{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# QuTiP example: Landau-Zener-Stuckelberg inteferometry"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "J.R. Johansson and P.D. Nation\n",
    "\n",
    "For more information about QuTiP see [http://qutip.org](http://qutip.org)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qutip import *\n",
    "from qutip.ui.progressbar import TextProgressBar as ProgressBar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Landau-Zener-Stuckelberg interferometry: Steady state of a strongly driven two-level system, using the one-period propagator. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up the parameters and start calculation\n",
    "delta  = 1.0  * 2 * np.pi  # qubit sigma_x coefficient\n",
    "w      = 2.0  * 2 * np.pi  # driving frequency\n",
    "T      = 2 * np.pi / w     # driving period \n",
    "gamma1 = 0.00001        # relaxation rate\n",
    "gamma2 = 0.005          # dephasing  rate\n",
    "\n",
    "eps_list = np.linspace(-20.0, 20.0, 101) * 2 * np.pi\n",
    "A_list   = np.linspace(  0.0, 20.0, 101) * 2 * np.pi\n",
    "\n",
    "# pre-calculate the necessary operators\n",
    "sx = sigmax(); sz = sigmaz(); sm = destroy(2); sn = num(2)\n",
    "\n",
    "# collapse operators\n",
    "c_op_list = [np.sqrt(gamma1) * sm, np.sqrt(gamma2) * sz]  # relaxation and dephasing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ODE settings (for list-str format)\n",
    "options = Options()\n",
    "options.rhs_reuse = True\n",
    "options.atol = 1e-6 # reduce accuracy to speed\n",
    "options.rtol = 1e-5 # up the calculation a bit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for function-callback style time-dependence\n",
    "def hamiltonian_t(t, args):\n",
    "    \"\"\" evaluate the hamiltonian at time t. \"\"\"\n",
    "    H0 = args[0]\n",
    "    H1 = args[1]\n",
    "    w  = args[2]\n",
    "    return H0 + H1 * np.sin(w * t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# perform the calculation for each combination of eps and A, store the result\n",
    "# in a matrix\n",
    "def calculate():\n",
    "\n",
    "    p_mat = np.zeros((len(eps_list), len(A_list)))\n",
    "\n",
    "    pbar = ProgressBar(len(eps_list))\n",
    "    \n",
    "    for m, eps in enumerate(eps_list):\n",
    "        H0 = - delta/2.0 * sx - eps/2.0 * sz\n",
    "\n",
    "        pbar.update(m)\n",
    "\n",
    "        for n, A in enumerate(A_list):\n",
    "            H1 = (A/2) * sz\n",
    "\n",
    "            # function callback format\n",
    "            #args = (H0, H1, w); H_td = hamiltonian_t\n",
    "\n",
    "            # list-str format\n",
    "            #args = {'w': w}; H_td = [H0, [H1, 'sin(w * t)']]\n",
    "\n",
    "            # list-function format\n",
    "            args = w; H_td = [H0, [H1, lambda t, w: np.sin(w * t)]]\n",
    "\n",
    "            U = propagator(H_td, T, c_op_list, args, options)\n",
    "            rho_ss = propagator_steadystate(U)\n",
    "\n",
    "            p_mat[m,n] = np.real(expect(sn, rho_ss))\n",
    "\n",
    "    return p_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.9%. Run time: 110.27s. Est. time left: 00:00:15:02\n",
      "20.8%. Run time: 175.55s. Est. time left: 00:00:11:08\n",
      "30.7%. Run time: 235.74s. Est. time left: 00:00:08:52\n",
      "40.6%. Run time: 296.38s. Est. time left: 00:00:07:13\n",
      "50.5%. Run time: 353.54s. Est. time left: 00:00:05:46\n",
      "60.4%. Run time: 415.11s. Est. time left: 00:00:04:32\n",
      "70.3%. Run time: 474.25s. Est. time left: 00:00:03:20\n",
      "80.2%. Run time: 545.30s. Est. time left: 00:00:02:14\n",
      "90.1%. Run time: 676.78s. Est. time left: 00:00:01:14\n"
     ]
    }
   ],
   "source": [
