determinant_equation_numerics.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'divide': 'warn', 'invalid': 'warn', 'over': 'warn', 'under': 'ignore'}"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import cmath\n",
    "from scipy.optimize import fsolve, minimize_scalar, minimize, brentq, curve_fit\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "\n",
    "class SimpleNamespace(object):\n",
    "    \"\"\"A simple container for parameters.\"\"\"\n",
    "    def __init__(self, **kwargs):\n",
    "        self.__dict__.update(kwargs)\n",
    "        \n",
    "fparams = {'axes.labelsize': 18,\n",
    "           'axes.titlesize': 18,\n",
    "           'font.size': 18,\n",
    "           'legend.fontsize': 16,\n",
    "           'font.family': 'serif',\n",
    "           'font.serif': 'Computer Modern Roman',\n",
    "           'xtick.labelsize': 16,\n",
    "           'ytick.labelsize': 16,\n",
    "           'text.usetex': True,\n",
    "           'image.cmap': 'seismic'}\n",
    "           #'figure.autolayout': True}\n",
    "plt.rcParams.update(fparams)\n",
    "\n",
    "# Pauli matrices\n",
    "sx = np.array([[0, 1], [1, 0]], complex)\n",
    "sy = np.array([[0 , -1j], [1j, 0]])\n",
    "sz = np.array([[1, 0], [0, -1]], complex)\n",
    "s0 = np.array([[1, 0], [0, 1]], complex)\n",
    "\n",
    "# Physical constants\n",
    "MU_B = 5.788381 * 1e-2 # Bohr magneton in units of µeV * mT^(-1).\n",
    "GAP = 151.8 # This is the gap from the zero-field data, in µeV.\n",
    "TAU = 0.56 # This is the transmission from the zero-field data\n",
    "\n",
    "# 8x8 Identity matrix\n",
    "eye = np.eye(8, dtype=complex)\n",
    "\n",
    "np.seterr(all='raise', divide=None, over=None, under=None, invalid=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dimensionless parameters:\n",
    "\n",
    "$$x = E/\\Delta$$\n",
    "\n",
    "$$y = B/\\Delta$$\n",
    "\n",
    "$$z = \\alpha k_F/\\Delta$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def compute_gap(p):\n",
    "    energy = lambda q, sign: np.sqrt(1 + q**2 + p.y**2 + p.z**2 + 2 * sign * np.sqrt((1 + q**2) * p.y**2 + q**2 * p.z**2))\n",
    "    gap_plus = minimize_scalar(lambda q: energy(q, 1))\n",
    "    gap_minus = minimize_scalar(lambda q: energy(q, -1))\n",
    "    return min(gap_plus.fun, gap_minus.fun)\n",
    "\n",
    "\n",
    "def x_c(p):\n",
    "    return np.sqrt(p.z**2 / (p.z**2 + p.y**2))\n",
    "\n",
    "\n",
    "def z_c(p):\n",
    "    return np.sqrt(p.y * (1-p.y)) if p.y <1 else 0.\n",
    "\n",
    "\n",
    "def yc(p, s):\n",
    "    if p.z < 0.5:\n",
    "        return 0.5 * (1 + s * np.sqrt(1 - 4 * p.z**2))\n",
    "    else:\n",
    "        return 1 - (-1)**s\n",
    "\n",
    "    \n",
    "def pole(x, p, sign=-1, tple=False):\n",
    "    pol = cmath.sqrt(-1 + x**2 + p.y**2 + p.z**2 + 2 * 1j * sign * cmath.sqrt(p.z**2 * (1 - x**2) - x**2 * p.y**2))\n",
    "    # Makes sure that the pole has positive real part, and positive or negative imaginary part\n",
    "    # depending on the value of 'sign'\n",
    "    if not np.sign(pol.imag) == sign:\n",
    "        pol = np.conj(pol)\n",
    "    if np.sign(pol.real) < 0:\n",
    "        pol = -np.conj(pol)\n",
    "    if tple:\n",
    "        return (pol.real, pol.imag)\n",
    "    else:\n",
    "        return pol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p = SimpleNamespace(z=0)\n",
    "ys0 = np.linspace(0, 1, 100)\n",
    "gap0 = []\n",
    "for y in ys0:\n",
    "    p.y = y\n",
    "    gap0.append(compute_gap(p))\n",
    "ys = np.linspace(0, 2, 200)\n",
    "gap1 = []\n",
    "gap2 = []\n",
    "for y in ys:\n",
    "    p.y = y\n",
    "    p.z = 0.25\n",
    "    gap1.append(compute_gap(p))\n",
    "    p.z = 0.6\n",
    "    gap2.append(compute_gap(p))\n",
    "p.z = 0.25\n",
    "yc1 = yc(p, -1)\n",
    "yc2 = yc(p, +1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Yx7bmb6X79O7YTtqYlDGJRy95tNrHq5IvvzSNPHLE5F0WLoQmTaxpS4SQS2GV8/ZSmJoQ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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b8e2ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ys0, gap0, lw=2, label=r'$z=0$')\n",
    "plt.plot(ys, gap1, lw=2, label=r'$z<z_c$')\n",
    "plt.plot(ys, gap2, lw=2, label=r'$z>z_c$')\n",
    "#plt.plot(ys, np.sqrt(p.z**2/(ys**2 + p.z**2)))\n",
    "plt.axvline(yc1, c='k', ls='--', lw=2)\n",
    "plt.axvline(yc2, c='k', ls='--', lw=2)\n",
    "plt.xlabel(r'$y$')\n",
    "plt.ylabel(r'$\\Delta(y)/\\Delta$')\n",
    "plt.legend()\n",
    "plt.savefig(\"induced_gap.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evolution of the poles in the complex plane"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mog2tDrG5bHPa0s/BYwfdNW6Wyc0dJn4vrcM8u11PDh48iWU1Ii9YtchHgLQCv9PONQZN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f3f4390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = SimpleNamespace(y = 0.5, z = 0.6)\n",
    "xs = np.linspace(0, 2*x_c(p), 500)\n",
    "q0s = [pole(x, p, sign=-1, tple=True) for x in xs]\n",
    "q1s = [pole(x, p, sign=+1, tple=True) for x in xs]\n",
    "req0, imq0 = np.array(list(zip(*q0s)))\n",
    "req1, imq1 = np.array(list(zip(*q1s)))\n",
    "plt.figure(figsize=(4,4))\n",
    "plt.grid()\n",
    "plt.axvline(0, c='k')\n",
    "plt.axhline(0, c='k')\n",
    "plt.scatter(req0, imq0, c='r', s=30, lw=0.2)\n",
    "plt.scatter(req1, imq1, c='b', s=30, lw=0.2)\n",
    "plt.scatter(-req0, -imq0, c='g', s=30, lw=0.2)\n",
    "plt.scatter(-req1, -imq1, c='y', s=30, lw=0.2)\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)\n",
    "plt.yticks([])\n",
    "plt.xticks([])\n",
    "plt.title(r'$y=0.5, z=0.6, z>z_c$')\n",
    "plt.savefig(\"poles_z>zc.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Tk8CFCw+Qk5PvJ9Bgn3vwYD6pqR5uvRXeeqtzgMoXU8Sn9u5lxksvMa6piUrg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\nngAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f5306a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = SimpleNamespace(y = 0.5, z = 0.4)\n",
    "xs = np.linspace(0, 2*x_c(p), 500)\n",
    "q0s = [pole(x, p, sign=-1, tple=True) for x in xs]\n",
    "q1s = [pole(x, p, sign=+1, tple=True) for x in xs]\n",
    "req0, imq0 = np.array(list(zip(*q0s)))\n",
    "req1, imq1 = np.array(list(zip(*q1s)))\n",
    "plt.figure(figsize=(4,4))\n",
    "plt.grid()\n",
    "plt.axvline(0, c='k')\n",
    "plt.axhline(0, c='k')\n",
    "plt.scatter(req0, imq0, c='r', s=30, lw=0.2)\n",
    "plt.scatter(req1, imq1, c='b', s=30, lw=0.2)\n",
    "plt.scatter(-req0, -imq0, c='g', s=30, lw=0.2)\n",
    "plt.scatter(-req1, -imq1, c='y', s=30, lw=0.2)\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)\n",
    "plt.yticks([])\n",
    "plt.xticks([])\n",
    "plt.title(r'$y=0.5, z=0.4, z<z_c$')\n",
    "plt.savefig(\"habby_birthday_dima.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BE098BHwG+BKSk+wGZgNuVTEOQok2BFvXbiX3fK6vkjwScV6d8M6R+M5t09ONnPZLAcf0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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f3c1f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = SimpleNamespace(y = 0.5, z = 0.5)\n",
    "xs = np.linspace(0, 2*x_c(p), 500)\n",
    "q0s = [pole(x, p, sign=-1, tple=True) for x in xs]\n",
    "q1s = [pole(x, p, sign=+1, tple=True) for x in xs]\n",
    "req0, imq0 = np.array(list(zip(*q0s)))\n",
    "req1, imq1 = np.array(list(zip(*q1s)))\n",
    "plt.figure(figsize=(4,4))\n",
    "plt.grid()\n",
    "plt.axvline(0, c='k')\n",
    "plt.axhline(0, c='k')\n",
    "plt.scatter(req0, imq0, c='r', s=30, lw=0.2)\n",
    "plt.scatter(req1, imq1, c='b', s=30, lw=0.2)\n",
    "plt.scatter(-req0, -imq0, c='g', s=30, lw=0.2)\n",
    "plt.scatter(-req1, -imq1, c='y', s=30, lw=0.2)\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)\n",
    "plt.yticks([])\n",
    "plt.xticks([])\n",
    "plt.title(r'$y=0.5, z=0.45, z=z_c$')\n",
    "plt.savefig(\"poles_z=zc.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11096f358>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8hBdZjMblWv3xB4HhoCDXb5/20y5lyfWFmEW4/EFEBkVkt4gM+DO/uLF7/PHd\nItLhP9/YGEvjqfXcN5uv6rC3EzgIXMATqNE8Cg00sPJfVXP/h+e071UxbrKk3Q/8JGv7K7yu3SXt\nPTHjB4B5/28ivG/Wf7We+yb0Va2v7ylgDbAxa9treI0VP2fANmAiom++0vFzPbOphSa9/KHWbwgF\n1gI9qtpVsm9m1Hrum81XddorqjqjOZ3NLIO6K/9duhwu9iSo6kzjTSrPct7AQK5eC7Wf+6byFXXa\nKyJP+ft1AR3qhSrNTqXK/7K+c0ls6j4JGeHSG7jWc99svqrH3uN4odcMgIgcEpEBzXkSvArqrvxv\nuNjY5Q8LuPQGrvXcN5uvarY3Inw6DrwAZO2r5TKJ994N0wFQaUbaULGp5vIHEVly+UOV1H0SkqQG\nMXXpDVzruc+Fr2qgJnv998AU3swz2D4NdKdpZCPQOiv/ocFiozm8/CFJahRTZ97AtZ77PPiqFuq0\n94USP/bgFa82HSLSDTykt+poXhGR3aEFiqoq/5s6Z5PUSUiKWsTUwTdw7LnPm6/qoOrXp6pXRGSi\nZP8ngAMNsrUmQpX/e4BOERklVPnvb3sC/72tqs+KyH7/UqMe4EI1K6O5riB2/fIHEXker/IyXIkZ\nrsxc9AEVkf2q+lJo/5/g1UX8qPHWLyXu3De7r6C21+fPRPfhzT43EfJzUcm12BQBewMbRcHExjCM\nhuBMBbFhGPnGxMYwjIZgYmMYRkMwsTEMoyGY2BiG0RBMbAzDaAgmNoZhNAQTG8MwGsL/B+MSJ5JF\n5fSDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e152ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = SimpleNamespace(y = 0.5, z = 0.)\n",
    "xs = np.linspace(0, 1, 100)\n",
    "q0s = [pole(x, p, sign=-1, tple=True) for x in xs]\n",
    "q1s = [pole(x, p, sign=+1, tple=True) for x in xs]\n",
    "req0, imq0 = np.array(list(zip(*q0s)))\n",
    "req1, imq1 = np.array(list(zip(*q1s)))\n",
    "plt.figure(figsize=(4,4))\n",
    "plt.grid()\n",
    "plt.axvline(0, c='k')\n",
    "plt.axhline(0, c='k')\n",
    "plt.scatter(req0, imq0, c='r', s=30, lw=0.2)\n",
    "plt.scatter(req1, imq1, c='b', s=30, lw=0.2)\n",
    "plt.scatter(-req0, -imq0, c='g', s=30, lw=0.2)\n",
    "plt.scatter(-req1, -imq1, c='y', s=30, lw=0.2)\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)\n",
    "plt.title(r'$y=0.5, z=0.45, z<z_c$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def a(x, p):\n",
    "    s = np.sqrt(p.y**2 + p.z**2)\n",
    "    a = x * (1 - x**2 + p.y**2 + p.z**2) * eye\n",
    "    a -= 2 * x * p.y * np.kron(sx, np.kron(s0, sx))\n",
    "    a -= 2 * p.y * p.z * np.kron(s0, np.kron(sz, sx)) / s\n",
    "    a += p.z * (1 - x**2 + p.y**2 + p.z**2) * np.kron(sx, np.kron(sz, s0)) / s\n",
    "    a += p.y * (1 - x**2 - p.y**2 - p.z**2) * np.kron(sy, np.kron(s0, sy)) / s\n",
    "    a += (p.y**2 * (1 + x**2 - 2 * p.z**2 - p.y**2) - p.z**2 * (1 - x**2 + p.z**2)) * np.kron(sz, np.kron(s0, sz)) / s\n",
    "    return a\n",
    "\n",
    "\n",
    "def c(x, p):\n",
    "    s = np.sqrt(p.y**2 + p.z**2)\n",
    "    c = x * eye\n",
    "    c += p.z * np.kron(sx, np.kron(sz, s0)) / s\n",
    "    c += p.y * np.kron(sy, np.kron(s0, sy)) / s\n",
    "    c += s * np.kron(sz, np.kron(s0, sz))\n",
    "    return c\n",
    "\n",
    "\n",
    "def g(x, p, q0, q1):\n",
    "    g = (np.kron(sz, np.kron(sz, s0)))\n",
    "    g += c(x, p) / (q0 - q1)\n",
    "    g += a(x, p) /  (q0 * q1 * (q0 - q1))\n",
    "    return - 0.5 * g\n",
    "\n",
    "\n",
    "def T(p):\n",
    "    s = np.sqrt(p.y**2 + p.z**2)\n",
    "    r = np.sqrt(1 - p.tau) / np.sqrt(p.tau)\n",
    "    T = eye - 1j * r * np.kron(s0, np.kron(sz, s0))\n",
    "    T += p.z * r * np.kron(sz, np.kron(sx, sy)) / s\n",
    "    T += p.y * r * np.kron(s0, np.kron(sy, s0)) / s\n",
    "    return T\n",
    "\n",
    "\n",
