088145471.py:7: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.\n",
      "  If increasing the limit yields no improvement it is advised to analyze \n",
      "  the integrand in order to determine the difficulties.  If the position of a \n",
      "  local difficulty can be determined (singularity, discontinuity) one will \n",
      "  probably gain from splitting up the interval and calling the integrator \n",
      "  on the subranges.  Perhaps a special-purpose integrator should be used.\n",
      "  P12_ana2 = [0.5 * np.exp(sp.integrate.quad(integrand, 0., np.inf, args=(lam,gamma,T,t,))[0]) for t in tlist]\n"
     ]
    }
   ],
   "source": [
    "def JDL(omega, lamc, omega_c):\n",
    "    return 2. * lamc * omega * omega_c / (omega_c**2 + omega**2)\n",
    "\n",
    "def integrand(omega, lamc, omega_c, Temp, t):\n",
    "    return (-4. * JDL(omega,lamc,omega_c) / omega**2) * (1. - np.cos(omega*t)) * (coth(omega/(2.*Temp))) / np.pi\n",
    "\n",
    "P12_ana2 = [0.5 * np.exp(sp.integrate.quad(integrand, 0., np.inf, args=(lam,gamma,T,t,))[0]) for t in tlist]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Compare results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_result_expectations([\n",
    "    (resultMats, P12p, 'r', \"P12 Mats\"),\n",
    "    (resultMatsT, P12p, 'r--', \"P12 Mats + Term\"),\n",
    "    (resultPade, P12p, 'b--', \"P12 Pade\"),\n",
    "    (resultFit, P12p, 'g', \"P12 Fit\"),\n",
    "    ((tlist, np.real(P12_ana)), None, 'b', \"Analytic 1\"),\n",
    "    ((tlist, np.real(P12_ana2)), None, 'y--', \"Analytic 2\"),\n",
    "]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8))\n",
    "\n",
    "plot_result_expectations([\n",
    "    (resultMats, P12p, 'r', \"P12 Mats\"),\n",
    "    (resultMatsT, P12p, 'r--', \"P12 Mats + Term\"),\n",
    "    (resultPade, P12p, 'b--', \"P12 Pade\"),\n",
    "    (resultFit, P12p, 'g', \"P12 Fit\"),\n",
    "    ((tlist, np.real(P12_ana)), None, 'b', \"Analytic 1\"),\n",
    "    ((tlist, np.real(P12_ana2)), None, 'y--', \"Analytic 2\"),\n",
    "], axes)\n",
    "\n",
    "axes.set_yscale('log')\n",
    "axes.legend(loc=0, fontsize=12)\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>QuTiP</td><td>4.7.0.dev0+b71625e</td></tr><tr><td>Numpy</td><td>1.21.2</td></tr><tr><td>SciPy</td><td>1.7.1</td></tr><tr><td>matplotlib</td><td>3.5.0</td></tr><tr><td>Cython</td><td>0.29.25</td></tr><tr><td>Number of CPUs</td><td>6</td></tr><tr><td>BLAS Info</td><td>INTEL MKL</td></tr><tr><td>IPython</td><td>7.29.0</td></tr><tr><td>Python</td><td>3.9.7 (default, Sep 16 2021, 13:09:58) \n",
       "[GCC 7.5.0]</td></tr><tr><td>OS</td><td>posix [linux]</td></tr><tr><td colspan='2'>Thu Dec 30 12:06:30 2021 CET</td></tr></table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 24,
     "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
}