    "p_mat = calculate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9ZIRtvRCZz/teABCRc0XkxIg2Hsxf9i8H8AEAb6i7fcjGvD9E5sM/H0e/Bj0DwO68reeL\nyFPyL0ddZBqHgXOMMq5B9oI/wv0AdonIQ0TkCgCzyNwPu5F9ffhjVR0gM0q2wYzP+TX/bgAfqdAW\nQtaFhgBpIhfj6K80AA/4ax+MyU4dvBPAU1T1+5BNaxzWL7wAwHnIXkrDfz+MzMVxA4BXInv53Abg\nQQAuV9VkqI5PAXghgJ9X1f4I2/qXAHoA7hSRg8h+5XdU9fqyNorIEwD8FIBfyF+Kdbfvx5BNy3up\nqt5z5A/Adcj879+FTB/wKgD7kX32Pw2ZcbJR3g7g8tzoAbJ77t3IrtULkU3//F5kWorPIvvqAFVd\nRmaofFVE7hqq79kAPn5Ej0BIXUg4e4oQMmlE5LcAfElV/66m+k5B9sv7YwB6qvqaOurN666lrSLy\n3QB+AcBVNRgqw/XW2pcbPPbvAdirqn9cQ12fBfBCVf1KaWFCNgANAUKmDBF5MLJfjt9nftFXrW8O\nWeyBlyET8X0KwKX5L8/jrbu2torIt5F9KUgA3KCqxx2at+6+JGQrQkOAkCkiF6f9I4CfUVU7B32q\nmPa2Tnv7CJkWqBEgZEoQkRlkv15/a9pfXNPe1mlvHyHTBA0BQqaHK5Cp3X8jnzNvo8pNE9Pe1mlv\nHyFTA10DhBBCSIPhFwFCCCGkwdAQIIQQQhoMDQFCCCGkwdAQIIQQQhoMDQFCCCGkwdAQIIQQQhoM\nDQFCCCGkwdAQIIQQQhoMDQFCCCGkwdAQIIQQQhoMDQFCCCGkwdAQIIQQQhoMDQFCCCGkwdAQIIQQ\nQhoMDQFCCCGkwdAQIIQQQhrM2AwBETlHRP5FRL4qIjeJyH/P158kIh8Rka/n/564zv7PFJGvicit\nIvKr42o3IYQQspURVR3PgUTOAHCGqn5BRHYC+DyAHwBwJYD7VfVV+Qv+RFV9mdm3DeDfATwdwF0A\nPgfgClX96lgaTwghhGxRxvZFQFW/rapfyP+/COBmAGcBeA6At+XF3obMOLA8AcCtqnqbqvYAvDvf\njxBCCCHHwcwkDioi5wF4DIDPAjhdVb+db7oHwOnOLmcBuHNo+S4AT1yn7qsAXAUA2xfkux/58NkH\nttlvHwMMivtCwvrMurBEiAZHctoZVVN53d6RYtps60nNct+pOA3qLT/PtrdObJnyfvf61LbZP75t\nc3m9fds3ER/N5iW0qZfM17a2c6zOiPrCu34W2+ZVHaxT8iizzs3UKuljIGxzgvBYPS22x+uvbabN\nPU3DBpnD2/bV1cdpxNfUOQmfgK7acSek2jNSxI5vHrZv/HrL+2Lg9EVifmfOOPXYFracMm2pcv1g\nlsN6bS0xY7J/xesZ72PGdlum5fyW/8KNa/tV9dTSAw4xdkNARHYA+FsAv6iqh2XoIquqishx+SpU\n9WoAVwPA4y6a1+s+dO4D2+yDsTLoFZbtDQcAc9IpLHsdb0m0X1qmI9W63tY9cF8uxcHHa7OtZ0mL\nfXGv8/ZbHMwWljviDMKGna2wL3a3iv28S+aCMrZ/vD61bfbYIbbN5fUeGHQLy4ec8dQaRY/sbA/K\nfGatWPd2SYIyZ84UK6/aF4d1rbC8r/zSBG2+KVkp3ecc+4YCsM08I969bdu8d7AalLmzv62w7PXX\no2eLZb7VXwzK2CYumOfB3hNAtfvt0KC8k8+b2RmsuyVZNscOn7Uqz0jZ+OYx51yrKn2x6PTFvkGx\nzbtbYXtWBsVr440XJ7Q2fv1sXySOwWiNoJgx2TOu0ggDOqZu2899hG22xudCy+mLM75xR+nBDGOd\nNSAiHWRGwDtU9e/y1ffm+oEjOoK9zq57AJwztHx2vo4QQgghx8E4Zw0IgDcDuFlV/3Bo0/sBvCD/\n/wsA/L2z++cAPEJEHiIiswCel+9HCCGEkONgnF8E/iOAnwDwFBG5If+7HMCrADxdRL4O4Gn5MkTk\nTBG5BgBUtQ/gxQA+hExk+DeqetMY207IpmZByj9fEkKaydg0Aqp6LdbX2j3VKX83gMuHlq8BcM3x\ntCHGl7PZ8MQ+VbACnI7z4rCagItn54MyX+4Vfb8DT3Ro/FyDirIQq4+orS8CrUi5XsIjNeK3Tmt0\n95/tUytCBMqNgQe1w/NcHhT3SV35Zzn2WnmCLysO9PzFlnlH12PP0jtWFWw93q+oJOJYVl8y7/id\nY7RIddB2RK4x2Ovpnfes8XE/bGZHUOYb/aXCsteauq7fqBjVODROGFmQEEIIaTA0BAghhJAGQ0OA\nEEIIaTATCSg0LQRz8P3oPBH1bD7tQeAbNOfuBXPZLjE+24gJ7BXw4iWMC+vTBYBWhK6hq8X59YmZ\n659Rz70T6BqMZsDzpVu8ADlrWtxvd03+Ty8YlNWgLES0ecGZn70UEcejCjEBrLpa/ttqYPp0ki5l\nTzfVMmOD9+zFBFOKGQu2m3PvOJqFzehzHxWjGgf5RYAQQghpMDQECCGEkAZDQ4AQQghpMI3WCNSF\nnfObRvh9PV3BuOYOe1g/nNeSuQi/uC1jfcwAkNiEJRX95OHc+bDVVeZJh0lqqrVvd7sYU8H3mY7G\n/2k1HvMRsc69/ltojUbz4R9/YJarPQ+dCG1BFRLjT/fuCk9bY7H3gRfzIYi7UKEvvNwp9hzqwosX\nEjNe2GsVoweoGvtgXHh+fDvGxYz1MTqMumLjTHePEkIIIWSk0BAghBBCGgwNAUIIIaTB0BAgpAFw\nLjYhZD0aLRa0AUK8wdKKMWywDSAUgnhikXEOxFVEh1ZYNOsIjWJEWHa/tZriX0xb0KZd0jNrwiRE\nu1vFMokjnKzrvrDCIu8OKDvWvIQJhdbUJh2qmiCq/PrNW7FgxPDUcdq8MuibMqXVRFEWtCk7Vnn/\nLLSMyNW5Lp0p+o3mXTu7puX0cUwQK3ueiXMsT/S4FSkL8gYAB829va3dCQtVYHruNkIIIYSMHRoC\nhBBCSIOhIUAIIYQ0mEZpBKzv3gbXaIovKoYFx/caQxAgxPGZpmqXHWeYlJcZlWrA3iee3zfGgu4E\ngZO8Y22cmMQjbbHL1e5te55+sJSYwCdqlsMyNhhP1TZXDURURlyinZgyJgCZU++oNEVW41Hl2gFA\nL1jnaYrKr4MtE9PHW5WY4ECedqsO+EWAEEIIaTA0BAghhJAGQ0OAEEIIaTA0BIaoOkd6K1KXjzIm\nCUuMn3KS1PWQxCRhGVVfxMSWqCsRylYg5jpM++BZ17WK6QurhyGbi0aJBWMYlTEQZBMbyVGqE2ZQ\nTCsZA2EglEFgDPiiuWP3+ziNBe+87Vltb5W/BmxAla5qYAwEojmpdq62T9vuOWzcGLCCvVQ1fMFE\n3CZRLxNTT1x7RyfwrWIMWCGgx5x5+vdrEpRZqOm07LXy7osYbF8EAYUQGgMxQZGC+23KAodNEu/+\nmxuREHbajVpCCCGEjBAaAoQQQkiDoSFACCGENJhGaQRs8owk8NtT8HIEL5hLFZ+tt0diyniJRsJ9\nwjLjEnfa4DxAnP/TBkvpalpLe2IS+IzKwvf1HfX4db3kO3VQ130Sc5Yx94V9tk5ojU8xZPsice7J\nOSkmsonpP+8ZiQkIFY4X9dwDdqxqbULtwaL2g3UxGpQq8IsAIYQQ0mBoCBBCCCENhoYAIYQQ0mAa\npRGweHO4yfFRJVFMEhH4JKbMqPDn5Jefp/UXtyX0x1rPZVV/u/XjVvG9emVigtLY5F3bnENZjUfM\nWVb1F9vrFR47JrBTuSbF84tXabN3f40qAVqVGBX2+gJAato87+wXoymyVNUmWerSrVTBP/bGdSBe\n4jd7LfrOmFIFfhEghBBCGgwNAUIIIaTB0BAghBBCGgwNgSGaklCFkCYzSf8xIdNIo8SC9kXvDQdB\nmYiMcRZvoKkieBkl5QE3wvZWEULNOuKfNXOoXoSAqesYaUELRyT29K5cjJjLlmlruE+vgvHpGaxW\n+Drfqil7pDkHXzhWj9izLoGcbY+XJKnMGIj5UVBV5DdjhGNusKwKiZ2qsOIErdlhlr1nz8rYRpn8\nabPh3jsVEnOtOc/aqN4i0/V2IoQQQshYoSFACCGENBgaAoQQQkiDaZRGwPpgbFCMUUqIQp/k+BKN\njJNQe+CUMf6yRS3vi2WnzM6agmlYrO93UDkBU0wCmuJyjH/R8ymPS/4WBOECsILidTjR2c/6md37\nYkR+Zts3MX0cE3jHP4eN/7Ya3Xl7WpLiOs//b1lztC0dscGVqgXdapskOoOI9kyb3soSk0QtBk97\nY/u0LoH7dPcoIYQQQkYKDQFCCCGkwdAQIIQQQhpMozQC1ufS1aIdNF+Tz9nz24wqicio8Px71p8X\ng3veNlaD44O0eGUSU7fnU0vNXNxWxDmUJfCpE+tzT6Tcv+jN5beMy98OAEnE9bPP2oJzntanXeV+\niyHG/x/j5636TAfnNcY4ZlYTkETcJ1ZLBQALRiNgE2zVyWaLUeDFl6irnjBJGTUChBBCCDlOaAgQ\nQgghDWZsrgEReQuAZwHYq6oX5uveA+D8vMhuAAdV9WJn39sBLAJIAfRV9XFjaTQhhBCyxRmnRuCt\nAF4P4O1HVqjqjxz5v4i8FsChY+z/ZFXdP7LWIfPX2nndhGwF2tIK9BJka5NCa/NXk63N2AwBVf2E\niJznbRMRAfBcAE8ZZRussGJgBEyQULwVk6mMA+xRRiXsaTnJn9rjVFkZYs7Tluk44jKbdChGCBgT\nBMajDvGdJxyzQkCPZe0UlhdkLShT5d5xz6mke2KEgF6SJDs2tCoG0bF4osMqgWK8ccgKX6uMVDZ4\nEFCfIG4rYN8RMUm4qrJsqp6rkBTPY1o0Ak8CcK+qfn2d7QrgoyLyeRG56lgVichVInK9iFy/777R\nRJ4jhBBCtgrTMn3wCgDvOsb2S1R1j4icBuAjInKLqn7CK6iqVwO4GgAed9H85H4yEkIIIZuAiX8R\nEJEZAD8E4D3rlVHVPfm/ewG8F8ATxtM6QgghZGszDV8EngbgFlW9y9soItsBtFR1Mf//MwD8dpUD\nWb9fzyT+GaBfpdoAN8iDXdUQF5sbmMj41DoRQXRmHe9mmDRquj8AxfiPqyaBsdTVF56v3NLVjQ8j\nnih3VH5n67ON8b9712GSv5o8/39McKwyBhG3ybzjh7b3cl0ByOrSGNnERAlCN/E4AxXFBDazWgNP\nU2SDsdXF2O5tEXkXgE8DOF9E7hKRF+abngfjFhCRM0XkmnzxdADXisiXAFwH4AOq+k/jajchhBCy\nlRnnrIEr1ll/pbPubgCX5/+/DcBFI20cIYQQ0lAmrhEghBBCyOSYBo3A2LC+wsTMf/bmSI+sLSPy\n+Y0S63eLwfP72lq8BDTBPq5PuVx4UYevfJxzphe1XVrmsM4G67ZLUliuy/8Z+Cm9hFoRs9PnpVx/\nM6r5112jqXCTJJlu98ostExSpCkX+sTc+16MAMu8My5ttkRAo2zvvrRXWN7eqmccXx6Ez5V9ZzHp\nECGEEEKOGxoChBBCSIOhIUAIIYQ0GBoChBCyBamSr4A0k0aJBRO1y8XT94JrBA+Tozmxgo1RJp2I\nwQamqCLyq0oQRMTpilmxwUjK2e70e9fU7Q58JRohT2xj13misDoS+ABAYupeGXTWKXmUgSNkS73g\nIzUQ8zLZHiEEPLllE7OEdCrcpzEJv+xzXVUUPE5xYBURmLdP2fWbj7hvYq6Llzhpktgx0OubKgJC\n736za7pOmV01dU8gcNd68unwiwAhhBDSYGgIEEIIIQ2GhgAhhBDSYBqlEbBWj02W0qvJLvL8UVX8\ni9bPtRnx/HC2l+elPIiOl4CjF+G/nvY+tEGROuJ7z8vKzAdBmUZj44dBnID5iEOFgYnCMnUFRymr\nx/pZPbxAO6NKtBNDNc1AiG3dXER7O06ZJEKbEYPVL60hCcrM2GhPU4bVnJzgJhQqv35Wz2H1QwBw\n49pZheWnLnwrpoml8IsAIYQQ0mBoCBBCCCENhoYAIYQQ0mAapRGwPpfU2EHe/Owqvjlv7m4rIrlH\nDDHtmW6PWjjnOGY+rz+XueinTCr5UUNfp71+cxXnSFt/cdu5v0K9RPm84JNaoR+1zGNbNclVjPLA\nS0pjmTN3ZYow9sC4Etl0IpJcxcyvnzbsvRwTzyRGu+TFIWmZuuuKVTLOmCd2LPXGAtseb/ztjEjb\n4iW+Oq+AqyKkAAAgAElEQVSzv7C8XFPIGn4RIIQQQhoMDQFCCCGkwdAQIIQQQhoMDQFCCCGkwTRK\nLGiTj3RNgpe07QlnNh60xpMi1RUsZbPhJSNpGRFMTMISP3hL+fHLkkZNW4a2na1yIZtN2gTEBVeq\nA6/PrRDQ36+4Y5UEQ7GUXdOdEYJML4CVl0xmVCRmFOlEBMaKuZft9YsRaPrP3nQnYBon9spUba8V\nd3qBrxLzrHmCwirwiwAhhBDSYGgIEEIIIQ2GhgAhhBDSYBqlEejqsX2ZibM9dZJgBGWMb84L5NEx\nfrZp93uNEhvEJCaIiOeTtAF6PD95UhI8xvpigfLgPHVifbZRwXmcMinK/d514AWgidN42DaPp70A\n0Ar6uJpffCEiOdaocP3/pol2TEmdXay+pKqvf1SBf7x+r2OsjAkWVLWeUWGTGQFAanQDZe+0WPhF\ngBBCCGkwNAQIIYSQBkNDgBBCCGkwjdIILGsxbkBXZwvLnk+min8qcXYJElNsvpwmtWH9gHFzmb3E\nJ+UkJXO/y7aPGutzj5lf75VpB7EsqiRgCvexeherdQHq8xeHPu56EiW1Tb3zUj7seX08Kl2P5/+3\n68q0LgDQ1XLdhT2rOH2O0xfmWN4zXF8iouMfLOtqizdenNAq+um9+yQx/TUnHadMse7PrD4iKHNW\n50Bh+TQsrd/YDcAvAoQQQkiDoSFACCGENBgaAoQQQkiDoSFACCGENJhGiQW7Riy4MiiKBe9LdwT7\nPHSmW1qvFYd4iSASqUdoZANajCqwR1Vse7z2jSv4DQB0SxKxeNtjkhnVhe2dToQYzk/kVFODKhw7\nBiv48gITeYG4yogSOFZItONRh2gtFitJixG1JhH9F3N/bUXiAgFVC85jr413Har0+yPn7g7Wffjw\nowvLZ+4+uOF6PZp5VxBCCCEEAA0BQgghpNHQECCEEEIaTKM0AouDbYXl5cFcYdlqCIC4BDTWJ9lz\n7KsF4xevK3mFX8/kkqPEYP3MXsASi+eftfUMvMAsJX7dxNtu6hnUpO/wsOcQo/nwypT57mOC4cTc\nk37gmMlFx4pps9UjxOgcOk6CIRsUpqpeIoZgTIm4BW0gM6uN8JjktQPGm8SnDmL6ywso14q4V2xP\n2ARDALA2KL6yE6dMFfhFgBBCCGkwNAQIIYSQBkNDgBBCCGkwjdIIWE3Aof5CYfnUmcVgn5i5zcE8\nUg271foXY/CSrthkJKP0U047Mf66Qcnl87a3R2QeV5knH4vtC3tPDiKS1vjJb8yKEd5u1pcfo2vw\n2mypkmhnvDED6rkvrB4mSHQGP37DNNF3YozMjEjzZJ+RuZq6xtMlJRFaCBvTJHHO22oE9qW7Ntg6\nH34RIIQQQhoMDQFCCCGkwdAQIIQQQhoMDQFCGkCML50Q0kwaJRZM1Qqq2sdcBoCuk0DIEiYICetJ\n0TdtcQbm6dbx1EZdiZKs8MkLoOIF9xjGDzgUI1IzyZ+coEi2TIxQK0akVlXIFtxzppq6RGseQdAo\n51BWTBkTbMZNOmRWzbds0KZq/WePNU7hXVzKnPL21SWCrK+e0fwW9YTWVfaxz7Unzi4TJANxz9a+\ndL6wvJhuC8pcsBAmIqqDsX0REJG3iMheEfnK0LpXiMgeEbkh/7t8nX2fKSJfE5FbReRXx9VmQggh\nZKszTtfAWwE801n/R6p6cf53jd0oIm0AfwbgMgAXALhCRC4YaUsJIYSQhjA2Q0BVPwHg/gq7PgHA\nrap6m6r2ALwbwHNqbRwhhBDSUKZBI/ASEXk+gOsB/LKqHjDbzwJw59DyXQCeuF5lInIVgKsA4Nyz\niqd3f7qjsLyUFgMMHUyLAYYAYGVQHsyipzZBSLhPjB8phsDX5NXbEK1BDJ2ShEHzMYF2agv4Mj7B\nnj2rGB9lTNATj5ikUTHYNsboaGLaXJc/u1PTeY6KhSCZV3mirriEX47+ZUTJgkYVPMgNllXheYyp\nZ+DoymLEugutpLD8+eXzgjJ3rp5YWH7eadeV1hvDpO/sPwfwUAAXA/g2gNceb4WqerWqPk5VH3fq\nydOdhY8QQgiZNBM1BFT1XlVNVXUA4E3I3ACWPQDOGVo+O19HCCGEkONkooaAiJwxtPiDAL7iFPsc\ngEeIyENEZBbA8wC8fxztI4QQQrY6Y9MIiMi7AFwK4BQRuQvAbwK4VEQuRubpvh3Az+ZlzwTwF6p6\nuar2ReTFAD4EoA3gLap6U8wxFcW5yHt7xQQNB5PiPM2V2dmgjl6EzyqxCV+cfXrG5qo6Z9v6ozz/\nZ8wc93Hhta/KuXu+zJbxxXnzptsl7mEv9sA4qWsuelk9Mf7QbsTc61HOnU+MH7VM3+HtUxfe/dav\nkDjMwz6fMddmPiK52LRrGKaNMDFXtXvJxirxYpPEjHlWW+DGtUk7hWVPj1aFsRkCqnqFs/rN65S9\nG8DlQ8vXAAimFhJCCCHk+KAJSQghhDQYGgKEEEJIg6EhQEgDWKsQe50Q0gymIaDQ2LABhHqD4umv\nmO0AsDIIBYSWxIg8utoJylghSIxAKEpgUlF0GJPQZbPhWbVlAqp5Z3uMaG5UxAR4cctE3AZlxoCX\noGmcvxTsM9F1xHm7zHLXEQtaAagVONYVAMkPLjMaoW4nRiy4CX/XTXIcqnJkb7y14/+i885YkG5p\n3V0tvo/2r+0Iyjxix97isZzERFXYfHcOIYQQQmqDhgAhhBDSYGgIEEIIIQ2mURqB1bTou1npF5dX\nHd9OGLAh9FsuG03A8iDUGnRbtquToEwMVTUBdWD9eV4ykkni6QHK/Kbe9sQmEXH6vIp+w9tnXH5d\nz5dusb5OAFholQewqgvry6/aZhuIaJRtrkLMfWH7IuY+sQmFPA3DtD2zMdQx5nl12GRxMXjaLhtA\nyAsotKLl/b6nv7uw/Mgd9wRlDvS3F5bv7VvVTDU2311BCCGEkNqgIUAIIYQ0GBoChBBCSIOhITDE\nShrO/ydbm2nzH48Kz29JtjZWM9BkVmpKGLVVaZRYcNmIBQ90i8EYzth2KDAGVtQK/1aCemeNgDDR\nsFvtQBwnNgtDXthsa3M1Pey2PaN8QdZVtx3ovIA4MYOhbY+1jj3RVcwpxARLqUv8ac8hFDXJ1BsD\nts0xAiuPUWZILKPK9XTvL0PMM2OFgAMMRmYM2KBMNqNiVaqOi+G5h/VYY8DWUvV5Tcx96onFO1Je\n993JiYXlxXQ+KJMaceyh/kJpvTHwiwAhhBDSYGgIEEIIIQ2GhgAhhBDSYBqlEbCJfyyrjliwFeE3\n6qEYdMhLVGR1A6mWJ6Hwk5rUE+ymDD/IycbxErxYf2JdQU4833BZ3a4PNaL7YvyJ9vp517MujYel\nip98TsoD24yTGE2DDR4EjE8AOsqEX/auraJ12XppxeKxfRETPChGC+SVsQHlEmekjElet2K0Bcv9\nUGuwZHRuuzurpfXGwC8ChBBCSIOhIUAIIYQ0GBoChBBCSIPZ4hoBLfij93eLCRsGxgG04vhkDqZ2\nnmbo2+8OZsxyqDWwyYti/Hf+nNXicsfzU07RdPG65hd7WP9/y+mLMn+xpyEI4xM4Wg27zjnMJBNE\nWdz7xDDr+KG9JCujIjWHmo+Yez3vtNlev3EG1qmiHfH26IiNbRGTdMjMpXeTDm28Xo/EzMnfjIG5\nvIRVZXjXyuq/Om5iOqsR6AVl7jcJhaweAADuWS0mGdrRDuupAr8IEEIIIQ2GhgAhhBDSYGgIEEII\nIQ2GhsAQZXEGCNmseL50srXZjH57Mhm2uFiwSH9QtHu6iRH1bQuNARvkwWPFCEE6EopFbJCJGBGW\nVyZMXhQSI1gq26euID/jZJyisCSij2PKjArv6pUZA3NO8KdxCh7bpnnlIVj8Nq9ZgWpNt4V9JlJH\nFNaKEJHG3BehqK/aSWwFYyAcz8pDm9n7NnH6oWeuZ8x18cZkKwS/IzklKHPB3B6zJnz1tiuMF/t7\n28sLRbD5RntCCCGE1AYNAUIIIaTB0BAgpAHMS5VMEYSQJrClNQKKoq9ouVf096/1i4NjbxAOlomW\nD6DLRkfQ1TCgkA0yZIOnePgBhUwyjUanFinHS3o0jOdDDdd51yFCIxCR6GRUeHqJMmPASzA0Ko2A\n52u1x/f8/5ZORECouojR3kRpRyLunUkme5okXh/HBO+y2IBHA+c2tnowu49fb7huRYvjv6sR0/JX\n7QkzxQRC/750elDmtv0nF5YvfNA9pfXGwC8ChBBCSIOhIUAIIYQ0GBoChBBCSIPZ0hoBoOhz6ibF\n0+2Z5cO9MGbA4mC+9BhWI7CUhvsstreZdpUT+MYQahYGEYlZ/LoHZtn64bx6Jyc48+Ma2MQn9di1\nMf7ZpEIciM4E/b6dCH97nF6iGvZ+8/o47K+YRDthPWvG1xtTT13EaCrsvVOXHiCMczDKhF+Tu5e9\nRGatkvvbxl8BgJ4ZzxL0S48dk6jI05W1gmsRtnfRvDfuX9sWlDn9hMVimW5Ypgr8IkAIIYQ0GBoC\nhBBCSIOhIUAIIYQ0GBoChDSAzZg7ghAyHra0WFChBRHc8kpR1CdSFO2sJmGak6V+UcDhBbwY2OQV\njljECkG6Wj4we4I0K3DxEp9UCcBB1scLfuMFFikrY5PqjBJf+Hfse84T3sWcZxViAgrFBAbyzmlc\n4kA/4FeEiNQU6Tinaa9fWWCsUVIlidmksdfGEwsmZgyOEfN69RxMFwrLi2ko4Lu7f6Jp34GgzLX7\nHlpsnxPg7tBKse7ZTrnAMQb+TCCEEEIaDA0BQgghpMHQECCEEEIazJbWCABFX5GmRf9OmpqkQ2no\nk1kZhLoBy77+zuI+abhP0i52tfVPeXj+2e7A1CNJUKZKophgH6+KKdMaWD9qlfP2fK8tEzTEC/gS\nE1BoklQJUuP529vGP+z1sQ3wUhbcZf3jl7cn3CcmMNH48LQPFqsV8YI9jSpx0qiompzKCw5UV93D\ndJ2kP/NS9K/HKCG6jv7LJpTz3hkxgenUjDtrSdjmw/u3F5Z3nbJcWm8M/CJACCGENBgaAoQQQkiD\nGZshICJvEZG9IvKVoXV/ICK3iMiNIvJeEdm9zr63i8iXReQGEbl+XG0mhBBCtjrj1Ai8FcDrAbx9\naN1HALxcVfsi8moALwfwsnX2f7Kq7t/IARVAMuT5SVeKvhyZLc7BHzgJJRb75b6dQ/3iPFIvjoCd\nf3p4ECY4snixBrpaPIdE10rr8Qjn2RaXXd9rTb7gzYZ3lt7c77Iyk+ytmCQxo0wkY+83z+9r/eJ1\ntaeuYEo2PoeXFCyGSSafGhX1JadyNCgR907pPs7Yvm+wq7B8Uuu+0no9rYEdkz2N2HK7fLz/1t6T\nCsvz23pBmbldxfF+ebm83hjGNjap6icA3G/WfVhVjyg2PgPg7HG1hxBCCCHTpRH4KQAfXGebAvio\niHxeRK46ViUicpWIXC8i19933+aLiEUIIYSMk6mYPigivwagD+Ad6xS5RFX3iMhpAD4iIrfkXxgC\nVPVqAFcDwMUXzU73HC9CCCFkwkz8i4CIXAngWQB+TNV3uqnqnvzfvQDeC+AJY2sgIYQQsoWZ6BcB\nEXkmgP8B4PtVdWWdMtsBtFR1Mf//MwD8dkz9imISEOmJ2V4U9a31wu5YTcvDkayaABJ713YGZXa0\niyKPtnhuC5u8qFwsaJMQAUCK409EUUcQj3FTJdGOhxWtucF5IrrHisK8Kz6qfh6V8C8mYE5VqrTZ\nCwjVdoRh4yJGCDgv4TM7zXjPUBoRaKoKddWTBMJmL8lVsUwSce3s+AsASyah3FIaCvhOMEGHvEBK\n7ZlyV3a/V7x3Bkk999I4pw++C8CnAZwvIneJyAuRzSLYiexz/w0i8sa87Jkick2+6+kArhWRLwG4\nDsAHVPWfxtVuQgghZCszti8CqnqFs/rN65S9G8Dl+f9vA3DRCJtGCCGENJaJawQIIYQQMjmmYtbA\nqBgosDzkGmr1inbPwPiIemuh/2fv6o7Csufbua9XDCi00g8DSlgdgZ+Eoujbjwle4ekIYvxs9tzt\nPlWS1nj1bgU837WXKKasjPVbenj3lw3cFJOoxeL50mPK2ARMnkagyv3mHt/0c0ybPWy/h8eu5leN\nOc8q94UXRKeuIEiWqn1aBdvvdZ1TlTFmFmmwrmWuZxKhLVl2AsF95J5HFpYfvPNAUGZbO0wOZ0mW\nTcC7nc6ztmbeCUldQbcIIYQQ0lhoCBBCCCENhoYAIYQQ0mC2tkYAJnFPiTsl7YW+w6VeeVKHpaTo\n71/ph1qDFROP4PBgm1PTYmGp5yQvGqj1O4eXMNXuek1dF+un9ObdVsHzq1qfu+fzG5WPtAqeXiLK\nF2zjQoxRP2FjIdSFdz1jfLZWH+H5xedG1GZLXToMr4/tNfcI7m03psjxU5cewLu+feNzry2xU4QG\nxU32ZC6FbbEXbyVGb2VZcTQCF520p7C8v7cjKNM3Y7ntPwBAq3he/bu2h0XMuFxXyIzpGW0JIYQQ\nMnZoCBBCCCENhoYAIYQQ0mBoCBBCCCENZkuLBVO0cHAoIcTMYlFZ0d9pBEK9UITST21wkrDM/WtF\n4V86CO2rAybokCfys6xoGJgoSDrkCQpLaw4FN0kQUKha4JitgBU+2cAjXhmPmORFdSXxqSsgVBWs\nEHCbc+hRJisaFzHnECPSDANUVRAYTpj6ggOV9+nyoHh/zbXKA0L1zPh2f7oQlBmYc/AEhZYbV84J\n1n3+vuK6U7ctB2Wu239uYbl12nVh5UvFd0KrFxbpby+e18zSJks6RAghhJDpg4YAIYQQ0mBoCBBC\nCCENZmtrBFSwqEPBfoxrrr1qAtvMhf69Xlr0wXjBNZJBsUySlgcCOuj4rIBisgrPN72YFoMXDWaq\n+Z3DIB0RddTkdg792ZsPLxFRWMZqDcJ9bF/EJfCZnL/dD+ZSrkpZMzqCjuNLrysIku33RIvBW5xH\nJiCmj73rGacdMboj9RLijE/jMU3Udf8npv+8sbQ7KOqtDqZekLfULIXX1yYZ8pLOWda0H6ybPW21\nsNy/0wkoZBLn1TUU8IsAIYQQ0mBoCBBCCCENhoYAIYQQ0mC2tEagpzO4vXfqA8st45YZGP+KJKFf\nbnmlmGTC85HuXyz6cmbaoc90ab7oN1oyvn6PFQ0TXNikF8tOEgzr74/B+tQ8L1dMcpmYfaZpTrTf\nlqJfcFQJfDxi+rjKdRgl3YgEPXZet6cRqIuy/onzQ4d12P18jUAzfft14Y2viyZWys4KjnEbfwUI\nY7AkjlppgKSwvOBM7r9/raj3Wk3CY23vFPfrOrqQfmL0aHPhPdheLY5XbSfWQBWmZ0QmhBBCyNg5\nLkNARHbX1RBCCCGEjJ8o14CIbAfwKAAXDv17IYDtAGgMEEIIIZuUUkNARG4H0AHwVQC3ALgZwBUA\nLlbVvSNtHSGEEEJGSswXgX8AcCmAN6nq3wCAiLx0MxgBA7SwMjgqe2slQYECMgiFPv1usYs8oVHf\nBBDqzIRCkOWkKL8bbtfRuosNOuwICjtSrNtLXmSFfx6JOZYVTqay+ZPEVCUmKYwNChNTj5cIKAzs\nVB7IyStjA0CFcqVqBEJJp3lJhVsl5jzrIgzaVC5udNtnqCux0zgFhqkRdrYi7mOPOMFqeagwW49X\n60CL/WMDRHmsmCBvnljQCq9nU6/ebmHpsBN06Ov3nFpY3rWjG5Tpm4By8xL2zcw3i3UnOx2x4JoZ\nU8JDVaL0LlDVlwB4FoDLReRzInIZaotnRAghhJBJEmUOquodqnolgCsB/AyAB4nIk0fYLkIIIYSM\ngQ19F1LVm1T1hwA8GcCvici/jqZZhBBCCBkHlQIKqepnATxNRJ5ac3tqZW0wgztWT3lgub1S3J7a\n+Q6OX1z7JoGJ48Xqrxl/lIT+qG6nGM1oJS1PTGF9WNm64n5eQKFEy32O1gfaMzbhnOOHC/ymzmGs\nD9LztbYYc2Vdpj3pkEfMr4nZMQZlKiNGn1A16dA0YZ/FSR8/Ro9gA08BQA828Vu5RqBlxnKbYAgA\nDpnEb1Z/5bHkJBQ65YTlYr0robarn5qkc4Mw6VDv1OK62X3h69k2sb22blM3xHHFEVDVj9XTDEII\nIYRMAkYWJIQQQhpMtCEgGT8uIv8zXz5XRJ4wuqYRQgghZNRsRCPwBmTTPJ8C4LcBLAL4WwCPH0G7\namEtncG/Lx6d42lyTARJiFrd0C4azBpfk+N3G/SKFfc8H/321cLiwWQhLGNYHIS+pgP9YoKjE6zw\nAUCi5fZdYnygdp9ERudfDOcgl8833ozYWAOtCO2Gp0GJKTMuf7WXgKlc7RKXZGhcyaiq9nEMcfEl\nimXSKUsiVQVPdzETcUva/bwYKHZs6kbEeOia+Cqe3ioxL4Rvrp0alAHuKSwt9sMx+Z57i2IzcZLO\nYaGYHajt9M3CHcU2r+0Oz7OzVNzRvsOqshFD4Imq+lgR+SIAqOoBEYkZAwghhBAypWzEBE9EpI08\nmJCInAo/EBQhhBBCNgkbMQReB+C9AE4TkVcCuBbA742kVYQQQggZC9GuAVV9h4h8HsBTkc26/QFV\nvXlkLSOEEELIyNlQQCFVvQVZBsJNwVp/Bt/cf/IDy9tM0iGbr8cLztBPi+KMFScxkZoy4vTqSq8Y\n0OJQEiavsAE4DiTbgzIrabEeL+nQspNgw2ITxVhxzbwTUKhKIBtvn7qStYwLT4g3KmFbEiGE8oM0\nTa5P5yIEcp1AIDe5oEhJRKAdr4+tUNITTtZFjOhwXHiBiWz/1BXkanHgJFEzY1NMwLSuqcdLOrRn\nzUaUC7HnfvN9pwdldp1YDCi0tBgKCntrdtwOj9U9pbhyZtkZd3rHXq5KTBriXzrWdlX9w3qaQggh\nhJBxE/NFYGf+7/nIpgq+P19+NoDrRtEoQgghhIyHUkNAVX8LAETkEwAeq6qL+fIrAHxgpK0jhBBC\nyEjZiEbgdADDHolevm5q0VSwduhoIAnrlZeIYAytXtFPs+z45MXoBtTREawlJsBFv9yPf7gf6gj6\ng2IQjENpWMbTDVi6QZAO68MyggrU59e1/kUvoEpMgpLNhutTNl0a08c2GBQAtMfkc/f0Etb/79Gx\n13OECXHCgD1FvUvMkb0ynU2mbRknXgCmuah72SQpc15JVr9kE6R5rGgxxM2hfhjAzSYZuqd7QlDG\nah92zXWDMt8+tKuw7A1daVJc6Wkh5u4z7xFnGG8bTcDMaj3P/UYMgbcDuE5E3ots1sBzALytllYQ\nQgghZCJsZPrgK0XkgwCehOx3zE+q6hdH1jJCCCGEjJxoQ+BIsqEhni0iz1bV3665TYQQQggZExtx\nxC4P/aUALgNw3gjaNDFiNANeIqCAtfIkOou9MAmGZSmdXCqHXk2JgCY5X3wzMu1+6M0WA8IjZtCb\npiRJm4FxJb2qyprjk7ecs3CgtMwg4jzT3ua7LzbiGnjt8LKIvAbAh2L3F5G3AHgWgL2qemG+7iQA\n70FmUNwO4LmqGlwNEXkmgD9BlqbuL1T1VVEHHQjai0dPsRXq3wr0ERoDrSS88NYYkLXihde5QWAM\npPPhzWGNAS8ohzUGlpLisXd3wuyDe9OdZs1iUKZrMm9ZseBOrAXGwAAlHQj/HKwxMO2DxjixfZFC\nS40Bb/s4+9QaA6MMrDMqqhgDnhFUhzEwTcGDYvGe8yr3oK1n4AQL6hrhX4wwdtnJNmiNga8cPKOw\n/JiT9lQyBtotJ+CSMQbUiAW/1T8x2CfZUVyeCYf2INtgOlfPs3c8d+ACgLM3UP6tAJ5p1v0qgI+p\n6iMAfCxfLpAnOvozZF8gLgBwhYhcUKXBhBBCCCmyEY3Al3F0slMbwKkAfid2f1X9hIicZ1Y/B8Cl\n+f/fBuDjAF5myjwBwK2qelvejnfn+3019tiEEEII8dnI9MFnDf2/D+BeVY3wqh+T01X12/n/74Ef\nl+AsAHcOLd8F4InrVSgiVwG4CgDaJ4afXwghhBBylI0YAj+vqoVf6yLyaruuKqqqInLcyjJVvRrA\n1QCw7YxzdP7eoz6UQAxo9HCehsAmIjrsiAWlbwJBtEK/zaBf9MIs90Ih4MAE17h/LUw61E2Ll+xg\nEgbK6A7KgxUtD2bNctGntrsVOqi8RCxleL7EuhKUxB2/2KeTFHh5x27bQCwR/mLPJz/OPrXE9OmM\nedhGKSK119wSo2mICZLUZOz18xI5DWTjyZ285EB2bLL6JiC85nafA05Aoa4J6pYMwmtu6z3cDcf/\nNZNQSPthPZ39xTKDiPvLBg8CwnfY3OF6AnNt5G5/urPusuM8/r0icgYA5P/udcrsAXDO0PLZ+TpC\nCCGEHCelhoCIvCjXB5wvIjcO/X0TwI3Hefz3A3hB/v8XAPh7p8znADxCRB4iIrMAnoejiY8IIYQQ\nchzEuAbeCeCDAH4fRVX/oqreH3sgEXkXMmHgKSJyF4DfBPAqAH8jIi8EcAeA5+Zlz0Q2TfByVe2L\nyIuRTVVsA3iLqt4Ue1xCCCGErE9M9sFDAA4BuOJ4DqSq6+3/VKfs3QAuH1q+BsA1Gz9o0e/f7hX9\nUTpT9BXGKBTuTE52j1PGoF/0a631w64P/GVpWMbudygJkw6tqfVHhX6kRS36uqyuwJuHO0CYcCMs\nY5KIOLqClunoGP+2dw4x+9UTFml8RCXwccqMK3CTN1d8s8WFqJQkCdU0MtNGFS3JKPUnNoFWz/H/\n27EpccpYFgfFcfHe7q6gTGo0Ad9aOSlsn9E+DJyEcjbJnCThvZOcWhSgfXrp4UEZGzfA6tMA5x1V\n06UpNQRE5FpVvUREFs1hBZnGL+xhQgghhGwKYr4IXJL/a8PVEUIIIWSTwzkyhBBCSIOJcQ0ccQl4\njsAt5RqYWQX6ocudELKF6EjLnfdOti6He3PYNes43QmAONfApnUJtHvArm8dfeAHnaIt03eEFjOr\nxWUbm+dQGloKM6umXk9oZISKa0nY9YkNipGEQYfUJOXwBIWLThvLyliBYeLI7HoRYikrqPKG21GJ\nj+ONZncAACAASURBVEYlWhtlUhjb5phgN9Mmzovpn6CMcwuEgtDRST09MeAwbpAkscGpRpOEqCpl\ngZRi94k5B/sMW9EfEArttjm3bWJ28wIK2XX3pCc4LVoqLK0MwrHzsEnytnOuKH62ImYAODgoRvBZ\nWXUCwdlss2nYupml4jh90sxyUMYefuDc/rNrJoHb8cb2zdlIroF5AD8P4BJkj/EnAbxRVcul5IQQ\nQgiZSjYSYvjtyPLZ/mm+/KMA/grAD9fdKEIIIYSMh40YAheq6nD6338REWYAJIQQQjYxGzEEviAi\n36OqnwEAEXkigOtH06x6kIFiZvWon2pttuh0sQGGBjOOz88kfrhjNQwoZH057a6TFGauuC5ZczQC\nxqe2moT+MqsRWOmEZe7vh8mKLIsmedLBtJiU46R20ecG+P7+sIwNEOIEFLIrpsvlHZA6wrJWhF/c\n+lpbTg9aTUCMf7YjofNwRYsBS1q232vq4xgNwzjr8bA6lTY23se+DmNzTbIaZSCgrtrAYWGZNCJC\nW2LGMzsOAcC8FO/tVMvvnaW0OL4t9cIAabvni4Kwe1d2BGXsE2uTxwEAesV1kobts4np9qztDspY\n2YDr/7eP9aCea7wRQ+C7AXxKRL6VL58L4Gt5HgJV1e+qpUWEEEIIGRsbMQSeObJWEEIIIWQiRBsC\nqnrHKBtCCCGEkPGzkemDjwPwawAenO93JNfA9LoEFGivHfXytNKiL8cmkPB8MmbqMPashL6dttER\n9LeFfhvPb2Sxc3GXV0O/VmemOEk1SUN/8VIa7meZM343m8jDSzrU1XIfqY2FkDi+VjsTt8r8Zw/P\nJ1rHTPRRxhGwVI0RYP3glhidg1cm8LeP0LcfHrtam8n6VInV4D2f9n7z5pDHaBSWtfgKaju6ghUj\nwrIJhfK1haW7uicWlr0YAYtGN+DFdrG4GgHj/7d6ACCMEXD7cqg1M7IGzBwID2XfNeKJMyqwEdfA\nOwC8FMCXEacbI4QQQsiUsxFDYJ+qvn9kLSGEEELI2NmIIfCbIvIXAD4G4IGgzar6d7W3ihBCCCFj\nYSOGwE8CeCSADo66BhTAljEEJAV0dOHNCSGEkKljI4bA41X1/JG1ZAyIEQNacWDayYyBwj5GDbHP\nCTphy7jCQCO6UqfMihEv9h1hihjVycARia2mxSBDnqDqkAncsWIEhivtUCyYRIgFg6RDEYFG7D4A\nogLgWBHTJBO+VMW2OUaY6Ce7GY+Ir64+9uqpSzQaHssGFCrvK/c6NFSY6D2fy2aVFfQBwE47mDp0\njVjQSxa0YoTLqXPv2DHOjoHzM0VxNADcfu8pheX2TNjexUGxfZqEx26