    "def bound_state_determinant(x, p, remove_asymptote=True, tol=1e-6, warn=False):\n",
    "    q0 = pole(x, p, sign=-1)\n",
    "    q1 = pole(x, p, sign=1)\n",
    "    phiexp = np.cos(0.5 * p.phi) * eye - 1j *  np.sin(0.5 * p.phi) * np.kron(sz, np.kron(s0, s0))\n",
    "    tfactor = np.dot(phiexp, T(p)) - eye\n",
    "    gfactor = np.dot(g(x, p, q0, q1), np.kron(sz, np.kron(sz, s0)))\n",
    "    m = eye - np.dot(gfactor, tfactor)\n",
    "    mdet = np.linalg.det(m)\n",
    "    if remove_asymptote:\n",
    "        mdet *= (q0 * q1 * (q0-q1))**8\n",
    "    if warn and (mdet.imag > tol):\n",
    "        print(\"Imaginary part large at:\", x, np.abs(x - gap(p)), mdet.imag, mdet.real, mdet.imag/mdet.real)\n",
    "        print(Warning(\"The imaginary part of the determinant is greater than %s\" % tol))\n",
    "    return mdet.real\n",
    "\n",
    "\n",
    "def func(xs, p):\n",
    "    D = compute_gap(p)\n",
    "    domain = lambda x : ((x >= 0) & (x <= D))\n",
    "    if isinstance(xs, np.ndarray):\n",
    "        vals = np.array([bound_state_determinant(x, p) if domain(x) else 100 * abs(x) + 100 for x in xs])\n",
    "        return vals\n",
    "    else:\n",
    "        return bound_state_determinant(xs, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def find_abs_energies(p):\n",
    "    \n",
    "    # Take care of y=0 case\n",
    "    if p.y == 0:\n",
    "            Ea = np.sqrt(1 - p.tau * np.sin(p.phi/2)**2)\n",
    "            return (Ea, Ea)\n",
    "    \n",
    "    gap = compute_gap(p)\n",
    "    xs = np.linspace(0, gap, 1000, endpoint=False)\n",
    "    sample = func(xs, p)\n",
    "    sign_changes = np.nonzero(np.diff(np.sign(sample)))[0]\n",
    "    intervals = [[xs[s - 1], xs[s + 1]] for s in sign_changes]\n",
    "    Ns = len(sign_changes)\n",
    "    \n",
    "    # Discard sign changes in consecutive values of the sample\n",
    "    # These are assumed to be fluctuations\n",
    "    if Ns == 2 and np.diff(sign_changes)[0]==1:\n",
    "        print(\"Discarding sign change detections: too close to each other.\")\n",
    "        Ns = 0\n",
    "    \n",
    "    # Adjust the boundary conditions in case solutions\n",
    "    # are very close to x=0 or x=gap\n",
    "    if Ns:\n",
    "        for s in sign_changes:\n",
    "            if s == 0:\n",
    "                print(\"first sign change very close to x=0\")\n",
    "                intervals[0][0] = 0.\n",
    "            #if s == (len(xs)-2):\n",
    "            #    print \"second sign change very close to the gap x=0\"\n",
    "            #    print Ns\n",
    "            #    intervals[1][1] = gap\n",
    "\n",
    "    if Ns == 0:\n",
    "        print(\"No sign changes:\", Ns)\n",
    "        return(gap, gap)\n",
    "    elif Ns == 1:\n",
    "        x_1, x_2 = intervals[0]\n",
    "        try:\n",
    "            sol1 = brentq(lambda x: func(x, p), x_1, x_2, full_output=False)\n",
    "        except (Exception, e):\n",
    "            print(\"Parameters: \", p.y, p.z, p.tau, p.phi)\n",
    "            print(\"Bracketing interval: \", (x_1, x_2))\n",
    "            print(\"Function values:\", func(x_1, p), func(x_2, p))\n",
    "            plt.plot(xs, func(xs, p))\n",
    "            raise e\n",
    "        return (sol1, gap)\n",
    "    elif Ns == 2:\n",
    "        x_1, x_2 = intervals[0]\n",
    "        x_3, x_4 = intervals[1]\n",
    "        try:\n",
    "            sol1 = brentq(lambda x: func(x, p), x_1, x_2, full_output=False)\n",
    "            sol2 = brentq(lambda x: func(x, p), x_3, x_4, full_output=False)\n",
    "        except (Exception, e):\n",
    "            print(\"Parameters:\", p.y, p.z, p.tau, p.phi)\n",
    "            print(\"Bracketing interval 1:\", (x_1, x_2))\n",
    "            print(\"Function values:\", func(x_1, p), func(x_2, p))\n",
    "            print(\"Bracketing interval 2:\", (x_3, x_4))\n",
    "            print(\"Function values:\", func(x_3, p), func(x_4, p))\n",
    "            plt.plot(xs, func(xs, p))\n",
    "            raise e\n",
    "        return (sol1, sol2)\n",
    "    else:\n",
    "        print(\"Unexpected number of sign changes:\", Ns)\n",
    "        return (np.nan, np.nan)\n",
    "\n",
    "    \n",
    "def return_abs_pair_energy(p):\n",
    "    levels = find_abs_energies(p)\n",
    "    return np.average(levels)\n",
    "\n",
    "\n",
    "def fit_abs_pair_energy(B, z, gfactor, tau, phi, gap):\n",
    "    y = 0.5 * gfactor * MU_B * B / gap\n",
    "    p = SimpleNamespace(y=y, z=z, tau=tau, phi=phi)\n",
    "    if z <= 0:\n",
    "        return 1e5\n",
    "    if gfactor <=2:\n",
    "        return 1e5\n",
    "    else:\n",
    "        energy = return_abs_pair_energy(p)\n",
    "        return energy\n",
    "\n",
    "vfit_abs_pair_energy = np.vectorize(fit_abs_pair_energy, otypes=[np.float],\n",
    "                                    excluded=['z', 'gfactor', 'tau', 'phi', 'gap'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting at finite $z$, perfect transmission, and $\\phi=\\pi$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "first sign change very close to x=0\n"
     ]
    }
   ],
   "source": [
    "p = SimpleNamespace(y=0.1, z=0.3, tau=0.75, phi=np.pi)\n",
    "ys = np.linspace(0., 1.5, 150)\n",
    "energies = []\n",
    "gaps = []\n",
    "for y in ys:\n",
    "    p.y = y\n",
    "    sol = find_abs_energies(p)\n",
    "    energies.append(sol)\n",
    "    gaps.append(compute_gap(p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ens1, ens2 = np.asarray(list(zip(*energies)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+++/s3r2bPn36MGTIEPzl0JP3lZSk6NTpKxYufAtIpGjRlqxf/xvVqpW0ujQh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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e60a908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ys, ens1, c='r', lw=2)\n",
    "plt.plot(ys, ens2, c='b', lw=2)\n",
    "plt.plot(ys, (ens1 + ens2)/2, c='k', ls='--', lw=1)\n",
    "plt.plot(ys, gaps, c='k', lw=2)\n",
    "plt.xlabel(r'$y$')\n",
    "plt.ylabel(r'$x$')\n",
    "plt.xlim([0., 1.5])\n",
    "plt.yticks([0, 0.5, 1], [r'$0$', r'$0.5$', r'$1$'])\n",
    "plt.xticks([0, 0.5, 1, 1.5], [r'$0$', r'$0.5$', r'$1$', r'$1.5$'])\n",
    "plt.title(r'$\\phi=\\pi$, $\\tau=0.75$, $z=0.3$')\n",
    "plt.savefig(\"spectrum_weak_so.pdf\")\n",
    "#plt.plot(ys, [gap(y, p.z) for y in ys], c='k', lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "first sign change very close to x=0\n"
     ]
    }
   ],
   "source": [
    "p = SimpleNamespace(y=0.2, z=0.6, tau=0.75, phi=np.pi)\n",
    "ys = np.linspace(0., 1.5, 150)\n",
    "energies = []\n",
    "gaps = []\n",
    "for y in ys:\n",
    "    p.y = y\n",
    "    sol = find_abs_energies(p)\n",
    "    energies.append(sol)\n",
    "    gaps.append(compute_gap(p))\n",
    "ens1, ens2 = np.asarray(list(zip(*energies)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "135.4481154"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.5 * 12 * MU_B * 390"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib.collections import LineCollection\n",
    "from matplotlib.colors import ListedColormap, BoundaryNorm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/ftzsEkUmmBIowGLgaorrmqU1ZIAaNr6/BhB3n+/plo769LMTH6/U998r5eeX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\nbOd7j2vXrrFz5062b9/O9u3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AcbNXMUKkpkkTvb/KK6/ozbu6d4e2beHSJbMrE0LYkwSK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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a295780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ys[:73], ens1[:73], c='b', lw=2)\n",
    "plt.plot(ys[73:], ens1[73:], c='r', lw=2)\n",
    "plt.plot(ys[:73], (ens1[:73]+ens2[:73])/2, c='k', ls='--', lw=2)\n",
    "plt.plot(ys[73:], (ens1[73:]+ens2[73:])/2, c='k', ls='--', lw=0.6)\n",
    "plt.plot(ys, ens2, c='r', lw=2)\n",
    "plt.plot(ys, gaps, c='k', lw=2)\n",
    "plt.xlabel(r'$y$')\n",
    "plt.ylabel(r'$x$')\n",
    "plt.xlim([0., 1.5])\n",
    "plt.yticks([0, 0.5, 1], [r'$0$', r'$0.5$', r'$1$'])\n",
    "plt.xticks([0, 0.5, 1, 1.5], [r'$0$', r'$0.5$', r'$1$', r'$1.5$'])\n",
    "plt.title(r'$\\phi=\\pi$, $\\tau=0.75$, $z=0.6$')\n",
    "plt.savefig(\"spectrum_strong_so_different_colors.pdf\")\n",
    "#plt.plot(ys, [gap(y, p.z) for y in ys], c='k', lw=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting at zero $z$, finite transmission, and $\\phi=\\pi$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n"
     ]
    }
   ],
   "source": [
    "p = SimpleNamespace(y=0.2, z=1e-8, tau=0.75, phi=np.pi)\n",
    "ys = np.linspace(0., 1, 100)\n",
    "energies = []\n",
    "gaps = []\n",
    "for y in ys:\n",
    "    p.y = y\n",
    "    sol = find_abs_energies(p)\n",
    "    energies.append(sol)\n",
    "    gaps.append(compute_gap(p))\n",
    "ens1, ens2 = np.asarray(list(zip(*energies)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/bvh/anaconda/lib/python3.5/site-packages/matplotlib/figure.py:1744: UserWarning: This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.\n",
      "  warnings.warn(\"This figure includes Axes that are not \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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C+fBDcx0TEmKOX3wRtECtPMzx4zF07DiOTZsmAbFALu6661UWLRpEmTLBdoen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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11074e390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ys, ens1, c='r', lw=2)\n",
    "plt.plot(ys, ens2, c='b', lw=2)\n",
    "plt.plot(ys, (ens1 + ens2)/2, c='k', ls='--', lw=1)\n",
    "plt.plot(ys, gaps, c='k', lw=2)\n",
    "plt.xlabel(r'$y$')\n",
    "plt.ylabel(r'$x$')\n",
    "plt.xlim([0., 1.])\n",
    "plt.yticks([0, 0.5, 1], [r'$0$', r'$0.5$', r'$1$'])\n",
    "plt.xticks([0, 0.5, 1], [r'$0$', r'$0.5$', r'$1$'])\n",
    "plt.title(r'$\\phi=\\pi$, $\\tau=0.75$, $z=0.3$')\n",
    "plt.savefig(\"spectrum_no_so.pdf\")\n",
    "#plt.plot(ys, [gap(y, p.z) for y in ys], c='k', lw=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit to experimental data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "minima = [(0, 1.01809e-4),(50, 9.98742e-5),(75, 9.58812e-5),(100,9.2654e-5),\n",
    "          (150,8.38036e-5),(200,7.27897e-5),(300,4.26e-5)]\n",
    "Es1 = np.array([132.5,127.5,120.5,116,109,91.5,60.5])\n",
    "Es2 = np.array([112,108,103.2,101,91.2,78.9,52])\n",
    "Bs, Es = np.asarray(list(zip(*minima)))\n",
    "Es *= 1e6\n",
    "Es /= GAP\n",
    "Es1 /= GAP\n",
    "Es2 /= GAP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10e180470>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0Lb8F7PaCg5ndM7O1YQPHIiIye6MCwF5C2hJvvuEfkjDg2wLuAIkBYGNj4+B1tVqlWq2O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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f3b2eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Bs, Es, 'o', c='k')\n",
    "plt.plot(Bs, Es1, 'o', c='r')\n",
    "plt.plot(Bs, Es2, 'o', c='b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "popt, pcov = curve_fit(lambda x, z, gf: vfit_abs_pair_energy(x, z, gf, TAU, np.pi, GAP),\n",
    "                       Bs[1:], Es[1:], p0=[0.55, 10])\n",