ZsdwLKGffNV/6xjlBmV0r\nxWWv+1peprwa2MhT/SkRuaC8GCGEEEI2Cxv5IvA9AG4QkW8i0wgIgIGqXjSSlhFCCCFk5FSNLCgA\nzgHw8nqbQwgZBQPo2NwHhJDNxYYiC4rIY5ClH/5hAN8E8LejalgdSF/ROfDABAf0dho/lkle4eXI\naBnX0v2LYVKMttUeOL4dTYrHSpPQp9Y1SsVBGnpudKboC1vuhT611TRcZ7EagbAtYTIj68/zsEGR\nvH06ajos4v00ycAxVZMOTRIvmEtZgJdRJqkZFTHnSQPo+HD72KzyAvbYscCjDasXCp+rQ2kxgNAp\nVuzlsJQUdQX3HN4VlFlYWCss953xdm8aasIs9tRjAtOdfNrhoExPipoFTw9g67b1VqV0ZBeR7wBw\nRf63H8B7AIiqPrmeJhBCCCFkUsR8EbgFwCcBPEtVbwUAEfl/R9oqQgghhIyFmO+bPwTg2wD+RUTe\nJCJPxdRnkCeEEEJIDKVfBFT1fQDeJyLbATwHwC8COE1E/hzAe1X1wyNuY220EzPHvWN8ieFUU7Q6\nRZuntxjOr1+wmgDPb2PXJaEtdd+g6LcfODqCftvMl10Lffk9M6fX8/GtGB2BTTrkzef1dAMW08Xo\nOUlNUhQ7rKpvOpjf7DrMpjtCVBX/tTfH3SaBGXixGUZEXbEF7PX0/M6WmNgDNlFSXUmkRpmMyupS\nqmhSvL6xfZw6ZWKO1TPX3Isxkmp5HIHDg2KmHRszAACWTDaexIlZYMeQmVbxvE7esRzsc2C5ON6m\njkagbcYUWXNiu5ix3Au3YmUNB78aJh3aad4/ntbMxqNp9eoRCUTfXaq6rKrvVNVnAzgbwBcBvKyW\nVhBCCCFkIlQyaVX1gKperapPrbtBhBBCCBkf0z0HihBCCCEjhYYAIQ1gVHH8yfTi5vAgxGEjkQU3\nHwLo7FFhSZAcyCx74oxWzywfDrvMBnnw6hmYhEJwklfcZ4JXaD8UkqkJgmSXAWDvarEe7yVwX7K9\nsNwxnbGjXQy2AQDLagWEvaBMV8tFRIlpc1pRLGgFQlYwtxkZZeKkMmNglMZCeF7lQrKY9ozqZedd\nB09YN+0EScAqPGuJc94D81x7gcMWI4KAWQGyJ1K2HOiHwdASI0w8uFYUGB5aLS4DwFpSbHNvNRRD\n39PfXVieWfaSUZnAdM5pd4xWsfuwUJne+nrx3FtWeY0weFF7bcxiQUIIIYRsPWgIEEIIIQ2GhgAh\nhBDSYLa0RkBU0eoO+WIGRR+Q9cEMOqGPWYyPbWbRKWPcnV5OjKCM46qziYDE0QikvWIwjXQm9BGt\npcXLmji+usV+0Wc2a4QO29IwsMeyCfYxQDcsY3x+XhCiRIv+sRhfcIxv0/MXW7/uJJMFeQFoxpVM\nybsHtlnZipdcaYK6i5g2x9wXdekuRhlAqA6q3EtVnysbKGxxEPrgdxqBlfecBxoBJ2Ha4aRY97Z2\nqE1aMYnMuv1ive2WkxSpW/76u3n1zMLyYC6sp71sAlaF8iorIwiS0AHlGjYAkNQcvyaNzHTf2YQQ\nQggZKTQECCGEkAZDQ4AQQghpMFtaI4CBorV81GHT6m8rbjZJhwL/CxA4d2YPO8cxu7nJi4xuwPP/\n7+vvLK5IHf+snYPfD2251aToH/Pm6ffSY1/6VcdX5yUEsXQHxXo9jYCdc5yq41QzuAlUzHlN0p89\naUI/eLG/YmI1eGXG2ad2vrqnEdhllr02b4V4EnXg+f+rxOyIUR70nDgCXmwBi9VFLTnaJBuLZLm3\nIyxjzitJixqGbi9sixjdgDqxXQ4mRrfVi/DtOyEyZoycqr0cJk6ymjVPI9DuFldqu57f8vwiQAgh\nhDQYGgKEEEJIg6EhQAghhDQYGgKENIAqMeYJIc1ga4sFDdI34jIj6rCCPgBoG+GfFyzCjrEa6kCC\nIEPt1VB08u/Lpxf3ccSCg17RdkslPFg6KJZZc0RXKybgxsAIrFInuNJiGgYNsVhxoA1CBADbpRgQ\nJHECE8VgX25VXnaeCNHWM0rB3DiD1Ey7MWBFfuUSUp/NJhodV1ApIBRgDjxFmqHnBK2xAj5PSGyF\nwx5dE+RtzdmnPyiOcTNOm7tGRN03Y+DKYvnYhV74LN61Wkw6JDZ5HIB2heGrvRIeywav85IOacsG\nL3JeWhXgFwFCCCGkwdAQIIQQQhrMxA0BETlfRG4Y+jssIr9oylwqIoeGyvzPSbWXEEII2UpMXCOg\nql8DcDEAiEgbwB4A73WKflJVn7WhykWgc0d9UK2+CcawVvS3yGzo/7HBgdprTiIgE3vH0xrEJJS4\nf217aZlAN+D4rNK0aN91HR+f1Qj0jc9vx0zo87OJRTzfpi3j+g5bq4VlxxUW4CYUsj41J5PTtPvF\nq+An0UlNGTnmcvVjj8//3pHyY3nBg9py7HOvKwnRtGHvdS94kH1ivefKdmni9LHVAnmBw1a0ODCm\nGjrT701OKCz3HYHVwV4xENyhXujvXzTaguVu8did+XBQTpbMwG0zAwE40C0e25VUmN28gHL2UrRX\nwyJB0LlBeG3susFMXc/1dPFUAN9Q1Tsm3RBCCCGkCUybIfA8AO9aZ9v3isiNIvJBEXnUehWIyFUi\ncr2IXN/rr4ymlYQQQsgWYWoMARGZBfCfAfwfZ/MXAJyrqt8F4E8BvG+9elT1alV9nKo+bnZmYb1i\nhBBCCMEUaASGuAzAF1T1XrtBVQ8P/f8aEXmDiJyiqvuPXaUCg6NOHTep0HBpz90S+H8cv5vx03jT\nZ2M0AgfWtoUrLTZRhhNrYC0x/jLH79bthz69wvY03H6oX25YHUyLOgfPd2gTlCRuxxfxfP020Uh7\nC+oBYinz3XcibP6YZD3j1FzEtHmzxQyoihfvokzr4F0rGxMgiYgj4GGf65bTvjCGSPmE+1Vn3Jlp\nFeve2QkjTNhn394V/Z4T3GXN9J/TFfceLiaC8+LIBJoA5xFp98yy0xXtNXMOnnzDag3WnAxHFZia\nLwIArsA6bgEReZBIpgASkScga/d9Y2wbIYQQsiWZii8CIrIdwNMB/OzQup8DAFV9I4D/CuBFItIH\nsArgeaqe3JUQQgghG2EqDAFVXQZwsln3xqH/vx7A68fdLkIIIWSrM02uAULIiLBz6wkh5AhT8UVg\nZAwAGUrKIGlRDdJKisvtxLGLzAA65yWCaBfLqNOrA6vpcBwb+w7vMDs5g7dNjDEXKlzSpCiMOegk\nC+qboENLaVHYs3suVLPYhCCeGKltxEdrjvjHBhnqRdijXnAUq/30ylTRkoXCrLB9tsy0BanxXvxl\nxkDHSYDkBpwZEVWEfx0n6da04wn/wjJWCFtXvcc+jkdXw/siMYPcmiMKts9+H/cHZQ4mRQGyJ1K+\nr1ss03LafEvvQcX29Yrt077zfBrhdWs17OWWKdOPuEVtMjsgDAQ0uxRWFGimnUvTsuLAEgF8LNM1\nehFCCCFkrNAQIIQQQhoMDQFCCCGkwWxtjQAUSI/6VMQkHYJNWtPzggWZIA+OG876dsT1ER17GQBW\nDxV9+W2nnpaNgeEEFLLrFjXUCKz0igk3di8Us2AcXHMSe8wV13k+ye6g6ONbGcwGZWygka4nqjAk\nToIjmwwlPFKc33QrUkWz4O5TMeBMHcT4/z1dwVZINBXetxvXQriJukx/xWhAEkcjcDA1vv2BE4DM\nlPGOtWQyttlkaADQ6xfHB3Ei7dgAR/ZQ6jj3xWiw3CRv/1ZMitQKh8VgvBcn6Zwafc7MangOrb55\n1zj+f3vqMqjn+eQXAUIIIaTB0BAghBBCGgwNAUIIIaTBbHGNgADtId+adRzZedWOD8v6aWyCIQBo\nmTLqzf83Vbd6YREbI0Ac/3+QP8hxbNlERHcnJwZlUhNHYNloBmQu7AubEMTz+S0Oik60xEl4ZHUD\nno7AYhMMZXUXzyF1+iJoY8w84C1oH8fM0ff97eXExFSootVoTkKhejQN9l5fcZ7Prnke5z1Bk2HZ\neT5T8+zZ5x4AWuZ5TJx7YKVf1AsNnARkM0YsdWA5TH62r19MDjTw4gYYJLHjf1hm8TuKDv+FO8JX\nZoz+q92z7xGnPTahUG98+pytN+IRQgghJBoaAoQQQkiDoSFACCGENBgaAoQ0gLaTR4AQQoAtLxYs\nYgMKBUmIvOA8EXqNVmL2CWNiBIkoHA0dWsvFlRE6HsBps1XE3d/fEZSwYkG73E/DBh7uGSGgI/5Z\nchIcWWzCEi+g0AA9UyY8TysW9IIO1ZF0aKuIB6fdGKiSIdE9J3MfTPt5jwobPAjwnplwkLH3vw3W\nA4QC36V++Nx3zKDnPZ99056eM+7YsciKBwHgy4tnF5bVCq+7EQGZvHhaVmscEyzOG7fNpZhZcw5v\nAgp5+trgHWaD5FWkmU8IIYQQQgDQECCEEEIaDQ0BQgghpMFsbY2AKpAMBYSYL/q6Wr2iM2cwV+5H\naidOYBvrivN8OxFBJ4LkFU6Ai1bPHKxVrmvYn4QaARtrpNcvnvtsJ7QRe4NiGc/nd6i/rbC84ERO\nWpGif7GrXkCh4n6JoxHowbYndM55OoZhUk9XsAkJ/OAVzsvzpQ8iktKMiqb69j28+7Rl+scGJvKe\nGUvXSShkWdG5cJ1JHOYFDkuMb7/r3Es2ydBq4iQpWyuuS52AbUv9sI1ltMzAHQQYAtBaKp5Dy0ko\nZIe4mLG95bxHguR1XoC7pFi5tusJusUnjRBCCGkwNAQIIYSQBkNDgBBCCGkwW1sjYLHzlM2y2Hmc\nzjp1kg4F/h+nHjX+p9SJNSDG92XjEwCAcdMHfiUAQfKiO1edpEM9Mzd3xvienIptQhAvqcmal03D\nsNAuOtUOu7EHlgpLNlkKAHTNsebboQOvSkKXMFGR52+PmJdMNkSVeA3ePmmFBEeTxJ/LX7wHrR7A\nrcect40ZkK0r3rftiOdjeeBpBIp+e++5t8dacdpj4wZ4/n877vT74bO3Z/GE4gqzj/sIB0l+wiJi\n64mI7eL59oMybowAs59XjelCWWMcAUIIIYQcJzQECCGEkAZDQ4AQQghpMDQECGkAWyVfAiGkfhol\nFpSeEZPNm9P3AjhY/YYjzmv3ioXS2fIgD57opG0TUcQEJnKSDlmh3/1rC2E9rWKbB0ak00/DF8dK\nYgMBhWWWTWCPgRPwotsuKiXXnKQmNoDK8iAMNJIEAYU8cZQTAWS4fY4ix65rO8lbbPtixFxeUJhx\nBs2ZJmPAJrYB6mvftAciGlUQq8SMXzbgFgAcHhSFuWkrzH5j29d1sqitpMXncTUNn89BRMavtbQ4\nBntJh3q9Yhk7VgHAalIsY4MDecHZgkc/Qlfs1ROTmKi9ViwkA+ddY9bZpHgAwndCTQG/pvuJIYQQ\nQshIoSFACCGENBgaAoQQQkiD2eIaAQUGQw4b608x/hYvENAgNX4bJ8iPGhd8jD/KTSjk1G0JEhN5\nAS76Rf/Y4bUwYM/AaAAGJlNROnD87cZ/d9AJNNI1kZLmnCwdq8bf39Py27Dr6AisRqCrYQemOHan\ner7q1AZzcfxwTlypqWJUfnK3v4wmxdNLbJXkTsPEJAKqXLe5B71+L9vHw/rtE/fZKz6zh9JQY2SD\nBXkBhWwioPvSbUEZq2fqJWE97Xbx3Pu9cCyYmzEDodUROOIum3TISygUjNOeRsC+R7wx2caycy5n\nK40IRGTGIukzoBAhhBBCjhMaAoQQQkiDoSFACCGENBgaAkM409AbS+rEEdiKBAmGGsw0xRkgx48X\nV8NycBD6/7cicuxwIo1ni4sFUcwwaLINtkyAocF8OzAGwkxSTvbBIMiP04yIMlYs6CTcC4NXRAQd\num9xe1jIiGeseBAzg8AYsKKwfemuoNquCRAy0woDjcwYNc0hR0Rkg/qsaChMtO1JxMuAFqxy6rHC\nrGMvb2WsMdAyIrVRSv5a5tnaqoZJzP1l17kGqxmKvHvdGgN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5GslXTms8QrQZ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\n+X/2C6g4nYvTXQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10eeb3f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 8))\n",
    "\n",
    "A_mat, eps_mat = np.meshgrid(A_list/(2*np.pi), eps_list/(2*np.pi))\n",
    "\n",
    "ax.pcolor(eps_mat, A_mat, p_mat)\n",
    "ax.set_xlabel(r'Bias point $\\epsilon$')\n",
    "ax.set_ylabel(r'Amplitude $A$')\n",
    "ax.set_title(\"Steadystate excitation probability\\n\" +\n",
    "             r'$H = -\\frac{1}{2}\\Delta\\sigma_x -\\frac{1}{2}\\epsilon\\sigma_z - \\frac{1}{2}A\\sin(\\omega t)$' + \"\\n\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Versions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>QuTiP</td><td>4.2.0</td></tr><tr><td>Numpy</td><td>1.13.1</td></tr><tr><td>SciPy</td><td>0.19.1</td></tr><tr><td>matplotlib</td><td>2.0.2</td></tr><tr><td>Cython</td><td>0.25.2</td></tr><tr><td>Number of CPUs</td><td>2</td></tr><tr><td>BLAS Info</td><td>INTEL MKL</td></tr><tr><td>IPython</td><td>6.1.0</td></tr><tr><td>Python</td><td>3.6.1 |Anaconda custom (x86_64)| (default, May 11 2017, 13:04:09) \n",
       "[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td colspan='2'>Wed Jul 19 22:32:24 2017 MDT</td></tr></table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qutip.ipynbtools import version_table\n",
    "\n",
    "version_table()"
   ]
  }
 ],
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