    "popt, pcov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p = SimpleNamespace(z=popt[0], gfactor=popt[1], tau=TAU, phi=np.pi)\n",
    "fields = np.linspace(0., 500, 100)\n",
    "spectra = []\n",
    "gaps = []\n",
    "for phi in (np.pi/2, 3*np.pi/4, np.pi):\n",
    "    p.phi = phi\n",
    "    energies = []\n",
    "    for B in fields:\n",
    "        p.y = 0.5 * p.gfactor * MU_B * B / GAP\n",
    "        sol = find_abs_energies(p)\n",
    "        energies.append(sol)\n",
    "        if phi == np.pi:\n",
    "            gaps.append(compute_gap(p))\n",
    "    spectra.append(energies)\n",
    "#ens1, ens2 = np.asarray(list(zip(*energies)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ens1, ens2 = np.asarray(list(zip(*spectra[0])))\n",
    "ens3, ens4 = np.asarray(list(zip(*spectra[1])))\n",
    "ens5, ens6 = np.asarray(list(zip(*spectra[2])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pkzjwz+EoM+np6TCUQ9AzJCQEwcHB4n0rKyuEhobW6Z5RUVGwsLCoMF66nbIywWMuSsDr\n18DPPwM//AAUd0PV1k5C69a7YWQkgrW1cpaPefDgAf7zn//g4sWLAICJEydi8+bNMDIyUrBlnHel\npjEXga/sv8zIW/qf35CQEDg7O0v9vuVJTEwsIwQ2Njb44osv4OHh8U73EwqFCAkJwaJFiyocCw4O\nhqWlJby8vBAZGSnxXjzm0ogwMgIWLmRraU6cAGxtk/DmzVbcu7cIV6+y1f4DB26FUJikaFPL0KZN\nG0RERGDjxo3Q1tbG3r178eGHH+LEiROKNo3DKUNQUBCCgoIQFhaGo0ePYu3atTJ9XmlhiYmJgUAg\nKCMsISEhaNOmDYyNjWFiYgJjY2MYGxujbdu2WLJkSYX77dq1C9OnT68wHh4ejrFjx8rkNdQVKZZq\n5NQVVVVg+HDg119348qV4jUyAKCLx499MXDgOhw96o1evRRpZVlUVVUxf/58DB8+HP/5z39w6dIl\njBgxAhMnTsSmTZtgbGysaBM5MkAWswpZkJ6ejmnTpiEgIAAWFhY4evQoRo8ejfDw8Gozr9zd3av8\nC794XCAQYM2aNTAwMKjy2YcOHcKRI0cQFBQkHi92Yz148ADBwcFwc3NDXFwcAKBbt26V3ksoFFb6\nnPT09Cqfr3CkEbhRxg31ODBpb7+iTLC/ZGPjw4YRXb+uaCsrUlBQQOvXryctLS0CQO+99x4dO3ZM\n0WZxakF9/txUhouLi7i1d1paGsXGxhIRUUJCArVp00ZudvTs2ZMCAwOJiCg9PV08HhAQIP639Hhp\nYmJiKk0GOHLkiPjnsLAwHtDnSMbMTAVAdrnRbHTooAJdXeDkSVY489NPWTkaZUFVVRULFy7EzZs3\n0b9/fzx9+hSjRo2Cq6srUlNTFW0ep5GRnp6O8PBwODg4AADCwsLEM4OEhARYWVnJ9NmlmTFjBmbM\nmAEA4plG6UB8fHx8lTOQXbt2VXB9CYVCuSQm1AXuFlNC/Pwm4+pV7wol+//8cw709ID164Ft24A/\n/2TbmDHAypVAhw4KNryItm3b4ty5c9i6dSuWLl2KAwcOICwsDNu3b5dLMJXDASoKSOmMql27dom/\n7Cuj2C1WFVSNWyw8PBxOTk5IS0sTHys+PyMjQzy2Zs0a8dqUhOJMnkoQCAQVnhETEwOhUIjY2FgA\nwPXr15GWloZ169ZhzJgxlWaVyR1pTH+UcUM9n94nJCSSq6sPOTisIFdXH0pISCxz/PlzIg8PIi0t\n5jJTUSGaPJno4cOK97C3r/we8uD+/fs0cOBA8boYFxcXevbsmdzt4NSM+v65KU9pV1GxGykwMJC8\nvLxk9sy0tDRyd3cvM+bi4kLjxo0rM1baLefk5ETh4eEV7hUWFlajdTmBgYFK5xbjqcj1nORk4Lvv\nWAWAggJWXmbuXODLL5MwZoxyNCwTiUTYsWMHPD09kZ2dDRMTE2zZsgVffPGFUubnN2YaWvmXxMRE\nHD58GFZWVmJXkpWVFQYPHizT58bFxSE0NBQCgQAvX76EQCDA6tWrxcdDQkIQFRUlHluyZAl69eqF\n0aNHl7mPu7u7uJFfVQQFBeHw4cOIjo7GkiVLMH369GqD/PJKRVb4DENWGxrYX2CSePCAaNw4Egf/\nNTR8CMgqlxCQRa6uPgqzUSgUkqOjo3gWM2LECHr8+LHC7OFUpKF+buSxKl8WlJ8BSQNJv2PwgD6n\nNNbWwG+/AdevAw4OQF6eCGX7yQCALlJSRIowDwDL/T9z5gyCg4NhYGCAP/74Ax9++CGCg4Mb1F/L\nHOWjPv7/CgoKgouLi6LNeGe4uDQwevViVZgHDao848zUVLG/coFAgKlTp+L27dv49NNPxesQnJyc\nqg1qcjh1oT66X0NDQ2XuvpMlXFwaIAIB8PPPk2Fl5Y0SgckG4I23byfj6VMFGldEq1atcPz4cezf\nvx8mJiYIDw9H586dsWnTJhQW9yfgcKRE+VhGfcDa2lrRJtSJBh3Qd53jCr+FfrC0sFS0OQpBKEzC\n8uW78fChCC9fquDffyejsNAcenrA8uXAvHksAUDRvHjxAvPmzcOvv/4KAOjTpw+Cg4PRqVMnBVvW\n+GhoAX1ORXizsDoiEAgISwHrG9YI3RbaaAWmNPfvA4sWAcUFjNu2BTZtAoYNU6xdxfzxxx+YOXMm\nkpOToa6ujiVLlmDp0qXQVAYFbCRwcWn48MKV0kADiO8aj+UblivaEqWgbVvg2DHg1Cnggw+Y2Awf\nzjpjKkPDshEjRuD27duYMWMG8vPzsXLlSnTv3h2XL19WtGkcDqeWNGxxAQANICUjRdFWKBVDhwI3\nb7KV/vr6rBLzhx8CK1YAOTmKta1JkybYuXMnzp07h3bt2uHu3bsYMGAAZs+ejYyMDMUax+FwakzD\nF5c8wNTAVNFWKB0aGiVl/idOBN6+Bfz8gI4dS9xm0kIoTMKECb5wcPDGhAm+NWodMHDgQNy4cQNL\nly6FqqoqfvjhB3Ts2JE3JeNw6gkNPubSMqolnCc5o5lZM2ioakBdRR1aalrQUdeBtro2dNR1oK+h\nD31Nfehr6MNI2whGWkZQV1VX9EuQKxcvArNnAzdusP1PPwW2bAEs6xiqEgqT4ORUt0oBN2/ehJub\nm7gR0pgxY7Blyxa0bNmybsZxKsBjLg0fHtCvI8XZYjo2OggSBkm+oBy66row0TFBc93maKbTDM11\nm6OlXkuY6pvCVN8U7zd5H62btEYL3RaV5tALE4VYvmE5kjOSYWZgVi+y1goKWDfM5cuBzEzWfnnZ\nMpYE8K4x9QkTWLOzsgs6s+Hqug779nnX+D6FhYXYunUrli1bhuzsbDRp0gQBAQFwc3ODikrDn4DL\nCy4uDR8uLnWkuLZYWEIYLj+6jPzCfOQV5iGvMA9vC9/iTcEb5OTnICc/B5lvM5HxNgMZbzOQlpuG\ntNw0FFLN1lpoqmrC3NAc1kbWaGPcBm2M28DgjQF8AnyQ1D0J0ACQV7+y1p48YYJy4ADbb98e2L6d\nrfyvLQ4O3oiI8K10/OzZiuOSSEpKwqxZs3Dy5EkAwIABA7Br1y507Nix9sZxKsDFpeHDxaWO1KVw\nJREhMy8TqTmpeJ79HC9yXuBZ1jM8yXqClMwUJGcm41H6IySlJ+HVm1cVbxABoB+YsBSTBzg+dcTv\nO36HnobeO9klb8LDgVmzWFwGACZMYEkAzZvX/B7SmrmUhohw+PBhzJ07F8+ePYO6ujo8PT3x7bff\nQktL653uyWE0BnEJCQlp1K0fuLjUEXlVRc7Ky4LwtRDxr+MR/yoe91/dx29bf0N6v/SKJ/8FqAxW\nQYemHWBjagPbVrbo37o/OjbrCBWBcrp23r4F1q4FVq0CcnMBIyMgIACYMgWoiTdKGjGXqnj9+jW8\nvLwQGBgIgPWR2bFjB4YMGVKn+zZmGoO4FLc6bqxwcakjiiy5P2HuBOzX319h5mIUY4TMfpkoEBWU\nOb+JZhP0b90fDhYOGGw5GF1bdIWqiqp8jZZAfDybxZw5w/b79wd27WIpzJIorhSQkiKCqakK/Pwm\nS7Xs/8WLFzFjxgzcuXMHADBhwgSsX78ezWszxeIAaPjikp6ejujo6Hpds6uucHGpI4oUF2GiEE6z\nnRDfNb5CzKVlq5a48fQGridfx+XHl3Hp4SU8ynhU5nojLSM4Wjnikzaf4OM2H6OlvnJkRREBhw4B\n8+cDT58CamrAN9+woL+2tmJty8vLw7p16+Dn54fc3FwYGRlhzZo1mDp1Kg/414Iai4s8CkHK4PPb\n2F1iABeXOqPoZmHF2WIpGSkwNTCtNlvsYfpDnE86j7PCszgrPIuk9LLrQHq07IFRH4zCZ+0/Q+fm\nnRVe4TUtDVi6FNi5k33+razYz05OCjULAOtFPmvWLJwpmmLZ2tpi586d6NKli4Itqx80VHEJCmIZ\nozExMXByckJ8fDwWL14stfuXJyQkBJ6ennj16lWZ99TExARjxowp0zhM3nBxqSOKFpe68ODVA+w7\nvw9BPwXhSeYTEAjoBsAQsDS0hEtHF4zrNA7d3+uuUKG5cgWYPh34+2+2P2ECsGED0KyZwkwCwAL+\nBw8exIIFC/D06VOoqqpi/vz58PHxgZ5e/UimUBQNzS1W3NIhICAAFhYW4nhLeHg4QkND4e/vX+l1\n7u7uVb4XxeMCgQBr1qyp0PWxuLf96NGjERwcDDc3N8TFxQEAunXrJv0XWUt4J8o6bqjHHfUShAlk\nPdyasBQEHxCWgvTt9clkiQnbL9qsN1vT8rPL6d+X/yrM1rw8otWribS0WLdLY2Oin38mEokUZpKY\n169f09dff00CgYAAUKtWrejIkSMkUgbjlJT6/LmpDBcXFzp79iwRsd72sbGxRESUkJBQpoe9NElP\nTxf/HBAQIP639LgikfQ7Bu9EKRnfCROQJBQq2oxas3zD8pJ4DQBoAJn9MjE0ayjOTz6Pr3t9jRa6\nLRD/Oh5+5/3Qbls72P5oi51RO5GeW0mWmgxRVwe8vNjsxdERePUK+M9/2M8PHsjVlAoYGhpi27Zt\nuH79Onr27InHjx9jzJgxGD58OOKVoVInR6akp6cjPDwcDkULtMLCwsQzh4SEBFhZWcnkucUzGaFQ\nKPYsxMfHV9vXviHSoN1iWQC8ra0xJzQU5nWtYyJHHCY7IMIyouK40AFnd58FABSKChGRGIG9N/ci\n5G4IsvKyAADaatoY++FYuPVwg2mhKVZsXCG3KgFEwL59rGbZy5dshf+KFWxBprqCq+kUFhZi165d\nWLp0KdLT06GpqQkvLy94enpCW9HZCEpEQ3KLxcbGYvr06eKyQaVTkMeOHYvx48dXmZJc7BarCqrG\nLVb6Hu7u7ujWrRs++ugjcRxQ0XC3mDTcYgBlAeTj6lrtNFDZcJ3jWuIS8ylxjbnOqfx1ZL3Non03\n9tHgPYNLzp8PUh+gXsa1Zj3cmhKECTK3/8ULoq++Ym4ygKhLF6Jr12T+2Brx9OlTmjhxIgEgAGRl\nZUUnTpxQtFlKAxqYW8zGxkb885EjR4iIKDAwkLy8vGT+7NJuNycnJwoPD5f5M2uCpN8xpOQWa9Az\nl+JX5t25M3xXr2a5s+rqrCSwpibbtLQAHR1AV5f9q6EhlUyYJKEQu5cvhyg5GSpmZpjs51fj2VN1\nqcySZh7xr+LxY+yP2Lh6I3L75FZYa+Oa6Yp9W/a9+wurBaGhgLs7kJDA3tK5c4HvvgOUIaZ+/vx5\nzJo1C7dv3wYAjBw5Eps2bYJlPZrhyoKGNHMBgMTERBw+fBhWVlYQCoUwNDSElZWVzNe5hISEICoq\nSpwVtmTJEvTq1UspFm/ybLE6Uiwu2QDWAahxoRE1NcDAgDU6adIEMDRkm5ER0LRpyda8OfDee0CL\nFuzfUpUdk4RCbHVygm98fNGa9Nq752qTylwZ9pPscc7qXIXxpteaImRHCOxa28kl0ywnB/DxYVlk\nhYVA69bAjh3K0f0yPz8fW7duhY+PDzIzM6GlpQUvLy988803jdZV1tDEpZjGviq/NFxc6og45tKs\nGeZ06QJzDQ1W9jc/H8jLY3VN3r4F3rxhW04OkJ3Njr8LTZsCZmaAmRl879/Hovv3y1XTAta5usJ7\nn3xmDVVVCcBlAPZAH7M+8OzviVHtR8ml9ExsLDBtGhAdzfbHjwc2b65dnTJZ8eTJEyxevBj79+8H\nAFhYWGDTpk0YOXKkwtcUyZuGKi588WQJXFzqiEAgIB9X11q5owAwwcnMBDIy2JaWBrx+zbbUVBap\nfvECeP6cLVN/9oz9W1BS0sUbQGX1fr319eH7+edAhw6s1HCnTmwFogxWkFfmWrOItcCIiSNw4NEB\npL5JBQC0M2kHr/5emNBlgsx72BQUMEFZvpzpubExm9F89ZV81uRJ4ty5c5gzZw5u3boFABg6dCg2\nb96MDz74QMGWyY+GKi585lICD+hLI6AvLwoLiZ48IYqKIvr9d/Lp2ZOyiqPZpRMLyo0RQKSrS9S7\nN9G0aUQ7dxJFRhLl5krFrARhArnOcSWHSQ7kOsdVHMzPeptFW65uIfON5uIEAPON5rT9+nZ6k/9G\nKs+u1q4EIienkrfA0ZEoPl7mj60R+fn5tGXLFjI0NCQApKamRh4eHkqzRkHWyPVzw1EIkn7H4AH9\n6lHkCv3cXTKMAAAgAElEQVRKYy4WFpjj7w/z9HTgn3+AO3eAW7eAlJSKN1BXB7p1A2xtgb59gQED\ngPffl7qd+YX5+PXvX7H64mr88/IfAICZvhmWDFgCtx5u0FR7xw5hNYCK0pbnz2drY7S1gZUr2b6a\nmsweW2OeP3+OZcuWITg4GESEFi1aYPXq1Zg0aVKDrlXWUGcunBK4W6yOKLr8izhbLCUFKqamVbvn\nUlOZyMTGsoBEdDRw7x6SiLAbgAiACoDJZmYwd3QEBg1iKxSlKDaFokIcvXsU3134Djef3QQAtDJo\nhaUDlmJqj6nQUNWQcId358ULJijFjcl69ACCg4Hu3WX2yFoRHR2NOXPm4MqVKwAAGxsbbN68Gf36\n9VOwZbKBi0vDh7vF6pNbTMok3rhBHi1bil1rWQB5AJRY2p32wQdEX39NdOIEUU6OVJ5bKCqkkDsh\n1Hl7Z7G7zGKTBe2O3U0FhQVSeUZVnDxJ1Lo1e2mqqkTffEOUnS3TR9YYkUhEe/fuJVNTU/H6mC+/\n/JIePnyoaNOkTn3+3HBqhqTfMaTkFlO4CMhqq88fEh9X18pjNj16EI0cSaSvX+YYaWkRDRtGtGMH\ni/3UkUJRIR36+xB12NZBLDIdtnWgkDshMq3LlZlJNG8eEcsiJ7K2JgoLk9njak1mZiYtW7aMtLS0\nCABpa2uTt7c3ZWVlKdo0qVGfPzecmsHFpRGLywp7+7LiUbStcHBgJ+TlEV26RLRiBZGNTdnzBAKi\nfv2I1q0jSkqqkx0FhQW0J24PWWyyEItMn6A+FCGMkMKrrJqrV4k6dSp5SZMnE6WmyvSRtUIoFNK4\ncePEsxgzMzPas2cPFRYWKtq0OlOfPzecmsHFpRGLS5Uzl6rK2Dx5QvTjj0QjRhBpaoqvSQTIp2lT\nWtG2LfmMHk2JCe9W+uVtwVvadm0bNV/bXCwyw/YPo7+f/V2HVynhmW+JvvuOSEODvZzmzYkOHlSO\nasvFXLhwgWxsbMQi06NHD4qIkK3wyhpzc3Px6+Fbw9zMzc2r/T/AxaUBi0tiQgJ5WFuXjblYW9dM\nHDIziQ4dosRPPiGPomvF99DRocRt24jevFu6cebbTFoZsZL0v9cn+IBUfFXI7ZgbpWSkvNP9asI/\n/xANHFiisyNGEClTqKOwsJD27NlDZmZm4g/vZ599Rvfu3VO0aRzOO8HFpQGLCxETGB9XV1rh4EA+\nrq61nnVUOfsBiIyMiObOJbp1651se571nGb/OZvUVqoRfEA6q3TI5y8fynorm9hDYSHRrl1ETZqw\nl6KnR7R1K1FBLXIMEhISydXVh+ztV5Crqw8lJCRK1cbs7GxauXIl6ejoEMDWx8yePZueP38u1edw\nOLKGi0sDF5e6UmXcRk+v7FifPqy71ztknN17eY8+/+1zsavMbL0Z7YnbQ4WisrGH4sWc9pPsyyzm\nrC3JyUTOziWm9+1bM31MSEgka2sPArKKrs0ia2sPqQsMEVFKSgq5ubmRiooKASADAwP6/vvvKVtZ\nUt84HAlwceHiUi3Vxm1iYohmziQyMCg5bmxMtHgxkVBY62edSzxHPXf1FItMz1096ULSBSKqvKtm\nXUv///47kakpM1tdnWjZsuo9fa6uPqWEhcQC4+rq8842SOLmzZs0dOhQsavMzMyMfvzxRyqozXSL\nw1EAXFy4uFRLjeI22dksEaBnz5JvXRUVotGjiS5cqFX0vFBUSL/E/UJm683EIjPu8DgaNWNUrXrT\n1JS0NKaPxWZ/8AHRuXOVn2tvv6KySRw5OKyokw01ITQ0lLp37y4WmQ8//JCOHTvGWy1zlBZpiUvD\nrWPRyDG3tMSc0FBWidnBAetcXSuW/NfRAaZMASIjgatXgQkTAFVV4OhRwM4O6N0bOHSoTFHOqlAR\nqGBi14m4N/selg9cDi01LRy8fRDH7x0vW5kZADSAlIxKyt7UgiZNgO3bgYsXWR3Qe/dY8YJp01iN\n0dKYmamAFeEpTTZMTWX/39/R0RFRUVHYv38/LCwscPv2bYwaNQp2dna4ePGizJ/P4SgMaSiUMm5o\n5DOXdyY5mfmZTExK/sS3siL64YdaxWWS0pJo3OFxBHvIZOZSmtxcIh+fkrTlFi3Kpi3LM+ZSvZ25\ntGnTJmratKl4JjN8+HCKi4uTqx0cTnWAu8W4uMiUnBy24t/aukRkmjcn8vcnqkWF4F8v/Eoadhpl\nYi6tPm4lk3bLd+4QDRhQYu7w4USJRfpRnC3m4CCbbLHakJ6eTsuXLyddXV0CQAKBgL744gu6f/++\nwmzicIrh4sLFRT4UFBAdPlw2LmNoyKoDvHpVo1vcj79PvVx7kZqDGsEeJJgvoLkn59LrN6+lbm5h\nIVFgYEnasq4u0YYNRPn5Un9UnXn27BnNmzePNDQ0CACpqqqSm5sbJdWxsgKHUxe4uHBxkS8iEdGp\nU0R2diUiY2BQK5FJzUmlr//8mlR8VQg+oGYBzeinmJ8qpC5Lg5QUorFjS0zt0YMoOlrqj5EKiYmJ\nNGXKFFJVVSUApKGhQbNnz6bk5GRFm8ZphCiduABYDOCltO4nBXvq8v5yquP8edbhq7TI+PiwFK4a\nEPckjux+shPHYPoG96Wo5CiZmHriREm1ZRUVogULWBEDZeTevXv05ZdfkkAgIACkpaVF8+fPpydS\nKEbK4dQUpREXANMApAKIAlAoDaOk8sK4uMieixfLioyREdHq1UQ1qBIsEolo34199N669wg+IIGP\ngGaemEmpOdKvUJmZyURFRYWZ2bo10R9/SP0xUuPWrVs0ZswYcdBfW1ubFixYwEWGIxcULi5FovIK\nQCSAIUVjXFwaI+fPly0A1qIF0bZtrPqkBNJz02nhqYWk6qtK8AE1DWhKP8b8KBNXWVQUc48Vm+ns\nTPT4sdQfIzXi4uLos88+E4uMlpYWzZs3j7vLODJFYeJSSlROF4tKqWNcXBorIhHRmTNEvXqVfHtb\nWhLt3UuJDx6wOmn29lXWSbv17BYN/Hmg2FVmG2xLsU9ipW5mfj7Rxo0s0A+w1jhbttSuTpm8iY2N\npc8//1wsMpqamjRr1iwe+OfIBLmLSzlR6V7FOVxcGjsiEdHRo0QdOhCBlf330NCoUYXnYldZi7Ut\nxFWX5/1vHqXn1jz1uaYkJbG+a8U6aGPDquIoM3FxceTs7CwWGTU1NZoyZQqvwMyRKnITFwDOAB4A\nOAjAUsK5XFw4jIICop9+Ih9t7dr1piGitDdpNPfkXHFW2Xvr3qMDNw/IpGTK0aNEZmZUJuCfkSH1\nx0iVv//+m1xdXcXFMQUCAbm4uFCMsqsjp14gT3FZXNVMpZJzubhwyrCidCym1LbC1lbitbFPYsk2\n2FbsKhuyZwj98+IfqduYkUE0f35JwL9VKyY6yl7+699//yU3NzdSV1cXz2Y++ugjCg8P57XLOO+M\nXN1iAJoAsABgIOE8Li6cMlRZnVlFhWjpUonThEJRIQVHB5PxGmOCD0h9pTp9G/4t5eTVvkWAJKKj\ny3aN/vTTdyoSLXcePXpECxYsEPeSAUA2NjZ08OBBylfG1aMcpUYhAf0ikekOwKKK41xcOGWotDqz\nri4lls4sCwqSGFF/kf2Cph6bKp7FWG6ypBP3Tkjd3oICluhW3I1AW5tlV9cg8U3hpKamkp+fHzVr\n1kwsMubm5rRx40bKUHZfH0dpUGgqcpHIDCkvMlxcOJVRaVfNK1eIbG1JPE3o0oUoPFzivS49vERd\ndnQRi8znv31OD9Ok3/c4JYVo/PgS8zp2JIqIkPpjZEJOTg5t376d2rZtKxaZJk2akIeHBwnrw1SM\no1AUvs6F2QDLIpHpRlxcOLVFJCL67Tcic/OSb/HPPiOSUMAxvzCfNlzeQHrf6xF8QLqrdGntpbWU\nV5BX5TXv2g3zzBmiNm1KzPvqK6Jnz2rzIhVHYWEh/fe//6UBAwaIRUZFRYWcnZ3p/PnzPC7DqRSl\nEBfxTZjIOAMQvcO1iwGMLkp1nibhXOei8y0BGBb9bFHFuVJ6qzky580bolWrShafqKuzrpgSqi8/\nSn9EzgedxbOYTts70cWkixXOq2s3zDdvWHUbTU1mnqEh0fbtyr02pjyRkZHk6upKampqYqHp2rUr\nBQUF8RbMnDIolbiIbyYhVbmS8/0BjC6371zN+dMAFBZtqaWvreRcabzPHHmSkkI0eXLJNKFFC6Kf\nfmKljqvh5L8nyXKTpVhkpvx3Cr3IfiE+7jrHVSo9ZR48IPr44xLzbGyIrl9/p1eqMJKTk2nZsmXU\nvHlzscgYGhrSggUL+HoZDhEpqbjU+uHAq3L7QwCcqeZ8NwAGVc1Wyp1b1/eYoygiI8vGY2xsWIym\nGnLycmhZ+DJSX6lO8AGZrDERl5Gxn2RfVliKNodJDrU2TSQiOnKEpSsDRAIB0YwZRKnSL4kmU3Jz\nc2nv3r3Uu3dvscgAIEdHRzpy5Ajl5VXtYuQ0bKQlLtX2eRUIBDsFAoGbQCAwqO68d0EgEHQv+g9d\nmldgAlPlZUSUQUSJ0raHo0TY2ACXLgH79gGmpkBUFGBrC0yeDDx9Wukl2ura8Bvsh1szb2Gw5WCk\nvknF1ONTMfDngdDR0AHyyl2QB5gamNbaNIEAcHYG7t4FvvmGdYXetQto1w4IDgZEotq/XEWgqamJ\nCRMm4Nq1a4iKisLUqVOhra2NsLAwjBkzBq1bt8ayZcuQlJSkaFM59RQBE6pqThAInAGMAxOCg0R0\nVCoPFgiGANhJRG1LjVmCVQMwIqKMSq6ZVmTHKwAmAAyJaG0V9ydJr41TD8jKAr7/Hli/HsjLA/T1\ngRUrgLlzAQ2NSi8hIvz6969YeHohnmU/gyBNAIMbBki3TQc0AOQB1jesEbotFJYWlnUy784d4Ouv\ngYgItt+nD/DDD0DPnnW6rUJ4/fo19u7di507d+Lu3bsAAIFAgKFDh2LatGkYMWIE1NXVFWwlR9YI\nBAIQkaDON6rNNAcs5nEIwA4Ag+syZQILzqeWG2sCQISqg/QWKLWQE8BOVJEEAO4Wa1g8eFC2GFj7\n9iyVqxpev3lNX//5NQl8BIT5IB1HHers0rlW2WI1QSQi+vVXopYtS1xl7u5EL19K7RFyRSQS0blz\n5+iLL74Qd8kEQC1atCBPT0/6999/FW0iR4ZASm4xiTOXyhAIBE0ATAfgBCAabEYTV8t7DAFwiIhM\nSo1VO3Op5B7OANYQUZtKjpG3t7d4397eHvb29rUxkaOMnDoFzJsH/Psv2//8c2DDBsDCospLIpMj\n4f6nO2KexAAARrQbgS2fbIGFYdXXvAuZmYCvL7B5M1BQABgbs0mXmxtzn9VHXr58ib179yIoKEg8\nmwGAgQMHYurUqXB2doaurq4CLeTUlYiICEQUT70B+Pr6yn/mUtkGlhbsD1YteRFqEGwvuq47yq2L\nqWys1LHiWU3pmcuQas6vu4RzlJO3b4nWrClJXdbSIlq5kuUMV0FBYQFtubqF9L/XJ/iAtL/TptUX\nVtPbAukvvb99m2jw4JJJVo8eRJcvS/0xckUkEtGlS5doypQpZcrM6Ovrk5ubG126dImvm2kgQBmz\nxYrEYWeR0LhBci2y8m6xIQBOV3FuEwCry41NB3C/ivOl805zlJfHj4m++KLkW9zKiuj48UpPLa4S\n4GlnS4525oS5LGOsw7YO9JfwL6mbJhIRHTpUklVWvACzITSTzMjIoKCgIOrXr1+ZTLO2bdvSqlWr\n6OFD6VdM4MgPpRSXMjdmQrETwI5qzlmNiutcSu9botS6FwCLyl1/BsDnVdxbOu80R/mJiCDq1Knk\nW3z4cBajKaKy+mYzW7ckyxXm4rTkCUcn0NPMp1I3LSuL6NtviTQ0mGn6+kRr19aPWmU14e7du/TN\nN99Qy5YtxSIjEAhoyJAhtGfPHsrMzFS0iZxaovTiUmMDmCttNNhqe7dyx6aVnskUzV4WF42XEaZK\n7iuVN5pTT8jLI9q0qaTipKYm0fLlRNnZVVZmXv7FePKN8CVNP02CD8jQ35C2X99OBYXSX3p//z6r\nslxsQrt2RCdPSv0xCiM/P59OnjxJY8eOJU1NTbHQ6OjokKurK/3vf//jFZrrCXITl1Jf/t0kubmU\naePi0kh58oT5n4q/xS0saEXpWU2pbYUDW0T5IPUBfbzvY/EsxibQhiKTI2Vi3smTTFiKzRg2jKih\nLYx//fo1BQYGlqlpBoCaN29Oc+fOpWvXrvH4jBIjT3ERFQnMEJRLP0YllZGVZePi0si5eJGoa1ci\ngHyKZirlZy6lu2GKRCI6cvsItdrQiuADEvgIaOaJmfQq55XUTXv7lrnG9PWZOerqRB4eRGlpUn+U\nwomPj6eVK1dSu3btyghNmzZtaMWKFXT37l1Fm8gphzzFpcpyLEXHnSW5qBSxcXHhUH4+0ZYtlKin\nRx6lBCYLIA9ra1b6vxyZbzNp8ZnFpLZSjeADahbQjHbH7pbJX9pPnxJNncrWxQBEzZoRBQbWr4KY\nNUUkEtG1a9do3rx51KJFizJC07VrV/L39+ftAJQEaYlLTVbo7yQi92pPYucdKprZNJV0rjzgK/Q5\nYp49Q9KsWdh99ChEAFR0dTF5/XqYT5/O6rlUwt/P/8bXJ7/G+aTzAIABrQdg+7Dt6Nyis9TNi45m\nS3cuXWL7XbsCmzYBDXVZVkFBASIiInDgwAEcPXoU6enp4mO9e/fGuHHj4OLigvfff1+BVjZe5LZC\nH6WyvcBSjf3B3GTdKjn3VW3VTVYb+MyFU55SrjJxwKNUVll5RCIR/RL3CzVf25zgA1L1VaUFpxZQ\nem71rQDeheLWNq1bl5hXg9Y29Z7c3Fw6duwYjR8/nnR1dcvMaGxtbWnjxo306NEjRZvZqIAc3WI7\nKxl7BbaOZXS58UPSMEoqL4yLC6cyilxlZbLKVqwgysmp8pLiMjIqvioEH1DLdS3pwM0DMnGV5eSw\n9aA6OiSOxyxcSPRK+qEfpSM7O5sOHTpEzs7OpKWlVUZo+vbtS+vWreOuMzkgT3GpsE6lMsGpblwR\nGxcXTrU8fVohq4yOHWNTiCqITommPkF9Skr273agv5/9LRPzkpNZa5vieIyxMdPExlIJPzMzk377\n7TdydnYmbW3tMkLTo0cP+u6773gygIyQp7i8AvA9SmWKodxK+VLj/tIwSiovjIsLpyZcuEDUpUuJ\nyJRbgFmeQlEhBUUHkckaE4IPSG2lGnmc9qCM3AyZmBcdTWRvX2Jeu3YSNbDBkZWVRYcPH6Zx48aR\nnp5eGaFp3749LVmyhK5du0aFEprKcWqGvMXlAVhKciFYaZfTALpWcm6loqOIjYsLp8bk5xNt3lwr\nV1lqTiq5/+HOKi4Xucr239wvE1eZSET03/8StW1bIjKDBrGeao2NnJwcOn78OE2ePJmMjIzKCI2Z\nmRnNnDmTTp06Rbm5uYo2td4i95gLWM/66WAl91+VExsPsEWWVZZ6kffGxYVTaypZgClpmhCZHEm9\ng3qLXWUDfx5IN5/elIl5b98yDTQxKTHxyy+JGmsYIi8vj8LCwmj27NnUqlWrMkKjr69PLi4utHfv\nXkqtb21CFYy0xKUmqchNiCi9knFLsJL7jkWbYZFRSlFcnKcic96ZCxdYB7Bbt9j+sGGsjn6bCp0d\nAAAiEuHn2J/hFe6FlzkvoSpQxezes+Fj7wNDLUOpm5eWxkr5b97M+qdpaABz5gBLl7Iy/40RIkJ0\ndDSOHTuG48eP4+bNm+Jjqqqq6N+/Pz799FN8+umnaN++PQRVpKBzpJeK/E79XCq9kUBgBbbgsvJP\noJzh4sKpEwUFwI4dwLJlQEYG+wb/5htgyRJAR6fSS16/eY3lfy3HjqgdEJEIzXWbw3+IPyZ1mwQV\nQbUdxd+JxERm3v79bN/QkAnMnDmAlpbUH1evEAqF+OOPP/DHH38gIiICBQUF4mNWVlYYPnw4hg8f\njkGDBkGrsb9Z5VA6cQEAgUDgT0ReUrthHeDiwpEKz54Bnp7Anj1s39wc2LgR+OyzKhdg3nh6A7P/\nNxsXH14EAPQx64Otn2xFL7NeMjExJobpXng423//fWDlSmDixPrbpEyapKen4/Tp0/jzzz9x8uRJ\nvHz5UnxMR0cHQ4YMwSeffIJPPvkEFtU0nWssKKW4KBNcXDhS5dIl5iq7cYPtDx3K/FIffFDp6USE\nX//+FYtDFyMlMwUAMKXbFHw/5Hu00GshdfOIgDNnmA4Wm/jhh8x9NmJElTrY6CgsLMT169fx559/\n4s8//0RcXNkGuu3bt8cnn3yCjz/+GAMHDmyUsxouLhLg4sKROgUFwK5dzBeVlgaoqwMLF7J9Pb1K\nL8l8m4lVF1Zhw5UNyBflw0DTAN6DvDG792xoqGpI3USRCDhwgJmUlMTG+vUD/P0BOzupP67ek5yc\njFOnTuHkyZMIDQ1FZmam+Ji2tjYGDRqEoUOH4qOPPkKHDh0aRayGi4sEuLhwZMaLFyy48eOPbMpg\nZgasWweMG1flFOF+6n3MPz0fJ++fBAB8YPIBNn28CR+3+VgmJr59C+zcCXz3HVDsBfrkEzaTadIk\nCcuX70ZysghmZirw85sMS0tzmdhRn8jPz8fly5dx+vRpnDp1CrGxsWWOt2rVCk5OTnBycoKjoyOa\nNWumIEtlCxcXCXBx4cic69eB2bOByEi2P2gQsGUL0KVLlZecvH8S80/Nx/1X9wEAn7b7FOs/Wo92\nJu1kYmJGBrB+PbBhA5CVBQBJ0NXdiuxsXwC6ALJhbe2N0NA5XGDK8fTpU4SGhuLMmTM4c+YMnj9/\nXuZ4t27d4OjoCEdHR9jZ2UGnikSP+gYXFwlwceHIBZEI+PlnwMuLTRFUVIBZswBf3yrzgvMK87D5\n6mb4nfdDZl4m1FXUMa/PPCwbuAxNtJrIxMwXL4DVq4HNm30hEi0CE5ZisuHqug779nnL5NkNAZFI\nhJs3byI0NBShoaG4cOECcnNzxcc1NDRga2uLwYMHY8iQIejduzfU1dUVaPG7w8VFAlxcOHLl9WvA\n2xvYvh0oLARMTJgPaurUKlO2nmU9w7dnv8VPsT+BQGim0wyrBq/ClO5ToKoimzSvfv28ceWKb6Xj\nly5VHOdUzps3b3D58mWEhYUhNDQUMTExKP19o6urCzs7Ozg4OMDBwQHdu3eHmpqaAi2uOVxcJMDF\nhaMQbt0C5s4FIiLYfo8ezFXWv3+Vl0SnRGPeqXm49Ig1dOnaois2fbwJ9hb2UjdvwgRf7N9fceai\norIO8+d7w9MTaN5c6o9t8Lx+/RoREREIDw9HeHg4/vnnnzLHDQwMYGdnB3t7ewwaNEipxYaLiwS4\nuHAUBhFw+DDg4QE8fszGXF2BNWtY8L/SSwiH7xzG4tDFeJj+EADwWfvPsNZpLdoYS29dslCYBCen\nrYiPL4m56Op6Izt7DgBz6OiwMNLixUBTpWj7Vz958uQJIiIicPbsWURERODBgwdljuvr62PAgAEY\nNGgQBg4ciJ49e0JDQ/rZg+8CFxcJcHHhKJzsbCYoAQEsfUtXF/j2W2DBgiqX0L/Jf4P1V9bD/6I/\nsvOzoa6ijjm952DZwGUw0jaSillCIcsWS0kRwdSUZYulpZnD2xv44w92jq4uW+nv4cFFRho8evQI\n586dw19//YVz584hPj6+zHFtbW3Y2trCzs4OdnZ26Nu3L3R1dau4m2zh4iIBLi4cpUEoBBYtAo4e\nZfuWliyFq5pV/imZKVh2dhl2x+0GgWCsbQyfQT5wt3GHuqrsAsWRkYCPD3CSZUxDV5fNZDw8gAaa\neasQkpOTce7cOZw/fx7nz5/H3bt3yxxXVVVFjx49MGDAANjZ2aF///5oLid/JRcXCXBx4Sgd4eHA\n/PnA33+z/SFDWCmZzp2rvCTmSQw8znggIjECANDOpB0CHAMw8oORMl3Qd+0aS3j73//Yvo4OS4Lz\n8ADee09mj220PH/+HBcvXsSFCxdw4cIFxMbGQiQSlTmnTZs26N+/P/r164f+/fujQ4cOUFGRfs06\nLi4S4OLCUUqKV/kvX84yzFRUgBkzWDGwKvxPRITj945jcehi8fqYQeaDsO6jdbAxtZGpudevA35+\nwIkTbF9LC5g+ncVkWrWS6aMbNZmZmbh69SouXryIixcv4urVq8jJySlzTpMmTWBrawtbW1v07dsX\nffr0QZMmdU9l5+IiAS4uHKUmNZX5n3bsYKnLhoYslXnWLFaBuRLyCvOwM2onVp5bidQ3qQAA186u\nWDV4FcwNZbsAMjqarfb/73/Zvro6MHkyq2VmbS3TR3MAFBQU4MaNG7h06RIuX76My5cv49GjR2XO\nEQgE6NixI/r27SveOnToANVaVi/l4iIBLi6cesHt2yzAHxrK9tu1Y8vphw2rMh6TlpuG7y98j83X\nNiOvMA8aqhqY23sultotlVrQvypu3gRWrWLJcERs4jV+POtE0KmTTB/NKcfjx49x+fJlXLlyBVeu\nXEFMTAzy8/PLnKOnp4devXqhT58+6NOnD3r37g1TU9Nq78vFRQJcXDj1BiLmd/LwAO4ztxecnFjQ\nv5p4TGJaIr49+y0O3DoAADDSMsJSu6WY3Xs2tNSqruYrTBRi+YblSM5IhpmBGfwW+sHSwrJWJv/z\nD0uE27ePefoAVn3Zy4sVyuTIn9zcXMTGxuLq1avi7eHDhxXOMzMzQ+/evdGrVy/06tULNjY2MDQs\naWrHxUUCXFw49Y68PLbC39eXVV1WUQHc3Fg8pkXVZfqjU6KxOHQx/kr8CwDQuklr+Dn4wbWza4WV\n/sJEIZxmOyG+azygASAPsL5hjdBtobUWGIBVXl67ltXwLK6GYmfH3GXVTL44cuLp06e4du0arl27\nhsjISFy/fh0ZGRkVzmvXrh1sbGxgY2ODhQsXcnGpDi4unHrLy5dMUIpLyejrM7/T/PmAtnallxAR\nTj04Bc8wT9x6ztozd27eGauHrMawtsPEmWUT5k7Afv39TFiKyQNcM12xb8u+dzb5+XNWiGDbNiC9\nqBWWE+UAABgmSURBVCl6p04s8D9+fJVhJI6cEYlE+Pfff8VCExkZibi4OLx9+7bMeVxcqoGLC6fe\n888/bH3Mn3+y/datWfXJ8ePZrKYSCkWF2H9rP5b/tVy80t+utR3WOK6B7fu2cJjsgAjLiArXOQgd\ncHb32TqbnJEBBAWxDOvkZDZmZgbMm8eyzKSQzMSRMnl5ebh9+zaioqIQGRmJoKAgLi7VwcWF02AI\nD2fxmOIWk716sf4xAwdWeUluQS52RO7Adxe+w6s3rwAAIz8YiYKzBTjZ7KTUZy7lyctjTcvWrgXu\n3GFjenrAtGms9BrvJqy88JiLBLi4cBoUhYXAnj2sxeSTJ2xs1CgWVa+i1TIApOemY93lddhwdQNy\n8nOANEAvTg9Z/bKkEnORhEgEnD7NtPBs0cRIRQUYPZolydna8riMssHFRQJcXDgNkuxslkUWEMB+\nVlVl/iZv72qD/s+ynmHVhVXYGbUT+a/yIYgToKVeS/Ru1RsbPDfIRFjKExvL3GW//lqSYdarFwsl\njRnD4zLKAhcXCXBx4TRonjxhgvLjj2x6oKvLouceHsz/VAWJaYnwPeeLX278AhGJoKmqiZk2M+E1\nwAst9KoWJ2mSnAz88AMrVPCKeezQsiUwcybTyWo0kiMHuLhIgIsLp1Fw5w5bXFJczrhFCyY6bm5s\nGX0V/PPyH6z4awUO3zkMANBR18Gc3nOwuN9imOiYyMNy5OSwdTKbN5fEZTQ0gLFjWUXm3r3lYgan\nHFxcJMDFhdOoOH+ezVyuX2f7bduyTpjOztUGNeKexmHFXyvwx79MnPQ19DGvzzwstF0o89X+xRCx\nnIWtW5lGFn9sbWxYNZzx46vMwObIAC4uEuDiwml0ELGy/kuWlKz0t7EB/P1ZBeZquJ58HSv+WoHT\n8acBAAaaBpjfZz7m950vN5EBWHeC7duBn34qcZkZGbE6ZjNmVJu7wJESXFwkwMWF02jJz2exGF9f\n4OlTNuboyGYyvXpVe+nlR5fhHeGNsIQwAExk5vWZh/l958NY21jWlot58wY4eJAJTWRkybiDA+Du\nzlrh8AQA2cDFRQJcXDiNnuxstmx+zZqSZfOjR7Pyxh06VHvpxYcX4R3hjbNClj+sr6GPuX3mYkHf\nBXKLyRQTFcWC/wcOsDgNwLoTTJ7M1s20aydXcxo8XFwkwMWFwyni1SsmMFu2sAJgKirAxIks8G9Z\nfQryxYcXsfLcSoQmsKrNuuq6mNVrFjxsPeSWXVZMejpLAAgMZNWZi7GzA6ZMAVxcWNIcp25wcZEA\nFxcOpxwpKYCfH5ICA7FbJIIIgErbtpj8yy8w79u32kuvPLoCv/N++N8D1ppSS00L03pMw6J+i9C6\nSWs5GF8CEXOVBQYCv/3GJmgAK8E2bhzwn//wxZl1gYuLBLi4cDgVSRIKsdXeHr4PH0IXQDYAbwBz\npkyB+erVgIQ+7VEpUfju/Hc4du8YAEBNRQ1fdfkKngM80c5E/v6pzEzg0CEWYrpypWS8XTvmNpsw\nAXj/fbmbVa/h4iIBLi4cTkV8J0zAov37Udp7lA1gHQBvHR22wGTRoipbLhdz89lN+F/0x8HbByEi\nEQQQwLmjM7z6e6GnaU9ZvoQquXOHVcj55ZeSPAaBgCUBfPUVCzfp6yvEtHoFFxcJcHHhcCri7eAA\n34iIiuMmJvBNZa2ToafHRMbDAzCpPnh/P/U+Ai4FYM+NPcgXsS6IjlaO8OzviSGWQ8Sl/uVJQQGr\nZ7Z3L2vLXFxNXlsbGDkScHUFhg7l2WZVIS1xqbxuN4fDaZComJkhu9xYNgCVjz9mCzA/+QTIymKl\n/S0sgG+/Zf1lqqCtSVsEjQyCcJ4Qi2wXQU9DD2EJYXDa64QegT3w661fUSAqkOVLqoCaGjB8OIvH\nPH3KWgDY2ZWkN48cycrNzJgBRESwmqAc6cNnLhxOIyJJKMRWJyf4xseXxFysrTEnNBTmxZljV68C\nPj7sz3+ApWDNns1mMs2aVXv/129eY0fUDmy5tgXPsp8BAMybmGNen3lw6+EGfU3F+aWSkljRzH37\ngNu3S8ZNTVnhzLFjWSJAFa1yGg3cLSYBLi4cTuUkCYXYvXw5RCkpUDE1xWQ/vxJhKc2VK6wj5qlT\nbF9Hh61gXLSI/elfDbkFudh7Yy/WXVmHf1P/BcAWZE7vMR1z+syRe4ZZef7+mwnNr7+yqgDFtGrF\nKuaMGQP069c4hYaLiwS4uHA4UuL6dSYyxR0xNTXZ6sXFi1l3zGoQkQgn/j2B9VfW43zSeQCAqkAV\nzh2dsaDvAvRtVX0KtKwhYos0Dx5kWWePHpUca9kS+Pxztg0aVG0d0AYFFxcJcHHhcKRMTAxb3f/7\n72xfTY2lYXl61miZfGRyJDZe3YjDdw6L4zC9zXpjXp95GNNxDDRUFRthF4mAa9eAkBDgyBHmRivG\nyAj49FPWn23o0Gq7GtR7uLhIgIsLhyMj/v6b1Sk7eJB9IwsEzI/k6Qn0lJyG/DjjMbZd34bA6EC8\nzn0NAGip1xLuNu6Y3nM63tN7T9avQCJEQHQ009Hffwfu3i05pqnJ6oCOHMkSB1q1UpydsoCLiwS4\nuHA4MubBA9YRc/duViwTYAUyvbyAwYMlLpHPzsvG/lv7seXaFtx+wSLs6irqcO7ojK97fY3+7/dX\nSCpzZfzzD0trPn6c5TuU/mrp3p2JzLBhrAeNqqri7JQGXFwkwMWFw5ETycnApk3Azp0sjRkAevQA\nvvmGRcfV1Kq9nIhwVngWP0T+gGP3jkFEIgBA5+adMavXLLh2dlVolll5nj4FTpxgW2hoSTFNgC0L\nGjoU+Phj4KOP6mdXTS4uEuDiwuHImdevWf/iLVuAFy/YmKUlMH8+qyxZg0DFw/SH2Bm1E8ExwXiR\nw+6hp6GHCZ0nYHrP6ej+//buNTaK89wD+P+xCfH9stj4soQYOzedpgEbwklOK4oCTqqiplEgJR/a\nqlIhaStV7QdySKXz4Xw6hyjhUyvlQhq1/VIlFEobNSqXUJq0aVLIgaaHnJDGYC7G9wu214sN9nM+\nPLPe8Xq9u7Znvd7d/096Nbszo93Z8bv798w77zs1jcn8BLN2/Trwxz8Cb71l1zu4rzwD7Kjm4YeB\n5mbgC18A8vJSs52zwXCJg+FClCLBoI3Bsndv+KZlZWXWa/EHPwD8/rgvMXpzFAf/7yBePPUi3r30\n7uT8dbXr8FTTU3jy3icX1dEMYKfKPv3UgubwYeBPf7LwCcnPBzZssDOGmzYBa9YszlNoDJc4GC5E\nKTY+bo0Ue/cCf/mLzVuyxHor/uhHcW9cFnK26yz2/c8+/OLvv8DA9QEANvT/9s9tx3eavoMHVzy4\naNpm3IJB4N13gSNH7PSZ+zYBgF2B9qUv2dhnGzcC9967OPrVMFziYLgQLSIffGAhc+CAXWEGWC/F\nH/7QOpIk0IkkeCOI/R/vx89O/2yyzwwA3FNxD769+tv45upvora4NlmfYN46O4G33waOH7dpa+vU\n5T6fDVOzYYOFzurVcZurkoLhEgfDhWgRungR+OlPbcCv0N0x/X7g+98HduyIO+R/yLmec3jt9Gv4\n5Ue/RMewDYGcIzl4pOERfGv1t/C1u7+G/Fvyk/UpPHH+vI1tduKEtdtcuTJ1eWGhDUfzxS9ae836\n9UBJSfK3i+ESB8OFaBEbHrbx8X/yE+DcOZu3ZAnw1a9a4/+Xv5zQv+03J27iD5/9AT8/83P87tzv\nJkdmLrm1BE/8yxP4xn3fwIbbNyBHFsH5phhU7UjmnXesreadd4CWlqnriACf/7wFzoMPAg88ANx5\np/en0hgucTBciNLAxARw7JiFzFtvhU+Z3XqrtYAvXRoueXk2Py9vaikoAPLzEbxF8HGgFSevfYxP\ng20YXgoMLwXyypbhX+/ehI33PYq76tZCSkvtEKCgYFHfrrKjw5qq/vxn4L33bICEmxEDTJeXW9PV\n+vXhafU8+6AyXOJguBClmatX7SYsr71ml10lW26uhUxZ2fTi89kvt89nnVdC04oKK/kLf8otGLRx\n0N5/38pf/wq0t09fz++3gRLWrbPuRmvXzi5wGC5xMFyI0pSq9UwcG7MyOhqehkowaNf5BoNWRkbC\nJRCwMjwMDQTQ330JPZ2tCPZ3IT94EyWjQMkoUDCf28wUFlrIVFaGS1WVtRlVVU0tlZVJueZY1dpp\nTp60sUU/+MCGrBkamr5uTY1d+tzYaNM1a4CGhuin1BgucTBciMjt5sRNHL9wHL/631/h0CeHEBge\nQMkoUHYdWFvYgK9U/Bs2lq7GSi2B9PcDfX3WMbS3d2rp6bGwS1ROjoVOTU241NaGp36/leXL5x1C\nExM2Ks+pU1ZOn7bTaYOD09ctKLA2nPvus2moVFQwXGJiuBDRTMbGx3Ds/DG8fvZ1/PaT3+La6LXJ\nZXf47sBjdz+Gx+55DA+seAC5ORE/+Kp2eNDTYyMRdHcDXV1WOjunlo4OC6RE5OZa4Pj9NhrmihXA\nbbdNfVxbO+vrkycm7Mq0M2esnD5tfW4ir04LY7jExHAhokSMjY/h+IXjOPDxARw6dwg9I+HbOlcW\nVGLLXVvw6F2PormhGUVL5zDW/tiYBU97e7hcvWpjsrkfh4bMiSUnxwJm5Uort91m09tvD88rK0vo\nQoXeXguZjz4C/vEPK2fPAoEAwyUmhgsRzdb4xDjeu/wefvPJb3Dok0O4MBAeLGxp7lJsrNuILXdu\nwZY7t6DB1+Dtm4+OWthcuTK1XL4cLh0d8V+nuNjCJlTq6sLTujprA5ohfCYmgNxchktMDBcimg9V\nxdnus3jz3Jt489M38f6V96EI/6aU55WjwdeAhvIGrCxdifK8cpTnl8OX70N5nk1DpeTWEm+GqBkb\ns6Ocy5eBS5fC5eJFK5cu2cUMseTnTw2bVavCj+vqIFVVDJdYGC5E5KWuQBcOf3YYv//n73G45fDk\nOGeJWJKzBL58HyoKKibLsvxlqCyoRGVh5eR0eeFyLC9cjsqCStySO4f7KqvahQihsAmV1tbwtL8/\n5ksIwHCJheFCRMmiqugMdKKlrwUt/S1oG2zDwPUB9F/vtxLsR1+wD73BXvSO9CJwI87RRBTleeWo\nKqpCVWEVqoqqUF1YbdOiatQU1aC6qBrVRdWoLKzEkpxZNPIPDoaD5sIFK67nMjDAcImF4UJEi8Xo\nzVH0BfvQM9KD3mAvekZ60B3oRvdItz0e6UZ3oBtdgS50BbrQPdI9edO0eHIkB5UFlagprkFtcS1q\nimwaWZYXLk8ohNjPJQ6GCxGlqwmdQO9ILzoDnegc7kRnoBMdwx3oHO5E+3A7OgOdaB9qR/tw+5Sr\n22LJkRxUF1WjtrgW/mI//MV+1BbXYkXJCvhL/DYt9qMkr4ThEgvDhYiywY3xG1PCpn2oHVeHruLq\n0FW0D9vjtqE2dAe6p1yQMKP/ZJtLTAwXIqKwG+M3wmEz2Ia2oTZcGbyCtqE2tA2GH1//j+sMl1gY\nLkREs6OqyMnJ8SRcFvdNDoiIaMF4ebtohgsREXmO4UJERJ5juBARkecYLkRE5DmGCxEReY7hQkRE\nnmO4EBGR5xguRETkOYYLERF5juFCRESeY7gQEZHnGC5EROQ5hgsREXmO4UJERJ5juBARkecYLkRE\n5DmGCxEReY7hQkREnmO4EBGR5xguRETkOYYLERF5juFCRESeY7gQEZHnGC5EROQ5hgsREXluSao3\nQESeAdACYBkAqOo+L9cnIqKFl9IjFxHZA6BFVQ86IdEgIlu9Wp+IiFJDVDV1by7Sp6o+1/NNAHar\n6sPzXV9ENJWfjYgoHYkIVFXm+zopO3IRkUYAkb/+fQA2ebE+hZ04cSLVm7BocF+EcV+EcV94L5Wn\nxXywcHAbAAARKfFgfXLwixPGfRHGfRHGfeG9VIZLGSww3PoASJT5c1mfiIhSJJXhMhBlng926ivy\nCGUu6xMRUYqkrEHfaUM5paq5sebNY3225hMRzYEXDfop6+eiqqdFJPJoxAfgmEfrz3vnEBHR3KS6\nh/4rIvK463kzgJdDT0RkVUQ/lpjrExHR4pDSfi4AICK7AJwH0ACgX1VfdS3bCWCbqj6SyPpERLQ4\npDxcaO6co7r7VfXZKMtiDpPDYXQo24jIS6r63Yh5/J4kScrHFvNaNlQGZ2SCJthpwZYoy/cA+Juq\nHgw9F5GtqnogkeXpyPm7A8D9AE6q6vNRlmf8j4iIlAJ4CkA/gDsAIPKfj2zZF24i8hyAtRHzsuZ7\n4vwjWg/g17C6sRPAflVtda3jbb1Q1YwpAPYAeDzi+dZUb1eSP++LUeb3RTzfBOBIosvTrQB4KeL5\nKQC7Eq0XmVRvAOyJsi92ZOO+cH2GVc7nOBkxP2u+J06YjDul1/03Tla9SPmH9ngHZkxlSPDzTgsX\nAI0AeqPMG3ceN8Vanm4FQGmUH9Sd7rqQZT8i/4wIkzcAvJ6N+8L1GXY4n+Oka162fU92ACgBUDfD\ncs/rRaqvFvMMxx6bFG+YnPI4y9OND8AzIlIXMb8UAESkCTHqRbzlaahZp17kUg/gb0D870gG7ovQ\nKeQ3oizKtu+JqOqguk6DTS5IUr3IpDaXmJVFVQcXfpNSYqZhcuDMjzeMTlrtJ1W9ICJrI740DwM4\n6jyO9yMRc3m61Rudeg69yWbpXmfWvH5Q021fOEpVdVBkWre3rPqeAICI7IB9hmUAyjTcLpmUepFJ\n4ZJxlWGOZhomB7D9kXHD6KjqmdBjESkD8BDstAaQnT8ipQC+DmAb7BRhSFbtiziN79n2PTkKO7U1\nCNiVcyKyU61RPin1ImNOiyHzKsNc9cEqg1sZADgVK97ydPcGgIdU9aLzPNt+RKCq11R1n1r/sFed\n/1iBLNoXIrIK0T9PSFZ9T1S1NWK7jwLY7TxOSr3IpCOXjKoMc6VxhsmJtzydOZeO7lHVv7tmx6wX\nIpJR9UZESlX1mmvWywBeAfAqsmtfNAFY5bQnAMB6AGVOJ+xfZ9P3xDmS7YedCgv9HQdgV9EBSaoX\nGXPkoqqnMT1h07IyeCDeMDkZN4yOcx3/EVU97jxvBOLXi0yqN07jdX9Eg7MAUOfceNbsC1U9oKov\nhArsP/UB53mrs1o2fU+eiwiCBthIJ0n7jmRMuDgyqTLMSEQanQ5NWwF8XUR2icia0HJV/TGAehF5\n3FnvM3U6giWyPN2IyGZYZf9QREpFpB7Adtcq2fIjcgrAyxE/IpthneVC87JlX0xyhpF6Albnd4XC\nN1u+J86RbG/E7G0A/t313PN6kXHDv3DsseziOuSPrMj7VfVJ13ox60Wm1Bvnn4xm2P6ogF0t9uOI\ndbJiX1CYa+SGAdjl6Scjg9LrepFx4UJERKmXaafFiIhoEWC4EBGR5xguRETkOYYLERF5juFCRESe\nY7gQEZHnGC5EROQ5hgtRkjijBRwRkdej3G8mWe/5jIi84XR4I0qZTBq4ksgzziCYTzlPX4YzRhfs\n3hb1AHY7Yy7F82FkD/lZbkcjgA8B7If1ju4D8LSz+CVYL/x62FBADar6vNMbe89c35PICwwXoihU\n9VkR2Qa7jfRe9zJnrKoPRaRMkz9asA/ANvdQHSLSYJuoL7jm7YCFTGuSt4coITwtRhSFc9OxegBv\nR1l8ypmuW4BNqU9ksERnnKfyBdgeooQwXIii2wwbnO9MlGXfdZYdX4DtiBzNNhYOFEiLBk+LEUW3\nGVHuVyEiz8GGK39oNi/mtJ3sg7Wb/Bec+5gDuN85BbfJWbUJwPnQ7XlnM8R7Og4HT5mL4UIU3WYA\nR517WAjsFNl22E2nVs22rcW5s+FOWMP8QOiISES2i8h/uxr933bu/DfTvd+J0gJPixFFcK62qofd\nMvmgc1fD51V1Haxd4+nYrxBTuetOiIBzN8AIvRF3kyRKOwwXoumaYW0qF6Ms2w/guXn0W4kaJhHP\nZY6vTbRoMFyIpova3uIohzWcly3c5hClH4YL0XSbARyZYdnTmPkqMq/wqi9KewwXIhcRqccM/Vuc\nK8WaAGyKXJboyyOxU17x1vHN8f2JFgyvFiNyOEO+bIYdOewWkQHYD30Z7Ae9F3O4Usx57UYAzwJo\nFJFdqvqCiGyFDdsyICLnVfWgsw2rAOwTkd3uxn/ncuVmOOHmbN/RBepvQzQrosojcKJkcK46e3Y+\nY4vN4333qOr3FvJ9idx4WoyIiDzHcCEiIs8xXIiSi31WKCsxXIiSq2mhbxYG4BUALQvxfkQzYYM+\nERF5jkcuRETkOYYLERF5juFCRESeY7gQEZHnGC5EROS5/wfEhjQ1DSeA6wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1145100b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(fields, gaps[:100], c='k', lw=2)\n",
    "plt.plot(fields[1:], (ens1[1:]+ens2[1:])/2, lw=2, label=r'$\\phi=\\pi/2$')\n",
    "plt.plot(fields[1:], (ens3[1:]+ens4[1:])/2, lw=2, label=r'$\\phi=3\\pi/4$')\n",
    "plt.plot(fields[1:], (ens5[1:]+ens6[1:])/2, lw=2, label=r'$\\phi=\\pi$')\n",
    "plt.plot(Bs, Es, 'o', c='r')\n",
    "plt.plot(Bs, Es1, 'o', c='b')\n",
    "plt.plot(Bs, Es2, 'o', c='g')\n",
    "plt.yticks([0, 0.5, 1])\n",
    "plt.legend()\n",
    "plt.ylabel(r'$E/\\Delta$')\n",
    "plt.xlabel(r'$B$ [mT]')\n",
    "plt.savefig(\"absorption_frequency_at_different_phases.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "abs_en = lambda phi, tau: np.sqrt(1 - tau * np.sin(phi/2)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.66332495807107994, 0.7225026652322929, 0.84852813742385702)"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs_en(np.pi, TAU), abs_en(3*np.pi/4, TAU), abs_en(np.pi/2, TAU) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([<matplotlib.axis.YTick at 0x111bce438>,\n",
       "  <matplotlib.axis.YTick at 0x10f21a278>,\n",
       "  <matplotlib.axis.YTick at 0x10f3487f0>,\n",
       "  <matplotlib.axis.YTick at 0x10e0faa58>],\n",
       " <a list of 4 Text yticklabel objects>)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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e5pOl0WZAkMTr6QZJkkiX0pNnL14AEycCmzeLdVdXYP16oEkTedMlA/X3J0mS\nzCnRfa9fAytWAD//DERGim3NmwMzZwI9egDqUxgYGIg1a9bg77//Rnx8PADA2toagwcPxvDhw9Gg\nQQOZPgHTBZIkgYi0c8NpK7JoY4G+5RAyO3RIM65BiRJE334rei8ZkUOHDtG7775Lly9fljspeiMm\nRvRjsLXV5BgaNybatk2Mo6T2+vVrWrVqVYZKaADk4eFBa9eupdevX8v3IZhswEVGOiw2lujLL8Us\n7oAYEe3UKblTVWxSUlJo9erVVLlyZRo8eDAP15APcXFES5cS2dtrAkOdOkR//pm1o3xgYCCNGTOG\nypcvnxYYzMzMaMiQIXTq1Cmeo8GIcEDQB/7+RPXra+7sESNE4bGRiImJoZkzZ5K1tTVNmzaNW8rk\nQ0KCGCsp/SB6zs5Eq1aJfenFx8fTxo0bqX379hlyDc7OzjRnzhwKCQmR50OwYsMBQV8kJYkeSuqp\nO+3txQD7RiQ8PJy+/vprnpOhAJKTxVxOtWtrAkPlyqLdQkxM1uPv379PM2fOzDDdJ1QV0d7e3lyk\nZKC0GRC4Urk43LwJDB8O+PuL9Y8+An79FahcWd506YHHjx8jODgYLi4ucHBwkDs5skhNBXbtAn76\nCQgKEtusrIDx44EJEwBb24zHK5VKnDx5En/88Qd27dqFhIQEAECZMmXQq1cvDB48GJ07d0apUqWK\n+ZOwosCVyvpIoSD65Rcic3PxU69CBaLffzeYDm0Fkdv4Pbl1kDNWSqVot9CmjSbHULYs0RdfEIWG\nZv83r1+/pt9//53atWuXIddga2tL48ePJ39/f+4RrefARUZ6LDSU6L33NHd0p05ERljOq1Qqyc3N\njcaMGZNtj+echtDgYbiFs2eJunfXXEYlShANGkR07VrOfxMaGko//fQT1a1bN8M5rVGjBs2cOZP+\n+++/4vsATGs4IOg7pVLMyKbu0GZmJgbWN7JJ2l++fElffPEFVaxYkRYvXpxWz5DbIHs8DHdGV68S\nDRwoAoI6OHTtKhq25fTDX6lUUmBgIE2aNCnLeW7UqBHNnz+fK6P1CAcEQ/HsGVH//po7uXlzouvX\n5U5Vsbt16xZ1796dXFxc6NixYzwMdwE8eEA0frxmiC2AyN09a1+GzBQKBR0/fpw+//xzsrKyynCu\nmzdvTj///DOFh4cX2+dg+afNgMCVyrrgwAFg9GggIgIoVQqYNg2YPh0oXVrulBWrY8eOoUyZMnBx\ncUGzZs2z/89RAAAgAElEQVTw5MmTLMfY29vj8uXLRlvB/DYvXwIrV4o2C69eiW3OzsCkScCwYYC5\nec5/m5SUhKNHj2Lr1q3Yt29fWq9oAGjZsiX69u2Ljz76CFWrVi3iT8HygyuVDVF0NNHo0Zqfd/Xq\nib4MRorrEAonPl70ZXBx0VxSFSoQTZtG9PhxXv4+nrZt20Z9+vShsmXLZvgOPD09acmSJTwMuo4A\nFxkZsNOniWrVEl+NJIkZ2uLi5E5VseNWRtqhUBDt2EHk4aEJDKVKEQ0dKuof8iI2Npa2bt1KvXv3\nzhIc3NzcaN68eTwSq4w4IBi6N2+IvvlGU1Po7Ex07JjcqZJFREQEzZgxgxwdHWn79u3cRLIQzp0j\n6t1bM6oKIEZtP3SIKK8jXcTFxdH27dvp448/zjAVKACqW7cuTZs2jS5dusTfUzHigGAsAgOJmjTR\n3L2ffSYG1TdCJ06coEaNGlGbNm144LxCun9f9F1Qd4kBiN55h+i33/KXGX3z5g3t3buXhg4dShUq\nVMgQHKpWrUpjx44lHx8fSkpKKroPwzggGJXkZDFze+nSlDZ2wc6dcqdKFgqFgtauXUuVK1emYcOG\nUQrPO1EoUVFEixYROTpqAoOVFdHUqUQPH+bvtZKTk+nYsWM0btw4qlKlSobgYGlpSR9//DFt3ryZ\nIo30B01R0mZA4FZG+uL2bTH8xblzYr1PHzGYvhEOf/H69Wvs27cPgwcPljspBiElBdi9G1i2TDO6\niokJ8OGHwJdfAq1ba+ZmyAulUonAwEDs3bsXe/fuxY0bN9L2lShRAq1bt8b777+P999/H7Vr19by\npzE+2mxlxAFBnyiVwG+/iWapcXFAhQpidpWhQ/N3xzKWg4sXgeXLge3bAYVCbGvcGPjiC2DAAKBs\n2fy/ZnBwMPbv3499+/bB19cXqampaftq1aqF7t27o1u3bmjbti1KG1lTa23ggGDsHj4U/RaOHBHr\nnToBa9cC1avLmixd8OjRI24nrwWPHwOrVgFr1ogJAQHA2hoYMUJcegW91KKionD06FEcOHAAhw4d\nQlRUVNo+CwsLdOzYEV27dkXXrl3h6OhY+A9iBDggMFHk+9dfwFdfifkXzc3FcJjjxgElSsidOlkk\nJCSgTp06aNu2LebPn8+BQQsSE4Ft20RHt8uXxTYTEzHF57hxQMeOYr0gFAoFLly4gIMHD+LgwYO4\nfv16hv0NGjTAe++9h/feew+tW7fm3EMOuGMa03j6lKhfP02tYIsWREY8SFlMTAzNmDGDrK2tafbs\n2RRnhH04ioJSKfpJDhpEZGqqudxq1RLDcGmjrvjhw4e0Zs0a+uCDD8jCwiJDxbSZmRl169aNli9f\nTrdv3+ZmremAK5VZFnv3AmPGAE+eAKamwKxZwNSp4v9G6OHDh/j222/h5+eHLVu2oE2bNnInyWA8\nfw6sWyeKk8LDxbayZYH+/UVxkrt74au0kpOTcf78eRw5cgRHjhzB1atXM+x3cnJCp06d0LlzZ3h5\necHGxqZwb6jHuMiIZS86WgSBdevEesOGwPr14g41Uv7+/nByckKVKlXkTorBUSiAgwdFOwcfH812\nV1cRGD75BLCw0M57PX78GMeOHcPRo0fh4+ODV+qBmiAeiE2bNkWnTp3QsWNHtGrVCmULUvutpzgg\nsNydPClq/0JCRAHvpEnA3LmAmZncKWMG6u5d0a5hwwZRpQUA5coBAwcCo0YBTZpo772USiWCgoLg\n4+MDHx8fnDt3DsnJyWn7S5cujZYtW8LLywsdOnRAs2bNDHp2OA4I7O3evAFmzwaWLhXNVV1cRM7h\n3XflTplOCA0NhaWlJSpUqCB3UgxKQoJosrp2rabLDAA0by5+o/Tvr71cg9qbN29w9uxZHD9+HMeP\nH0dQUBDSP0csLCzQpk0bdOjQAe+++y6aNGmCEgbU8IIrlVneXbpE1LChphZw+HDRRdXILV++nCpV\nqkS//PILJScny50cg3T9uhgiw9JSc/lZWBCNHCkuy6KqF3758iVt376dRo8eTe+8806WEXMtLS3p\n/fffp//97390+fJlUuj5xFTgSmWWL8nJwKJFwA8/iP/b24uC3w8+kDtlsrp+/TomT56M0NBQLFq0\nCD179oTEHfy07s0bYMcOkUE9e1azvXFj4PPPRbGStXXRvX9ERAROnTqFkydP4vTp03jw4EGG/eXL\nl0fr1q3Rrl07tG3bFm5ubnpVxMRFRqxgbt4Uw1+oxyfo21c0MLezkzddMjty5AgmT56MmjVrYs+e\nPXInx6DdvCnaOfz5p2YCH1NTMUzG558DHToUfTeahw8f4vTp0zhz5gzOnDmDkJCQDPvNzMzg6emJ\nNm3aoE2bNvD09IR5bjMLyYwDAiu41FTN8Bfx8WL4i6VLgSFDjHr4C4VCgf/++w+NGzeWOylGISlJ\ntJT+/XfRQkl92zs6ipFYPv1UVHsVh/DwcPj6+qYtt2/fzrC/RIkScHV1RevWrdG6dWu0atUKdjr0\nI4oDAiu8hw9F84+jR8V6586iYTkPf8GKWViYyDFs2ACkL81p21YEho8+Ei2Wisvz589x9uxZ+Pr6\nws/PD0FBQVAqlRmOcXFxQcuWLdGqVSu0bNkS9erVk62imgMC0w4iYNMmYOJEzfAX8+YB48cb7fAX\nmSmVSmzZsgV9+/aFqZF28isuSiXg6ytyDTt2iBZLgGgt3bu3yDm8+27xX5qxsbG4cOECzp49i3Pn\nzuHChQsZ5psGRD2Eh4cHWrRogRYtWsDDw6PYWrBxQGDa9eyZGOf4n3/EuocH4O0NNGggb7p0QHR0\nNPr374/g4GAsWLAAvXv35ornYhATI4LCn3+KIKFWpQowaJAo4axXT560KRQKXL16FefOnYO/vz/O\nnz+PsLCwLMfVqVMHnp6e8PT0hIeHBxo0aICSJUtqPT0cEFjR2LcPGDsWiIgASpUS9QzTpwM8qBiO\nHTuGKVOmwMzMDIsXL0arVq3kTpLRCAkBNm4Umdn09b9Nm4rg8MknouGcnB49eoQLFy7A398f/v7+\nCAwMzNBZDhCV1W5ubvDw8ICHhweaN28OR0fHQv/A4IDAis7r18C33wKrV4v1unVFbqFlS3nTpQOU\nSiU2b96MmTNnYtWqVejWrZvcSTIqRKKz28aNYgTW16/FdhMTwMtLNF/98EOgfHl50wkASUlJuHr1\nKi5cuIALFy7g4sWLWVozAYCdnR3c3d0zLBUrVszXe3FAYEXP11d0Lb17V7Q+GjdODK9dnLV7Oiox\nMRElSpTQq7bqhiYxUYyjtGkTcOiQmPUNAMqUAd5/X0zm07WrbmVuX7x4gUuXLmVYItXjfKRTrVo1\nNGvWLG1xdXWFdS4dNXQqIEiS1AdADQA7AEQBGAFgOxGFpjtmCoBgADYAQETrcngtDgi6JDER+P57\n0aktNVW0CVy9GuBfxkyHREaK+obNmzPWN1haisroTz4RldFFUHxfKESE4OBgBAQE4PLlywgICMCV\nK1eyVFgDgLOzM9zc3ODm5gZXV1e4urqm5SR0LSCMAKAqX0A0gBFEtCvd/gUALqm3qdYDiGhnNq/F\nAUEXXb0qeg0FBor1AQPEBLy2tvKmS8f8/fffePr0KcaOHYsyZcrInRyjFB4ObN0KbNkC/PuvZrut\nreiH+fHHYo7ogk7qU9RSU1Nx+/bttAARGBiIoKAgJCYmZjnW0dERrq6u2Lt3r04FhOEAtgGwTp8r\nSLc/kois0617AfiGiDpncywHBF2lUIjJdmfNEu0BbWxEh7ZBg4y6Q1t6N2/exLRp0xAUFIS5c+di\n8ODBBjWImr65dUs0nNuyRZR8qtnbi+DQrx/QooXuBgc1hUKBW7duITAwEFeuXEkLEm/evEk7RlsB\nQRsD0o3IZV9TAK+y2Zaaw/E5jd/EdEVwMFHHjprRyjp3JgoJkTtVOuXs2bPUunVrqlevHu3atYtn\n95KZUkl05QrRN98QVa+uuXQBoipViCZMIPLzI0pNlTuleadQKOjWrVu0efNm3RrcTlVkRAAiIeoI\nrIhosWqfF4DVRFQr3fHOAO4DqEBEMZleiwqbHlYMiEQD8UmTgKgo0XPoxx+BCRO4Q5sKEeHw4cP4\n559/sGHDBpjo+s9QI0EEBASIVkrbt4te0mr29qLO4aOPgDZt9OdS1rU6hOoAItUPd0mSVgMIJKJ1\nqgrntURkk+54S4jK5xqUqYiJA4KeefYM+OorUWgLAM2aiSaqPB4Q0wPq4LB9u6iUDg3V7LO1BXr1\nAvr0EQPu6XIndZ0KCFleUASBhURUU5VD2JYpIOSaQ/juu+/S1tu3b4/27dtrNX2sCBw4IDq0hYeL\nn1WTJwPffScm2mXZioqK4sl5dAgRcOWKCAw7dgD372v2WVoC3buL0eK7dtX+BD/5dfr0aZw+fTpt\nfe7cuboRENL92rdKl0PwAuBDRCUkSWoK4DIRlUj3N1m2pdvHOQR9FRsLzJgBrFgh7i4XFzFYnpeX\n3CnTOUqlEg0aNEDjxo0xd+5c1K5dW+4ksXSIgBs3gF27gJ07gevXNftKlwY6dhTB4f33dWPkeG3m\nELRRsLkw0y99FwAhAEBE/0I0RU3PGsBxLbwv0yXlygG//AKcPw/Urw8EB4s7Z9gwzcD3DABgYmKC\nS5cuoUGDBmjVqhWGDRuWZdIWJh9JAho2FJnca9eAe/eAxYtFZ/3kZNEhbsQIUefQsiWwcKFo0WQQ\nv2ULWysNYHKmdR8AH6Zbnw+gd7r1BenXM/1tQSrcma5JSiL68Uei0qVFUw5bW6LNm4tuzkQ9FhUV\nRbNmzSJra2v69ddf5U4Oe4snT4jWriXq1o3I1DRji6WaNYkmTiQ6eZKoOGdlhY61MrIEMBIiJ1AD\notPZrkzHTIbINbgAiCIi7xxeiwqbHqZD7t4Vcy6oyzvfew9YtYrnXMjGq1evEB0dDZfimhWGFVps\nrJjcZ98+UY2WfhQKS0txuXfvLuod8jk8Ub7odKVyYXBAMEBEYuaTyZM1TVS//14Mt61rYwkwVkAK\nhZiZ9sABYP9+UYSkJkmAp6cY8aV7d6BJE+325eSAwPRP5iaqTZuKWdfd3ORNl46LiIjAwoULMXTo\nULx58wYuLi5wcHCQO1nsLYKDRV3DwYMig5x+JGx7e5F76NoV6NQJsLIq3HtxQGD66/BhYMwYMYWn\niYnozPbDD/K35dNRDx8+hJeXF0JCQkBEqFSpEjw9PbF582ZY8DnTC3FxwIkTIjgcOiSmG1ErUULk\nHt57TyyurvkfSoMDAtNv8fGiCcfSpWLeREdHYOVK0Y6PZdCrVy/s27cvy/bOnTvjqHo+bKY3iEQz\n1sOHxXLunChuUrOxEbmGLl3Ev1WqvP01OSAww3DlCjBypGYU1T59xAB6ebkLjMDjx4/RrFkzPHny\nJMs+W1tbBAUFcfGRnouJAU6eBI4cEcvDhxn316snAkOnTkC7dtlnpDkgMMOhUIjObDNnipxDuXLA\n/PnA6NH6M5hMEfHz80P79u2hVCqz7DMxMcGZM2fQunVrGVLGigKR6PNw9KhovXTqlLgl1EqWFKOz\nduwo+ns2by5muuWAwAxPWBjwxReiDR8grva1a416XKTccgj29va4fPlyhhzCvXv38OLFC7Tk6U4N\nQnKyaLl07JhYLl8WJaxqFhZA27bAoUO61VOZscJzcgL27BFjBTg4AJcuiRZIU6Zk/JlkRBwcHODu\n7p7tPnd39yzFRWFhYRg4cCDatWuHw4cPg39c6TdTU1FM9OOPwMWLosP/7t1iNts6dURl9aFD2n1P\nziEw3RMTI4qQ1OMiOTmJSucePeROWbGLi4vDwIEDERAQgGfPnqVNyp5TKyOFQoFt27ZhwYIFMDEx\nwdSpU9GvXz+U5D4fBiciQtQ/DBnCRUbMGAQEiJ7O6rkQe/cWlc5Vq8qbLhk8fvwYISEhqFGjRp4q\nkkk1H8OyZcuwadMm2OnCKGysSHAdAjMeCgXw669i6s74eFFw+sMPwPjx3NOZMXBAYMYoPFwMd7F7\nt1hv2hRYvVpUPrN8u379OkxMTFC/fn25k8IKSdeGv2as6Dk6igHq9+0TdQr//iu6eI4dC0RnHmGd\nvc3NmzfRsWNHdOnSBUePHuUKaAaAcwhMH8XHi2Kj//1PFCnZ2Yn/Dxig3VHDDFxSUhK2bNmCpUuX\nQqFQYMKECRg6dCjKlCkjd9JYPnCREWOAmNZq9GjR/x8Qk9+uXCna5LE8IyKcPn0a3t7eWLduHczM\nzOROEssHDgiMqSmVwB9/AFOniobapUqJ/0+fLobaZszAcR0CY2omJsBnnwF37gCffw6kpADz5olp\nPPfvlzt1BmH//v1YsWIFYmJi3n4w02scEJhhsLEBvL1F8VGjRkBoKNCzJ9Crl/g/KzB7e3v4+vqi\nWrVqGD16NIKCguROEisiHBCYYWnZUoyeunSpGChv3z4xZOS8eUBSktyp00vNmjXDtm3b8N9//6FK\nlSp4//334enpiYj0A/szg8B1CMxwPX4spu7cskWs16olhsPo3FnedOk5hUIBHx8fdOnSBSUyjUib\nkpKCZ8+ewdTUFKVLl0771yS/s76wPONKZcby4+RJ0bNZPdFtnz7Azz+L/gxMqx48eIA2bdogKSkJ\nSUlJSE5ORlJSEurWrYubN29mOT48PBzDhg2DmZkZzMzMYG5uDgsLCzg5OeHrr7/OcnxSUhJCQkJg\naWkJS0tLmJmZQTLypsYcEBjLr+RkMQ7S3LmiH4OZGTBjBvD110Dp0nKnzqARERQKBUqVKpVlX3x8\nPPz9/fHmzRvEx8cjPj4ecXFxMDMzw8iRI7Mcf//+ffTo0QMxMTGIjo5GSkoKLC0t4e7ujsOHD2c5\n/tWrV9i3bx9sbGxQsWLFtMXKyspgci0cEBgrqEePgEmTgO3bxXqtWsAvv4gJbZneSU5OxuvXr5GY\nmAhHR8cs+x8+fIjZs2cjMjISL1++xKtXr/DixQvUrl0bFy9ezHL806dPsW/fPtjZ2cHOzg6VK1eG\nnZ0dypYtWxwfp0A4IDBWWCdOiAl51MVIvXqJimhnZ3nTxYqFUqnMNodw//59LFiwAM+fP8fTp0/x\n9OlTPHv2DB06dMg2B/Ly5UvcuHEDDg4OcHBwyHZI8qLGAYExbUhOFiOpzpkjZhspXRr45huxcKc2\npkJESEhIyLYHd0BAACZPnoyIiAhERETA1NQUVapUwQcffICffvopy/GpqakwMTHRar0HBwTGtOnx\nYxEE/vpLrFerJsZG6t2bx0ZieUZEiI6ORkREBCRJynYk2X/++QeffvopqlatCkdHR1StWhVOTk5o\n27YtOhew9RsHBMaKwtmzojXS1ati3ctLVETzENFMi+Lj4/Ho0SOEh4enLbVr10b//v2zHHv06FHs\n2bMHTk5OcHJyQrVq1eDk5AQHB4e0WfA4IDBWVFJTgbVrxRSekZFAiRJiEts5c4AKFeROHTMyt2/f\nxvHjx/Hw4UOEh4fj4cOHePjwIT799NO0IikOCIwVtVevxCxta9aIAfRsbMRs5yNGiCDBmIyIKK0e\nggMCY8Xl6lUxU9uZM2K9USNg2TLg3XflTRdjKjzaKWPFpXFj4NQp0W/ByQm4dk3Mu9CnDxASInfq\nGNMqDgiMvY0kAR99BNy+LWZqMzMT03nWrQtMmwbwsNDMQHCREWP59eiRCATqZqp2dqJ+Ydgwrl9g\nxY7rEBjTBRcvAl99BVy4INYbNxaD5nXoIG+6mFHhOgTGdIGHB3D+vBhe28lJVEB7eYmJee7ckTt1\njOUbBwTGCkOSgP79Rf3CTz8BFhZi6s769UUntxcv5E4hY3nGRUaMadPTp8Ds2cD69aL/QvnywPTp\nwIQJgA6PmMn0F9chMKbrbtwApkwBjhwR646OYhrPgQMBAxmHn+kGDgiM6QsfH2DqVM34SE2aAIsX\nAx07ypsuZjC4UpkxfdG5MxAYCPzxB1C1KhAUBHTqJLb/+6/cqWMsA84hMFZcEhLE6Knz52s6sw0Y\nIDq71aghb9qY3uIiI8b02atXoj5h5UoxSU+pUsCoUWIwvUqV5E4d0zMcEBgzBKGhwHffAZs2AUSA\nubmY7/nrrwFLS7lTx/QEBwTGDMn166Jp6oEDYt3aWgyNMW4cN1Vlb8UBgTFDdO6cCAy+vmLd3l5M\n1DN8OGBqKm/amM7igMCYoSICjh4VgUHdCqlaNdHZbcgQQDVtImNqHBAYM3RKJbB7twgEN2+KbTVr\nijqHTz7hUVVZGg4IjBmL1FQxeN7cucD9+2JbnToiUPTrx4FB36SmiibHr18D0dHi35gYIDZWLHFx\nQHy8WN68EU2V1UtSEpCYKP5NThZLSgqkmzc5IDBmVBQKMf/C998DDx6IbRwY5EckmhFHRIhxrJ4+\nBZ49A54/FwMbvngBvHwJREaKJTpa/I0WSQAHBMaMUkoK8Oefoh9DaKjY9s47wIwZoiiJ6xi0KyFB\nnOf0S3i4ZnnyRPxSzw9LS7FYWYl/y5XTLBYWovmxubmYmc/MTLQ0K1sWKFMGKF1aLKamYilVClLD\nhhwQGDNqKSnAxo1ipjZ1YHBxEc1VBw/mVkn5kZIi5se+c0ezBAeLIrpHj97+91ZWQJUqQOXKYrGz\nE4utLVCxomaxthbHajk3x3UIjDEhJQXYvFnkGNR1DI6OYqTV4cO5H0N6RMDDh2KgwWvXxIi0//0H\n3L0rzmN2SpYUrbyqVwecncW/jo6axcFB/IqXEQcExlhGCgXwzz9ikh51q6RKlcQUn2PGiF+mxkSp\nFL/0AwPFcuWKGFhQPYZUZk5OQN26ovjtnXeAWrVEjsvJSeeL4TggMMayp1QCe/eKHENgoNhWrhww\nerQIDg4O8qavqLx8KaYz9fcHLl0CAgJEq53MKlUSc183agQ0bAjUqycCgYVF8adZSzggMMZyRwQc\nOwYsXAicPCm2mZoCgwYBkyeLh6C+IhItrfz8RK/us2dFsU9mjo5As2aAmxvg6go0bSrK+A0MBwTG\nWN4FBAALFoiObur7q0cPMYheu3ZiXmhdFxYGnDolgtvJk1kre8uWBZo3B1q2BDw9AXd3MfSHEeCA\nwBjLv3v3gKVLgQ0bRAcnQMzgNmkS8PHHutUyKS5OBAAfH7FkzgFYWwNt2gBt24p/mzQRw4gbIQ4I\njLGCe/EC+O03sTx/LrbZ24vK51Gj5JmTgUg89A8dAg4eFEVB6Vv+lC8vcjMdOoilQQOem1pF7wKC\nJElTAAQDsAEAIlqXw3EcEBgrLomJwN9/Az//LJpfAiKXMGCAGHq7WbOifX+FQlQE79snlnv3NPtM\nTEQRUJcuYrrR5s11vrWPXPQqIEiStADAJSLalW49gIh2ZnMsBwTGihuRKJdfvlzMyaC+Bz08RGDo\n21f0ktWGpCTgxAlg1y7RGurlS80+a2uga1egWzcRCGxstPOeBk7fAkIkEVmnW/cC8A0Rdc7mWA4I\njMkpOFgUJf3+uxh3BxAP5mHDgJEjRfv8/EpKEvUA27eLIJC+L0CtWkCvXsD774sKYc4F5Js2AwKI\nqMgWAE0BvMpmW2oOxxMTTp06JXcSdAafC6FYz0N8PNG6dURNmxKJPINYvLyItm4lSkzM/e9TUoh8\nfIiGDSOytMz4Go0bE33/PdGNG0RKZYGSx9eEhuq5qZVndlHXylgDiMy0LRoAJEkqX8TvrddOnz4t\ndxJ0Bp8LoVjPg5mZGPoiMBC4eFHkEMqWFcU9/fuLsXsmThR1AEql+BsicfxXXwFVq4qy/w0bxBDP\njRuLznJ374oew7NmAfXrF7jJK18TRaOo82dWEEEhvUiIEVutAeTQj5wxphMkSVToNm8uKp83bwbW\nrRPjAS1bJhY7O/Hwv3wZuHVL87c1a4oK6k8+EUN1M51X1AEhOptt1gAIWXMOjDFdZmUlKpnHjhUP\n/82bRZ1AaCiwaZM4pmJFEQAGDxatlPSh0xtLU6SVypIkNQVwmYhK5LYt3T6uUWaMsXwiLVUqF2kO\ngYj+lSQpcy7BGsDxHI7nnxOMMSaT4ujqt1aSpN7p1jsBWFMM78sYYywfiqun8mQAIQBcAEQRkXeR\nv6mOkiSpDwB3Ivo2m3259ujOa49vxgyFJEmriWh0pm18nxQRnRjLyBi+QFWHPFeIHFIwEY3JtD/X\nHt356fGtL1TfOwC4Q3yWxdnsN/gbX5IkSwAjAUQBqAkAmX8wGMu5SE+SpIUAOhCRe7ptRnOfqH48\n1gCwA+LaGAFgOxGFpjtGu9eFtjo0FHQBsABA70zrfeROVxF/3lXZbI/MtO4FwCev+/VtAbA60/pl\nAJPzel0Y0nUDYEE252K4MZ6LdJ/BWfU5AjJtN5r7RBUAUlXLq/TfcVFdF7rwoQ3mC8zj580SEPCW\nHt0QOYs89/jW9QWAZTYPwRHprwUju/HvZQoA2wD8Y4znIt1nGK76HAHpthnbfTIcQHkA1XPYr/Xr\nQtbxY1VNUDOXWUVCJNyYvK1Hd4W37Nc31gCmSJJUPdN2SwCQJMkVuVwXb9uvhzpRxnq1GgAuAW+/\nRwzwXKiLV7dls8vY7hOJiGIoXRFR2o4iui7kHkkq1y+YiIylJ3NOPbqh2m5QPb6J6IEkSW6ZLvTO\nAI6p/v+2GzvX/fp23VDGMmFXsYn+p9pUqIegvp0LFUsiipGydmozqvsEACRJGg7xGWwAWJGmnq1I\nrgu5A4LBfYEFlFOPbkCcD4Pr8U1EQer/S5JkBaADRJYfMM4b3xJAPwAfQRSfqRnVuZAkqQ/lXAFs\nbPfJMYhinxhAtLiSJGkEiYrhIrku5J5yyNC+wIKKhPgC07MCANXF8Lb9+m4bRGuSh6p1Y7vxQUSv\niWgdEXUB4K36ZQgY0bmQJMkZ2X8eNaO6T4goNFO6jwH4RvX/Irku5M4hGNQXWFD0lh7db9uvz1TN\nAhcQ0dV0m3O9LiRJMqjrRpIkSyJ6nW7TGgBrAXjDuM6FKwBnVfk4ADQHYKXqx7TDmO4TVY4xCqKY\nSEpL2K0AAAFVSURBVP09RkO0vgKK6LqQNYdARP8iayTTyy9QC97Wo9vgenyr2ln7ENFJ1XpT4O3X\nhSFdN6oK1KhMlZ4SAFKV9RrNuSCinUS0RL1A/CKOVq2Hqg4zpvtkYaaHtwtEB98iu0fkLjICDOsL\nzJEkSU1VnUT6AOgnSdJkSZKaqPcT0TQANSRJ6q067j6pOtfkZb++kSSpI8QFGihJkqUkSTUAfJzu\nEGO58S8DWJPpxu8I0QFJvc1YzkUaSZJGAOgLcc1PVgdMY7lPVDnGV5k2fwRgarp1rV8XutJTmYe2\nMCLpssOZL77tRNQ/3XG5XheGct2ofhh0gjgfFSFaGU3LdIxRnAumka4HezREU+SAzMFN29eFTgQE\nxhhj8tOFIiPGGGM6gAMCY4wxABwQGGOMqXBAYIwxBoADAmOMMRUOCIwxxgBwQGCMMabCAYExxhgA\nDgiMMcZU/g/tbBv6cvOrSgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f3569e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(fields, GAP * ens5, c='r', lw=2)\n",
    "plt.plot(fields, GAP * ens6, c='b', lw=2)\n",
    "plt.plot(fields, GAP * (ens5 + ens6)/2, c='k', ls='--', lw=1)\n",
    "plt.plot(fields, GAP * np.asarray(gaps), c='k', lw=2)\n",
    "plt.plot(Bs, GAP * Es, 'o', c='k', markersize=7)\n",
    "plt.yticks([0, 50, 100, 150])\n",
    "#plt.savefig(\"fit_fig_4b_new_ticks_yaxis.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Trying to fit the orbital effect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fit_orbital(B, b, tau, phi):\n",
    "    return (1 - B**2/b**2) * np.sqrt(1 - tau * np.sin(phi/2)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 390.39991161])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "popt_orb, pcov_orb = curve_fit(lambda x, b: fit_orbital(x, b, TAU, np.pi),\n",
    "                               Bs[1:], Es[1:], p0=[1.])\n",
    "popt_orb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1)"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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d6qhSbUsp+8/t1de7vlZ3Ht1Jl/u9cv9Ll5WLy3AF95/+Ge4rF5fhav36y8rZ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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118d112b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi/2))\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, 3*np.pi/4))\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi))\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, 0., np.pi/2), c='k', lw=2)\n",
    "plt.plot(Bs, Es, 'o', c='r')\n",
    "plt.plot(Bs, Es2, 'o', c='g')\n",
    "plt.plot(Bs, Es1, 'o', c='b')\n",
    "plt.ylim([0, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Including a g-factor = 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MmTIFnYZ1wj++/yAiMULvBJCqExEBHDgA7N8v1j8q5h0fISlEJCUBp04BBw8Cnp7C+WLV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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c22ba58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi/2), c='b')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, 3*np.pi/4), c='g')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi), c='r')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, 0., np.pi/2), c='k', lw=2)\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi/2) - 0.5 * fields * MU_B * 12 / GAP, c='b', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, 3*np.pi/4) - 0.5 * fields * MU_B * 12 / GAP, c='g', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi) - 0.5 * fields * MU_B * 12 / GAP, c='r', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi/2) + 0.5 * fields * MU_B * 12 / GAP, c='b', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, 3*np.pi/4) + 0.5 * fields * MU_B * 12 / GAP, c='g', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi) + 0.5 * fields * MU_B * 12 / GAP, c='r', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, 0., np.pi/2) - 0.5 * fields * MU_B * 12 / GAP, c='k', lw=2, ls='--')\n",
    "plt.plot(Bs, Es, 'o', c='r')\n",
    "plt.plot(Bs, Es2, 'o', c='g')\n",
    "plt.plot(Bs, Es1, 'o', c='b')\n",
    "plt.ylim([0, 1])\n",
    "plt.title(r\"$g=12$\")\n",
    "plt.ylabel(r'$E/\\Delta$')\n",
    "plt.xlabel(r'$B$ [mT]')\n",
    "plt.savefig(\"absorption_frequency_orbital_and_zeeman.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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p5/Jl8PWV1WSvXn3l6Rq1a7No3TrOnz9P//79yZQpE2vXrqVmzZo0adKEvXv36hC0omQg\nmzfLIqxGolou6Sw2NpZy5cpx8eJFPvjgA9asWcO7776rd1imERoK/v7y+OcfaN8eOnSAhg0hhRli\nN2/e5IcffmD27NnxSbh+/fqMGTOGRo0aWW/BTEXRmeoWS4G5JheA4OBgOnToQHBwMI6Ojvj5+eHh\n4aF3WMb3zTdyX5POneV04TeYhx8eHs7MmTP54Ycf4nfQrF27Nj4+PirJKIoJqOSSAnNOLgCPHz+m\nb9+++Pv7AzB58mRGjRqlc1RvKDbWaAu4kvPo0SNmzZrF9OnT4wtm1q1bFx8fH9zc3FSSURQjMVZy\nUWMuOnF0dGTFihVMnTqVTJkyUalSJb1DSpuoKFizBtq1kyvjTSxHjhx8+eWXXLlyhcmTJ+Pk5MSB\nAwdo1KgRrq6uHDhwwOQxKIqSeqrlYgauXbtmPhWEX0cIOHRIlglftUpWFu7eXY6l5MyZrqE8fvyY\nmTNnMm3aNO7fvw9AixYtmDhxIlWqVEnXWBTFmqhusRRYUnKxGELIMuD16smkUrSo3hHx4MEDvvvu\nO77//vv4gf/OnTszceJEypQpo3N0imJ5VHJJgTUklyNHjlC9evUMV135Tdy5cwdfX19mzZpFdHQ0\ndnZ29O/fnzFjxvDOO+/oHZ6iWAw15mLlAgMDqVu3Lp06dUrf9TBnz8Jnn8GMGen3nkaQL18+pk+f\nzqVLl+jTpw8Gg4HZs2dTunRpvL29M9aaIkUxAyq5mKnY2FiyZ89OQEAAdevW5WoSCw+N5skTWLAA\nataUxe1y5wYLnRpdpEgRFixYwNmzZ2nbti0RERGMHz+e0qVLM3/+fGJjY/UOUVEyBNUtZsYuXLhA\n27ZtuXDhAvny5WPt2rXUrVvXuG/y77/w/vtyHUq/frIEhJ67RhrZ/v37+eKLLzhy5AgA5cuXZ+rU\nqTRr1kznyBTFPFnNmIumaV7AZSAPgBBifiquvw9oQE4hxLRkrrP45AJywPqjjz5i+/btFCxYkJCQ\nELJkyWLcN7l9G/LnN+49zYgQAn9/f0aNGsWVK1cAaNasGd999x3lypXTNzhFMTNWkVw0TfMFjgoh\nAhI8PiaEWJPM9V5CiKkJHlcGGic8l+A5q0guIMv3e3l50bZtW1xcXN7sJqGhYG8PhQsbNTZLEhUV\nxcyZM5k4cSKPHj3Czs6OwYMH4+3tTe7cufUOT1HMgrUkl3AhhFOCx+7ASCFEkrXWNU07LoSolujc\nSiHER0lcazXJ5Y0ZDBAYCDNnyvUpCxZY7FiKMd2+fZsxY8Ywf/58hBA4OTkxadIk+vXrh60VdQkq\nypuw+NlimqZVARJ/+ocDr1vuHa5pmr+maTnj7tEPWGmiEC3Xkycwa5YcS/HygrZt4do1lVji5M+f\nn7lz53Lq1ClcXFwIDw9n4MCBVK9eXa30VxQj0XO2mBMymST0AEDTtBzJvKY/8CEQGjf2cu9Fl1pG\nNXfuXE6ePPnyyfBw2L0b5s2D06flTo7ZsukToBmrVKkSu3btYtWqVRQtWpRTp05Rr149evbsyc2b\nN/UOT1Esmp7JJRcywSQUjhyoT3weACHEFWAucA/wBaqbMD6zt2vXLgYOHEj9+vXZsGHDf08UKwar\nV8sZYKqg42tpmkbHjh05f/48o0ePJnPmzCxdupT33nuPmTNnEhMTo3eIimKR9EwuD5I454TsKkvc\nogFA07SfgRNCiDLAp0B/TdP8TReiGYuJoe7Nm/Ro2ZKnT5/Srl07fvrpJ72jsljZsmVjwoQJnDt3\njpYtW/Lo0SM+++wzatSoweHDh/UOT1Esjm4D+nFjLseFELavO5fouf5CiIEJzpUELiVzvfD29o5/\n7OLi8uYzrczJkyfwyy9yx7jChRHffsuEwEBe/K7Dhg1j6tSpamD6LQgh2LBhA5999hnXrl0DoH//\n/vj6+qpZZYrVCQoKIigoKP6xj4+PUQb0EULodiDHTBI+dge2JXOtO/BFEudXJnO9sCoPHggxerQQ\nefMK0aGDEIcOvfT0kiVLRKZMmUSBAgVEWFiYTkFalydPnohRo0YJOzs7AYgCBQqI5cuXC4PBoHdo\nimIycZ+db/35rnf5l3maprVP8LgxckwFkC0TTdM6AAghdpJojCVu1lhIegRqFh48kFOKV6+GWrVe\neqpnz55s376djRs3UrBgQZ0CtC4ODg5MnjyZM2fOUK9ePW7dukXXrl1p0aIFoaGheoenKGbNHFbo\nf4FMEM7AfSHEggTP9QM6CiGaxj0uAQwALiEH/kXC6xPdV+j9uynWw2Aw8Msvv+Dl5cWDBw/ImjUr\nEyZMYOjQodjZ2ekdnqIYjVUsojQli00uhw/LfVNq19Y7EiUJt27dYtiwYSxfvhyAatWqsXDhQipW\nrKhzZIpiHBa/iFJJZM8eaNQIPvpIFpM0Il9fXzZt2mTUe2ZUBQoU4LfffmPz5s0ULVqU48ePU7Vq\nVcaMGUN0dLTe4SmK2VAtFz0JIcuzTJgAYWHw1VfQowdkymS0t9i7dy8NGzbE1taWefPm8cknnxjt\n3hnd48eP+fLLL5k9ezZCCN5//30WLVpEjRo19A5NUd6YsVouus4WM+WBJcwWi44WonFjIZYuFeL5\nc5O8hcFgEKNHjxbI9UNi4sSJaraTke3fv1+ULVtWAMLGxkaMGDFCREZG6h2WorwRjDRbTLVcMohZ\ns2YxZMgQhBAMHjyYGTNmqLUwRhQZGYm3tzfTp0/HYDDw3nvvsWjRImolmtWnKOZODeinwKySixBw\n547ue6asXr0aT09PChQowPHjx8lvxXu46OXw4cN8/PHHnD9/HhsbG0aOHIm3tzeZM2fWOzRFSRWV\nXFJgNsllzx4YOxayZoWtW/WOhqCgIAoUKKA2yTKhqKgovL29mTp1KkIIKlasiJ+fH5UqVdI7NEVJ\nkUouKdA9uRw5Al9/LTfpGjsWPD1BrYfIUA4ePEivXr24dOkSmTJlwtvbm5EjR6p1MYpZU8klBbom\nFy8vWLECxoyBjz826uwvxbJEREQwatSo+KKitWvXZunSpTg7O+scmaIkTSWXFOiaXC5ehKJFwdh7\n3ZvQlClT8PDw4N1339U7FKsUGBhI7969+eeff3BwcOCHH36gT58+aGpLBMXMqOSSAt27xSzIsmXL\n6NGjB/ny5WPbtm1UqVJF75CsUnh4OIMGDWLlSrl5aps2bViwYAH58uXTOTJF+Y9aoa+3R49g4kR4\n/FjvSN5a+/btadq0KXfu3MHFxYX9+/frHZJVcnJyYvny5fz666/kzJmTDRs2ULFiRXbs2KF3aIpi\ndCq5pNWzZ/DTT1C2rOz+iorSO6K3li1bNjZs2ECnTp149OgRTZo0YasZzGyzRpqm0a1bN/744w/q\n16/Pv//+S5MmTRg+fLgqH6NYFdUtllpCwJo18OWX4OwMU6aAlU0tjY2N5dNPP2XhwoWUK1eOP/74\nQ81sMqHY2Fh8fX3x9vYmNjaWypUrs3z5ct577z29Q1MyMDXmkgKjJ5djx+DTT+Hbb2WBSSslhGDS\npEn06NGD4sWL6x1OhnD48GE8PT0JCQkhW7ZszJo1i169eqnBfkUXKrmkwCQD+kKA+h9eMYFHjx4x\ncOBAfvvtNwA8PT2ZM2cOjo6OOkemZDQquaRAzRZTLI0QgiVLljB48GCePn2Ks7MzK1eupGrVqnqH\npmQgaraYKcTEwJw54OOjdyRmRwjB9u3b9Q7DqmmaRu/evTlx4gSVKlXi8uXL1KlTh1mzZqG+KCmW\nRiWXF3bsgMqVwd8f2rbVOxqzM3r0aJo2bcro0aPVB52Jvffeexw+fJhBgwbx7Nkz/ve//9G5c2ce\nPnyod2iKkmoquVy+LJPJgAFy065du2SSUV5SoUIFbG1tmTRpEl5eXirBmFiWLFmYNWsWK1euxNHR\nkdWrV/Phhx9y8uRJvUNTlFRRYy5DhkDhwjBsGKiy6K+1Zs0aunTpQkxMDEOGDGHGjBlqRlM6uHjx\nIp07d+b06dNkzpyZH3/8kX79+qm/vWISakA/BWpA3zQ2btxIx44defbsGT4+PowdO1bvkDKEqKgo\nPv/8c+bOnQtAz549mTNnDtmyZdM5MsXaqAH9VPDp3p2roaF6h2FVWrduzfr166lYsSJ9+/bVO5wM\nI0uWLPz888/4+fmRNWtW/Pz8qFWrFn///bfeoSlKkqy65fIE8HZ2Zsjq1RRfsAD69bO6VfV6iY2N\nVdsk6+Ts2bN06NCBixcv4ujoiJ+fHx4eHnqHpVgJ1XJJBQfA5/JlFteuDbGxUKSI3iFZDZVY9FOh\nQgWOHz9Ox44defz4Me3atePrr78mNjZW79AUJZ5VJxeQCcbwwQdy/UqePHqHE+9qaCg+3bvj7epq\nNd13Qgj1AZdOcuTIgb+/P1OnTsXGxoZvvvmGFi1acO/ePb1DUxTAyrvFBBABTMudG++SJeWOkHZ2\n//3MkkXOEHvxM1s2eTg4yJ/Zs0OOHODoKH/mzAm5ckHu3PKczZvl5quhocxs3Bify5dxiIvR29mZ\nITt2ULxkSSP+FdKPEIJhw4Zx//59fvnlF9WySUe7du3io48+4u7duxQvXpx169ZRWU2nV96Qmi2W\ngvgxl1y5GLJoEcWLFJEr8J8//+9ndLQsmR8dDZGR8nj6VB4REfDkidy35fFj+fPhQ3jwQB4RETLh\n5Mkjj7x55c/8+aFAAfkzf34oWFAeefPGJyOf7t354tdfcUgQbwQwzdMT72XL9PhzvbWLFy9SpUoV\nIiIi6N27NwsXLsTmDZOvknbXrl2jY8eOHDt2jKxZs7Jw4UK6du2qd1iKBVLJJQWapolxLVvS+/Zt\nigsBP/8MxqzRFBMjk829e/K4e1ced+7ArVtw+7b8+e+/EBYmk1OBAlC4MN6XL+Nz9+4rt/R2ccFn\n927jxZjO9uzZQ4sWLXj69CmffPIJ8+fPVwkmHUVFRTFo0CAWLVoEgJeXF5MnT1atSCVNVHJJQfw6\nFyHAzw9GjoR166BWLX0Cio6WiebGDXxGjeKL/ftfbbnY2OBdpgyUKiX3jHnx88U5C1jkGRQURIsW\nLYiMjKRPnz7MmzdPJZh0JIRg9uzZfP7558TExNCkSROWL1+Ok5OT3qEpFkIllxS8sogyPFyOl5jB\nB12yYy7r1lFc0yAkRJalefHz0iW4elV2r5UtK49y5eTx3nvwzjtmtRXArl27aNWqFSVKlGD//v3q\ng00He/bsoVOnTty5cwdnZ2c2bNjA+++/r3dYigVQySUF5r5C/2poKIvHjMEQFoZNoUL0njDh9YP5\nz5/LBPP333DhApw/D8HB8ufz5/DBB1wtWpTFFy9iiI3FxtmZ3lOn6jZBYN++fbz77rvkz59fl/dX\n5DiMh4cHp06dwtHRkeXLl9OyZUu9w1LMnEouKUh1cgkOhnffNYsWzRu7e5erO3Yw87PP8Ll797/W\nkK0tQ+rVo3itWlClijxKl7bs31VJk4iICD7++GNWrVqFpmn4+vri5eWl6pIpyVKLKI1BCFmw0sVF\ntgAsVd68LN68OT6xQNwC0thYFgshp1WvXAlNmsiuwQYN4PPP4ddfZSvIYNAzesWEHBwcWLlyJRMm\nTEAIwciRI+nZsydRUVF6h6ZYOd2Ti6ZpXpqmtdc0rZ+maf1ScX1OTdN8E7ymylu8OWzeDJ07Q716\nMGmS7GKyQIZ//nlpggDELSC1tYWxYyEgAK5ckYe3NxQqJCc4NGsGTk7g7g5ffw0bNshZbiYghGDb\ntm0mubeSPE3TGD16NAEBATg4OLBs2TLc3d25ffu23qEpVkzX5KJpmi9wWQgRIISYDzhrmtbhNdfn\nBHYKIUYJIQLiTo96qyBsbeF//4OTJ2H/fqheHc6efatb6sGmcGEiEp2LAGwKFXr55ItEMmIErFoF\noaFywsDw4XJh6ezZcpJAqVLQvTtXx4/Hp0ULOU36LSsJDBo0iGbNmjF9+vQ3vofy5tq1a8eBAwco\nWrQoBw8epEaNGpy1wP/WFQshhNDtAMITPXYHtr/m+p+BvonO5UjmWpFmBoMQS5YIceZM2l+rsysh\nIWK4s7N4Ijv7xBMQw52dxZWQkLTfLDZWiL/+ElcmTxbDHR1fvqeTk7iyYoUQkZFpvu3ixYsFIAAx\na9astMf4+J8WAAAgAElEQVSlGMXNmzdFzZo1BSCyZ88uNm3apHdIihmJ++x8+893Y9zkjd4YqgD3\nkjgX+5rXGIASqbz/2/6NLc6VkBAxztNTjHV1FeM8Pd8ssSQwztMzPrGIBAlmnJOTEA4OQjRsKIS3\ntxBBQalONrNnz45PMIsWLXqr+JQ39/TpU9G1a1cBCBsbG/Hjjz/qHZJiJqwhubgDFxOdKwnEJtUa\nSfCcG9AB6Ad4veb+RvlDZ2RjXVxeSiwvjrGurkI8eiTEli1CjBghRI0aQmTPLoSbmxCTJglx5IgQ\nMTHJ3nfatGnxH2rr169Px99ISchgMIhx48bFJ/shQ4aImNf8e1MyBmMlFz3HXHIBiVfXhQNaEucB\nSr34ByHEGiHHaF6M25je11/DgQPp8lbm4rXjOI6OcjLAlClw5Aj884+ceXfnDvTpI2uptWsnq1GH\nhLx0j+HDhzN+/HgqVapE7dq10+33UV6maRre3t4sW7YMe3t7Zs6ciYeHB0+ePNE7NMUaGCNDvcmB\nbLkk7hZ7XculSuLn4s4Zkrn/26fwhNasEeKdd4QYPlyIp0+Ne28z9VbjODdvCrFsmRA9eghRoIAQ\nzs5CDBokxMaNQjx5IgwGg3iaQf6OlmDv3r3CyclJAKJy5crixo0beoek6AQjtVx0W0QZN4X4uBDC\n9nXnEjxXEriU6PqSwCUgtxDiUaLrhbe3d/xjFxcXXFxc3i7oO3dg8GA5m2zJEqhR4+3uZwHSXEkg\nKULAH3/Atm2wZQscPw516kCLFtCypVzYqeju4sWLtGzZkosXL1K0aFF+//13ypcvr3dYiokFBQUR\nFBQU/9jHxwdh6Sv0NU27J4TIk+CxOzBCCNE0ueuBqkKIK3GPPwSOJZOMhMl+N39/+OwzmD8fWrc2\nzXtYs0ePIDAQfv9drjPKlQtatZJH3bpySrSii3v37tGmTRsOHjxIjhw5WLt2LW5ubnqHpaQjqyj/\nomnaZGRyCIh77AscTfC4JPChEGJN3OMvgAdCiAUJrr8jhHhl4YTJa4v9+68cd3BIvHRRSRODQa4x\n2rSJ2A0bGB0cTN9mzXDu0QOaNlV/Xx1ERkbSs2dPVq9eTaZMmVi4cCE9evTQOywlnVhFcoH4hBEC\nOAP3XySOuOf6AR0TtmTirgc58C+EENOSua9pk4tidL6+vnz55ZeUzJOH/e+/T6HTp2VpnvbtZQvR\njLaptnYGg4ERI0bEL3idOHEiX331lapJlgFYTXIxFd2Si8GgCkO+ocePH+Pu7s6xY8coX748ezZs\nwOngQVizRnaj1awpE0379nLjNcXkZs6cydChQxFCMGjQIH788Ue1+ZiVM7vkommaFzBSCJHXKDd8\nS7okFyGgfn3o3VtOx1Xf8tLs7t27NGjQgODgYGrXrs2OHTtwcHCQ20pv3QqrV8tJAR9+KGvCtW8v\nt5NWTCYgIIBu3boRHR2Nh4cHv/32G1mzZtU7LMVEjJVcjDGluB9wDzjOa1bXp/eBXosoz54VolIl\nIdq0EeLWLX1isHDXr18XxYoVi1/Y94qnT4UICBCiSxchcuYUolEjIRYsECI8PP2DzSD27t0rcuXK\nJQBRp04dcffuXb1DUkwEvVfoxyWVcOAY4B53TiUXIYSIihJi5Ei5LkbVbXojFy5cEO3atRP3799/\n/YUREUL4+wvRvr0QOXLIpL5ihTyvGNWff/4pihQpIgBRrlw5ce3aNb1DUkzAWMklzd1icYPsU+KS\nyrdCiJ0JnosVSUwL1oNZDOjv3Qs9e8py9x9+qG8sVu5qaCiLR47EcPYsNg8e0DsiguLt24OnJ7i5\nyerXylu7ceMGzZs3588//6RIkSJs376dcuXK6R2WYkTpPuaSKKmMEkKcSuIalVwSe/pUbtalmMzV\n0FBmNm6Mz+XL/+3CWbw4Q7p3p/jWrRAWJpNMr16gFgW+tfv379O6dWsOHDiAk5MTmzdvplatWnqH\npRhJuu1EqWlaB03TLgGNkAsYmyaVWJRkqMRicovHjIlPLBC3C+fVqyy+ckVWAwgMlAszmzWDqlVh\nxgy4e1fHiC1b7ty52b59O61atSI8PBx3d3e2bNmid1iKmUnNnNlSQCchxEdCiDffKUp52bNnekdg\ncZ49e0avXr0ICAh46Xyyu3CGhckH778PkyfD1auy0OaxY7LkTMeOskpATEy6xG9NsmXLxtq1a/n4\n4495+vQpbdq0Yfny5XqHpZiRFJOLEGIqEKJpWglN03KkQ0zW7+5dePddWfpESbXVq1fj5+dHt27d\n2LdvX/z5VO/CaWsLjRrBsmVyu+fGjcHHB4oXl1WvE1VvVl7Pzs6OhQsX4uXlRUxMDJ6ensyZM0fv\nsBRzkZbRfyAnshJxiWSeV7PFUmvPHiGKFRPis8/k7DIlRQaDQQwaNEgAIleuXOLs2bNCCCPswnn2\nrBCffy5E3rxCuLvL2Wbq30ma+Pr6xu8LM3HiRGEwGPQOSXlD6FkVOW4v+2rAZRFXRDLuvBrQT4v7\n96FvX7mP/YoVULas3hGZvdjYWDp37kxAQACFCxfm0KFDFC1a1DjVm6OiYN06mDcPzp2Ti2H79wdn\nZ5P8LtZm/vz5fPrppwghGDZsGNOnT1flYiyQWSyiRO6/4g5UFqrl8mYMBiFmzxaiZMk32pc+I4qM\njBT169cXgPD09DTNm1y4IPfuyZtXiMaN5X4+z5+b5r2siL+/v8iUKZMARJ8+fdTOlhYIc9rP5UX1\nYmCVEMIsCmtZRMsloYgIVQE4De7fv8/YsWOZPHky2bNnN90bRUXJ2mZz5sgJAf37Q79+8M47pntP\nC7dt2zbatWtHZGQknTt3ZunSpdjb2+sdlpJKZldbDGSSEWYyo8zikoti/k6flknG319Oax4yBGrX\nVjXkkrB//35atmzJo0ePaNGiBatXr1b1yCyEWSYXc2IVyeVF/OrDy7w8eACLF8NPP0HOnHLjuI8+\ngixZ9I7MrJw4cYKmTZty7949GjZsyMaNG3F0dNQ7LCUF6bKIUtO0nzVN66umIOtkxQro0kXu3Kik\nSrp8ociVCz7/HP7+G8aPh+XL5XTmsWPlJnIKAFWrVmXv3r0ULFiQPXv20KRJEx48eKB3WEo6eW1y\nEUIMAO4DCzRNW6lpWvv0CUsBwMMDcueWq8pPn9Y7GrMXGRlJp06dWLVqVfq8oY0NtGwptwLYswfu\n3IFy5eQsM/XvC4D333+fffv2UaxYMQ4fPoybmxt3VXWEjCEto//ISsj+wBzAzRgzCkx1YCmzxVLj\nt9/krKV58+TsMiVJfn5+AhCZM2cW+/fv1yeIe/eE8PUVokgRIVxdhdi8WYjYWH1iMSNXr14Vzs7O\nAhDly5cXN2/e1DskJRmYwTqX/kBj4ASwUghhVl/VrGLMJaHz56FTJ+jQAcaN0zsasySEYMiQIcya\nNQsnJycOHTpEWb3WDj17Jgf+p0+H6Gj4v/+D7t0z9LhMWFgYjRo1Ijg4mLJly7Jz506KFCmid1hK\nImYzoB83DflT5Mr9HcBqkWBhpV6sLrmArLB87x4ULap3JGYrJiaGdu3asWnTJkqVKsXhw4fJly+f\nfgEJAbt2wbRpcOaMHPwfMECO22RAt2/fpnHjxvzxxx+UKlWKXbt2Ubx4cb3DUhIwm+Ty0s00rQoy\n0ZQEVgH+QghdRqOtMrkoqRIREUHDhg05ceIE//vf/5g5c6beIQFw9fffWTx4MIYbN7ApU4beCxdS\nvHZtvcNKd+Hh4TRp0oQTJ05QvHhxdu/eTcm0VlNQTMYsk8tLN9Y0d6ATsv9uoEne5PXvr5JLBnbz\n5k18fX2ZMmUKWcygKyrJPWdsbBjSqRPFJ06UVZozkAcPHtCsWTOOHDlC0aJF2bVrF6Uz2N/AXJl9\nctFbhkkuQsCECfDxx6q7zIz5dO/OF7/++tLWABHAtPLl8f73X3B3hy+/hEqV9Aox3T169IjmzZtz\n8OBBChUqxO7du/UbI1PipedmYV9omtZe07TKar2LmcqSBWrUgJ07U75W0UWye87kyydL/VerBs2b\nQ9u2cPSoHiGmuxw5crB161bq169PWFgYLi4uXLhwQe+wFCNJTR2wb5EbhuVBVkKOp2mau6ZpJYwf\nlpJqmgYjRsCvv8rZSFOm/LeyXzEbr91zxtERvvgCLl+GJk3kJmZNm8L+/XqEmq4cHR3ZsmULrq6u\n3Lx5E1dXV5VgrEVKc5WB7Sk83wGYDLQ3xtxoYx1Y0zqX1Lp+XYiaNYXw8BDi0SO9ozE7Dx8+FJ07\nd47fByY9pWnPmehoIebPl5WyXV3l3j9W7smTJ8LV1VUAomDBguL8+fN6h5RhYaR1Lqn5kP45VTeS\niyvvGiMoo/xiGTG5CCE3ufrmGyGePtU7ErMzcuRIAYhixYrpsojvSkiIGOfpKca6uopxnp4pb2b2\n7JkQv/wiRKlSMskEBaVPoDpRCcY8GCu5pDigr2naHBE32ytuqvFHwF0gUCRaOKlpWrgQwskYLaq3\nlWEG9JVUi4yMxM3NjcOHD1OzZk12795tGZV6nz+X3Z4TJsgaZhMmQN26ekdlEhEREbRu3Zrdu3dT\nsGBBgoKC1CB/Oku3AX0g/k2EEKeEEKOAr4BqSdQaC3zbgBTFVLJmzcq6desoXrw4R44coXfv3hgM\nBr3DSlmmTLJe2fnzclyte3dZ8t8KB/4dHBzYtGnTS2Mwly5d0jss5Q2kJrkk9fXfXwixQAgRkOh8\nuBFiUkzh8WO5rXIGV6BAATZt2oSjoyP+/v4sWbJE75BSL1Mm+OQTuHAB2rWTpYBat5Yr/61ItmzZ\n2LhxIw0aNCAsLAxXV1dCQkL0DktJo9Qkl480TftG0zS3BOeS+5RS9bTNVUCAnK587pzekeiufPny\n+Pv7M3DgQLp37653OGlnbw+ffgoXL0LjxrIV07Wr3ALASjg4OLB582bq1q3LjRs3cHV15cqVK3qH\npaRBasZcwpEtklLIVsyLrq8RQogzia6dLIT40hSBppUac0nC0qWygOLcudBe7Z5gNZ48gZkz4bvv\n5DoZb2+rWVD7+PFjmjZtyqFDhyhZsiR79uyhqJX8buYqPcdc/IUQpQEnYCDwEKgOnNI0LVbTtG2a\npg3XNK0ykDGr8VmKHj1gyxYYNkxubGUJ4w1KyrJnl6v7L16E/PmhcmW5bubePb0je2sv1sHUqFGD\n0NBQ3N3duXnzpt5hKamQmpZLTiHEwyTOl0SW3G8Ud+RCTmGzTVMAmuYFXEYu0kQIMT8Nr/1ZyA3N\nknpOtVySc+uWXKjXtSsMGqR3NIqx3bwpd8hctUp+kfj8c3BIXB/Asjx48AA3NzdOnTpFuXLlCAoK\nIn/+/HqHZZXSreWSVGKJOx8qhJgnhOgcN/24NBCaljfXNM0XuCyECIhLKs6apnVI5WunAFXT8n5K\nnAIFZKmYPn30jsSs3Lt3Dx8fH8uYQfY6BQvCnDlw6JAc7C9bFubPh5gYvSN7Y7ly5WL79u2UL1+e\n4OBgGjduTHi4mj9kzlLTLZYqQogQYHUaX9Y/0YyzHciS/a8V12pSzZK3YW8PmTPrHYXZEELQrFkz\nxo0bx+jRo/UOxzjKlJEblq1dK9fJVKwIGzdabHmgvHnzEhgYSNmyZfnjjz9o0qQJDx8m+d1XMQO6\nVUWOW5AZKITIk+jc8ZS61jRN64tsJfkKIaonc43qFlPSZMeOHTRv3pzY2FiWLl1qmTPJkiME/P47\njBwJefPKzcuqVUv5dWbon3/+oUGDBoSEhFC3bl22bduGg4V3+5mT9BzQNxUnXl0X8wDgddWX4/aJ\n8TdhXBnX/ftyptHz53pHoovGjRszY8YMAPr27ctRa1qkqGnQsiWcPg2entCmjZzgce2a3pGlWeHC\nheO3SD5w4AAeHh5ERUXpHZaSiJ7JJRcywSQUjqwI8LoSMjmFTrtbWj1bWzh5Uq6duHtX72h0MXjw\nYAYMGEB0dDQeHh7cunVL75CMy84O+vWTCzFLlIAqVeDrr+UiWwtSokQJdu7cSYECBQgMDKRz5848\nz6BfisyVnsklqQWXTsixlCRH6jRN65BEVQDFWHLkgHXroGZNefz1l94R6WLGjBk0bNiQbt26kTdv\nXr3DMQ1HR1mj7MwZuH4d3n0XfvkFYmP1jizVypYty44dO8idOzcbN26kZ8+exFpQ/NbOTsf3DufV\ndTG5AJJqmcQN4qepAsC4cePi/9nFxQUXF5e0xpjx2NrKPWE++ABcXOTCy6ZN9Y4qXdnb27N9+3bs\n7e31DsX0ihQBPz9Zp2zYMLkY84cfoGFDvSNLlQoVKrBt2zbc3d1ZsWIF2bNnZ968eWjaWw8ZZBhB\nQUEEBQUZ/b66bnOsadq9RAP67siV/698msVNUS6Z4FQNoAowF1gthLiS6Ho1oP+29u+HwEBIkKQV\nKyaEnF02YoRsuU6dKqswW4C9e/fSrFkzIiMj+eKLL/j2229VgnlDxhrQ1zu5TAaOvejqilv3cjTB\n45LAh0KINUm8th9yKrOaLaYoxvT0qZxN9uOPMHiwnGGWLZveUaVoy5YttGnThpiYGCZNmsRXX32l\nd0gWyRpmixFXh6yUpmnt41bqX0o0ptII6J/4dXGJpVPca7943ewyRTGWW7ducfnyZb3DML1s2WR5\noFOnZDHMcuXkan8z/7LWvHlzli1bhqZpfP3118yaNUvvkDI0XVsupqRaLiYkhJzamoGcP3+exo0b\n4+joyOHDh8mRIwN9n9m7F4YMketjfvxRjseZsfnz59O/v/xOumzZMjw9PXWOyLJYRctFsUDPnsld\nEA8d0juSdFW4cGFy5sxJcHAwPXr0sPwSMWnRoAGcOCH3kHF1lQP/Zrwyvl+/fnz77bcA9O7dm82b\nN+scUcakkouSNvb2MHq0XIS3YoXe0aQbR0dH1q1bR65cudiwYQM+Pj56h5S+7Ozgf/+T+wE9fgzv\nvy9Lyphp74CXlxejRo0iJiaGjh07sn//fr1DynBUt5jyZv74A1q1ggEDZLn3DNJNtm3bNlq0aIHB\nYGDt2rV4eHjoHZI+Dh+WFbVz5IBZs8yyq0wIQf/+/VmwYAE5c+Zk7969VKxYUe+wzJ7qFlP0VbGi\n/IBZvVqu+M4gibxp06b4+voCEBwcrHM0OqpVC44dg06d5HooLy+5aZkZ0TSNn3/+mfbt2/Pw4UOa\nNm2aMSZkmAnVclHezpMnsGEDdOumdyTpRgjBkSNHqFWrlt6hmIdbt2Ry2bNHDvi3bat3RC+Jjo6m\nZcuW7Ny5k1KlSnHgwAHeeecdvcMyW1axzsWUVHJRlHS2a5fsKitbVq70N6MFmI8fP8bNzY3jx49T\nuXJl9uzZk7Fm/KWB6hZTFMW8uLnJWmU1akDVqnIhpplsUObo6MjmzZspU6YMp0+fpl27dkRHR+sd\nllVTLRfFNJ4+tYhV3cZkMBiwsVHf1wC4dElO9rh3D+bNg+pJFtJId6GhodSpU4d///2XTp06sXz5\ncmxt07Qzu9VTLRfFfBkMUK+e3Fo3gzhw4ADly5fn0qVLeodiHkqXhh07YPhwaN0ahg41i7L+JUuW\nZOvWreTIkYNVq1bx+eefo76EmoZKLorx2djAypWyuvLYsRliJtmMGTMIDg6mXbt2RERE6B2OedA0\n6N5dro159AjKlwczWNBYqVIlNmzYQObMmfnpp5+YPHmy3iFZJdUtppjO7dtyLcwHH8iukUyZ9I7I\nZB49ekT16tX5+++/6dq1K7/++quqyptYYCB8+qkck5kxA/Ln1zWcNWvW0KlTJ4QQLF68mF69euka\nj7lQ3WKK+cufH3bvhjt35PRUKy6ZkiNHDtauXYuDgwPLly/nxx9/1Dsk89OoEZw9C8WKQYUKch8Z\nHb8AdujQIf7fU9++fdm2bZtusVgj1XJRTC8mRk5TbdJE70hMbtWqVXTu3Bl7e3suX75MkSJF9A7J\nPJ08CZ98AgULwty5MuHoZNSoUUyZMgUHBwf27NlD1apVdYvFHKh1LilQyUXRy/jx46lWrRotWrTQ\nOxTz9vy53JDsu+/AxwcGDpTjdenMYDDQq1cvli1bRv78+Tl06BClSpVK9zjMhUouKVDJRVEsRHAw\n9Okjx+QWLpQzzdLZs2fPaNmyJYGBgZQtW5aDBw+SJ0+elF9ohdSYi2L5zKwWlaKTcuVg3z7w8JA1\ny2bMSPfxOXt7e9asWUOlSpX4+++/adOmDZGRkekag7VRyUXRR0yM3Kfdz0/vSBRzYGsr94k5dAjW\nrJF7yPz9d7qGkCNHDjZv3kyRIkU4ePAgPXv2zFj79hiZSi6KPuzsZEXlMWNkmRArFxQUxIULF/QO\nw/yVKQNBQfDRR3JTunRuxRQuXJgtW7aQI0cOVq9ejZeXV7q9t7VRYy6Kvq5fh2bNoEULuejSCsun\nbNy4EQ8PD8qVK8eRI0dwcHDQOyTLcOkS9O4tWzWLFkE6DrLv2rWLZs2a8fz5c2bMmMFnn32Wbu+t\nNzXmoliHokVlf/vBg9C3r1Wu5ndxcaFs2bKcO3eOgQMHqnIjqVW6tCzj37at7EKdM+el/z6uhobi\n07073q6u+HTvztXQUKO9tZubG7/88gsAn3/+OevXrzfavTMMIYRVHvJXUyxGRIQQW7boHYXJnDt3\nTmTLlk0AYt68eXqHY3mCg4WoXl2IJk2EuH5dXAkJEcOdncUTmW7EExDDnZ3FlZAQo77thAkTBCCy\nZs0qjh49atR7m6u4z863/ww2xk3M8VDJRTE3y5YtE4DInDmzOHHihN7hWJ7nz4UYP16IfPnEuDp1\n4hOLSJBgxnl6GvUtDQaD6N27twBEgQIFRGhoqFHvb46MlVxUt5iipBNPT08+/fRTsmfPzsOHD/UO\nx/LY2ckJIFu3Yjh9msQjVw6AISzMqG+paRpz587Fzc2NW7du0bJlSx48eGDU97BWKrko5s1MNpsy\nlh9++IHTp0/j6uqqdyiW68MPsWnThsS1pyMAm0KFjP52L9bAvP/++/z111907NiR58+fG/19rI1K\nLor5un9fFjj84w+9IzGaLFmyqHpjRtD7m2/wdnaOTzARgHfJkvSeMMEk75crVy42b95MgQIF2Llz\np5qYkQpqKrJi3lauhM8+g3XroHZtvaNRzMjV0FAWjxmD4epVbG7coLemUXzVKrnFsokcPXqUhg0b\nEhUVxbfffmuV62BUbbEUqORiRbZsgZ494ddfrbaystoi2QhWroQhQ+D//g+8vOT6GBNYvXo1nTp1\nQtM01qxZQ7t27UzyPnpR61yUjKN5c1i7Vu5quHq13tEYlcFgYNKkSXh4eKhSI2/ro4/g+HHYuhXc\n3eHaNZO8TceOHfnmm28QQuDp6cmJEydM8j6WTiUXxTLUqwfbt8utc63IrVu3+O6779i4cSPffvut\n3uFYvmLFYOdOWfWhWjXZmjGBUaNG0bt3byIjI2ndujU3btwwyftYMtUtpig627x5M61atcLW1pbd\nu3dTv359vUOyDidOQNeu8ovJjz9C9uxGvf2zZ89o2rQpQUFBVKlShX379llFaR/VLaYoVqJly5aM\nGDGC2NhYunbtyt27d/UOyTpUrSp3vAT48EOZbIzI3t6e1atXU7p0aU6dOkWPHj1U12YCKrkoihmY\nOHEiderU4Z9//mHYsGF6h2M9smeHX36BCRPk2N20aUatspwnTx42btxIzpw5Wbt2LaNHjzbavS2d\n6hZTLNvRo7B8OUyfbvEVla9du8aQIUOYNWuWWgtjCleuQLdukDMnLFkC+fMb7dY7duygefPmxMbG\nsmTJEnr27Gm0e6c3q5mKrGmaF3AZyAMghJifiusBqgPHhBBTk7lOJZeM4NEjaNUKSpaUW+Ta2ekd\nkWLOnj+HceNg8WKZYBo1MtqtZ8+ezeDBg7G3t2fXrl3UrVvXaPdOT1aRXDRN8wWOCiECEjw+JoRY\nk8z1PwshBiR4fBxYIYR4ZbcplVwykIgIaNcOcuWCZcvA3l7viBRzt3OnXDvVqxeMH2+0LyVDhgzh\np59+In/+/Bw9epTixYsb5b7pyVoG9Pu/SCxxdgCfJnWhpmk5gcQV4+YCX5ooNsVSODjAhg0QHQ3t\n24Pa+1xJibs7nDolB/xdXOSmdUbw/fff06hRI27fvk3btm158uSJUe5riXRLLpqmVQESNy3CAfdk\nXuIEeGmaViLR+VzGjUyxSFmyyAWWTk5yIZ2VMBgMnDp1Su8wrFP+/PD777JbtVo12LTprW9pZ2eH\nv78/ZcqU4cyZM/Tq1SvDziDTs+XihEwmCT0A0DQtR+KLhRChQFUhxJUEp5sgWzuKApkygZ8fWMk6\nkWfPntGiRQtq167NmTNn9A7HOtnYwKhREBAAgwbB8OHw7Nlb3TJ37txs2LCBnDlzEhAQgI+Pj5GC\ntSx6JpdcyASTUDigJXEeACHE6Rf/rGlaLsCNZLrRFMXS2dvbU6JECaKjo/noo4+IiEhcZF4xmrp1\nZTfZhQvQsOFbl4557733WLlyJTY2NowfPx5/f38jBWo59EwuSe2444TsKkvcokmKP+AmhLhq1KgU\nxYx8//33lC9fngsXLjBkyBC9w7FuefLIsbt27aB6ddi8+a1u17RpU6ZPnw5A7969M1z3pm6zxeLG\nXI4LIWxfdy6Z1/oC24UQu15zjfD29o5/7OLigouLy1vHrVigPXugXDmjrmtIT+fOnaN69epERkay\nbNkyPD099Q7J+u3fL0vHeHrCxIlvPJtMCEGfPn1YtGgRxYoV49ixY+Q3s/8Og4KCCAoKin/s4+Nj\nFVOR7wkh8iR47A6MEEI0fc1rOgD3XyQWTdOqCCFe+UqgpiIr8caPlwUMd+6Ed97RO5o3smDBAvr1\n60ezZs34/fff0aysgKdZunNHVuKOioIVK6BgwTe6TXR0NC4uLhw+fJj69esTGBiIvRlPl7eWqcjz\nNE1rn+BxY+T0YgA0TSsZl0xePG6E7Do7oWlaTk3TSgEfpVu0imUaOxa6dJFTTo28x3p66dOnD8uX\nLx2+D3oAABIqSURBVGfjxo0qsaSXfPnkbDI3NzmbLMG3+7TInDkzAQEBFCpUiH379jF06FDjxmmm\nzGGF/hdACOCMbJEsSPBcP6CjEKJp3DqX+7w6fXmVEKJLEvdVLRflZb6+ss7Url2gyqsoabF9u1x0\nOWyY3IjsDUoNHT16lAYNGhAdHc2cOXMYMGBAyi/SgVWs0DcllVyUJE2fLhPMmTOqVIySNtevQ+fO\ncuxuyRJZESKNli5dSs+ePbGzs2PXrl1mub2CSi4pUMlFSdbVq2CBZTkUM/DsmVwLs3UrrFkDFSum\n+RbDhw/nu+++I3/+/Jw4ccLsipRay5iLoqQ/K0kst2/fZsKECagvUenI3h5mzpTFL93dZS27NJoy\nZQru7u7cvn2b9u3bExUVZfw4zYBquSiKBTIYDFSsWJFz584xY8YMPvvsM71DynjOnpW17Jo2he++\nS1PB1Lt371K9enWuXLlCr169WLRokdlM1FAtF0UxpufP9Y4gTV6s/AYYMWIEZ8+e1TmiDKhCBVnH\n7vp1OaPs5s1UvzRv3rysW7eOrFmzsmTJEn766ScTBqoPlVwU5fp1KF8eQkL0jiRN2rdvT79+/YiO\njqZr165EqmrQ6S9nTli7VrZeqleHgwdT/dJKlSrxyy+/ADBs2DD27Nljqih1oZKLohQtCkOHym+f\noaF6R5Mm33//Pe+++y7nzp3Dy8sr5RcoxmdjA2PGwLx54OEBs2dDKrvku3TpgpeXF7GxsXTu3Jkb\nN26YONj0o5KLooCsiDtiBLi6WlSCcXBw4LfffiNz5sw4OjqqwX09tWghWy5z5kDfvnJlfyp88803\n8QP8HTt2JDo62sSBpg81oK8oCc2aBVOnwu7dcutkCxEWFkahQoX0DkMBePIEPv5YVlYOCIDChVN8\nyd27d6latSrXrl2jf//+zJ07N8XXmIoa0FcUUxg8GEaOlGthLIhKLGYke3bw95ddZDVqwIEDKb4k\nb968BAQEkDlzZubNm8eCBQtSfI25Uy0XRVEUU9myBXr1ggkT4NOUt55avHgxH3/8Mfb29uzbt48a\nNWqkQ5AvUyv0U6CSi6IoZuHvv6FtWzmeN2OG3DH1NQYPHszs2bMpWrQoJ0+eJG/evOkUqKS6xRRF\nSVZQUBCtW7e2msFhi1a2LBw+LMdgGjeWpfxf4/vvv6dWrVpcv36drl27Ehsbm06BGpdKLoqSGlu3\nwq1bekeRKjExMfTv359Nmzbx9ddf6x2OAnI9zPr1UKeOHIf5449kL7W3t2fVqlXky5ePwMBAxo4d\nm46BGo9KLoqSGkePQqNGcPeu3pGkyM7ODj8/P2xtbZk+fTo7d+7UOyQFwNYWvvkGJk+W/y2tW5fs\npUWKFGHlypXY2NjwzTffsH79+nQM1DhUclGU1BgzBlq3lt0a4eF6R5OiWrVqMWbMGAB69erF/fv3\ndY5Iideli9yEbMgQmDQp2QWXrq6u+Pr6AtCzZ08uXryYnlG+NTWgryipJQR88QXs3QuBgbKrw4zF\nxMRQv359Dh8+TJcuXVi+fLneISkJhYVBu3ZQqpTcYyhr1lcuEULQsWNHAgICqFChAocPHyZbtmwm\nDUsN6CtKetM0mDYNatWCjh1TXeJDL3Z2dixduhRnZ2d69OihdzhKYoUKya2TbW2hQYMkt+DWNI1F\nixZRtmxZzp49y6BBgyymCoNquShKWhkMcOmSnAVkAWJjY7G1tdU7DCU5QshxmJ9/luMwH374yiV/\n/vknNWvW5OnTp8ybN49+/fqZLBy1ziUFKrkoimJR1qyBAQNkkunQ4ZWnly1bRo8ePcicOTMHDhyg\natWqJglDJZcUqOSiKIrFOXlSLrgcMAC++kp2xSYwcOBAfv75Z0qUKMGJEydwcnIyeggquaRAJRdF\nSV5MTAx2dnZ6h6EkJSwM2rSBDz6QZfwzZ45/Kjo6mnr16nH8+HFatWrF+vXrsbEx7tC5GtBXFHMS\nGCjLrBsMekfyWs+fP8fHx4c6derw7NkzvcNRklKoEOzZA48fy6nv9+7FP5U5c2ZWrVqFk5MTmzZt\nYurUqToG+noquSiKMdSuDRcuyLULZtxijoqKYsmSJRw7dix+m2TFDDk4wOrVckV/rVryv604JUqU\nwM/PD4Cvv/6avXv36hXla6luMUUxlocP5cprt/9v7/5iqyjTOI5/n0iiUSMUERF1I2XjlWaF1WjW\n+GfbojFqVoQVU0I02IOa7IUXdCmrEVITLeqqNwYB/9ysEmGtxqiJsiCGeKFCgMQLE/8sahSEAFUj\nFy722Yt5i4fp6TmnZc7Me+rvkzR0/rTzMJ15nzPvO+/7tkFf37D68lhs27aNa665BjPj/fff54or\nrig6JKnm+edh+XJ4+WW49tpjq5cvX05fXx/nnHMOO3fu5Oyzz87kcKoWE4nNxInJGGRvvZX0vI7U\nVVddRXd3N4ODgyxatIiffvqp6JCkmsWLYf16WLAAwhMLwEMPPcTVV1/N3r176ezsjG6ASyUXkSyd\neSZs2gSvvw579xYdzYh6e3u5+OKL+eyzz44NEyMRa2tLZkddsQJWrgR3JkyYwPr165k6dSpbtmyJ\nrppT1WIijeAebbXYkN27d/PAAw+wevVqzjvvvKLDkXp8913yJtmFF8Kzz8LJJ7N582bmzJkDwNtv\nv33s+7HSq8g1KLmIyLh05AgsWpS8Rfbqq9DSQm9vLytWrOCss85i165dJzTttdpcRER+i049FTZs\nSIaJufJK2LOH+++/n/b2dg4cOEBnZydHjx4tOkolF5HcNMFQ/dIkTjoJnngi6cl/5ZWctHMnL774\nItOmTeO9996Lov1F1WIiedi3Dy65JHmTrMLAhLEYHBzkyJEjnH766UWHIvV67TUoleCFF3j3tNPo\n6OjA3cfc/qJqMZFmMm0arF4NN94In3xSdDQVff3113R0dHDHHXc0zbDuAtxyC7zxBpRK/PnTT3nw\nwQdxdxYuXMjeAt9YVHIRycvcucnQ6tdfD199VXQ0wwwODrJ9+3b6+/t56aWXig5HRuPyy5NJ7B59\nlAd+/pm2tjYOHDjAwoULC+v/Uni1mJl1A58DZwK4+7os9le1mETrqaeSp5ht22Dq1KKjOc5zzz1H\nV1cXLS0tfPzxxyf01pEUYP9+uOkm9s2YwR+2bmX//v309vaOqi/TuKgWM7M+4HN37w9JYqaZDZ/I\nYIz7i0TpvvvgrrsqzjxYtMWLF3PDDTdw+PBhlixZouqxZjN1Krz7LtOOHOFf55+PmbFy5cpCxh8r\n9MnFzA65++Sy5XZgmbtfd6L768lFZGy++eYbLrroIgYGBujv72fu3LlFhySjdfQo3Hsv/3jjDR7Z\nt4/p06eze/dupkyZUvNHm/7JxcxmAenS/xDQnsX+zWLr1q1Fh1AXxZmd2GM899xzefrppymVStx8\n881Fh1NT7OdzSK5xTpgAa9fSWyrxp1NO4dtvv+XOO+/M9Um0yGqxySTJodwAgJmdkcH+TUE3Rraa\nIc5miLGzs5Pp06c3xYRizXA+oYA4zZjQ28v6FStoMePNN9/kySefzO3wRSaXSSQJo9whwCqsH8v+\nIs3lgw+ingtGmtPvenp4oacHgJ5ly9ixY0cuxy0yuQxUWDeZpOqrUlfm0e4v0jx+/jnpCBfxzILS\nvP7y8MP8bd48/nf0KLffeCM//vhjw49ZWIN+aEPZ7u4nVVt3AvvrI6CIyBhk0aBfWIWqu+80s/TT\nyGTgPxntH/d45yIi41jRPfTXmtmtZctzgDVDC2Y2I9WPper+IiIShxh66C8FvgBmAofd/dmybSVg\nvrtfX8/+MnoheV/m7j0VtlUdDWG0oys0Is6wvhX4N3AYKAEb3X1PEXGKNAMze8bd70mty/R+Lzy5\nZC3GgiTGAjB0QJ1N8vT3ubvfm9reB3zo7v1lyx+5+yv1bM8xzhLwTFgcAEpDMeUZZ9nxusO3l4Xj\nPFZhe+EJu1qcMVyvZjYRWBKO//twjPQHi8LPZa04YziXFWJeBbS5+2Vl67K/39193HwBfcCtqeV5\nEcRVAn4JXwfLYyw67nCs1RXWH0ottwPv1Ls9xzi7gDOAC0b4udziBJ5JLW8Hltb7d87rOqgjzsKv\nV6CvQoxdEZ7LWnEWfi5Tx5sRjvFRan3m93tD/gNFfeVd4I0irmgKwArHHlZoA7OAgxXW/RK+n11t\ne15xhvWlKj9T9f+RcXwTKxQ0pfK/bSNu4AzjPFi2XPj1CnyaKqQ3AC/HdC7rjLPwc5n6/V3hGB+V\nrWvI/V50g35mIh8extz9By97FD62Ic64a42G0FJje67MrMvMbjWzUll1D+Q7qsNkoNvMLkitnxiO\nN5sqf+da23OIc1LZ9zFcr3P8+PbUVuDDemLI8VxWjTOI4VwOHa+dJPmlNeR+j39sh/pVPUHu/kP+\nIf3KzLpI4jsTmOS/1nHHGPdIoyEQ1tcaLSHPmDeRfPr7AZKGSjMreVJvnVuc7v5fM/tjqhC5LsQH\ntW/Qqtuzug7qiJNwzEKvVz++TWJ2ssr/WU8M5HQu64hzaH0s9/5Ed//BbFgvjYbc7+MpucRU4KVF\nUQCOwkijIUASWzSjJVT4RLgJWAWsI+c43X3X0PdmNgloI6lSgIgSdo04IZLrNTSW3wbMJ6m6GxLN\nuawRJ8RzLuf5yI3vDbnfx021GBEVeGnuvif1KWQTsCx8H2Pchzi+moSh5fD/qLU9F2Y20cwGU4/m\nAySNllBsnBtI3sj5siyutBgSdjrOaK5Xd//e3dd50hXh2fAEUC0GKOBcVoizVLat8HNpZjNGONaQ\nhtzv4ym5RFHgpUVeAFbk7jsZfjEeGw2h1vacrUqdp5kk/aAKizO8ptnn7rvLVkeXsCvFGcv1Gp4G\nyq0B1tYZQ27ncoQ41wxti+FckjyVzjKzpaGf4N3ApLB8QaPu93GTXCIr8NKiKwDrUGs0hMJHS3D3\n70le7yw3H/h72XKucYZ+De+4+5awPCvEGlXCHinOoNDrNTQ8H04VygZ4aIuI4lzWijMsF37vu/sr\n7v740BfJ09NAWN4Tdsv8fh83ySUovMBLi7EAhKQwCW9WzQNuC59iLhna7u7LgdbwFlY38JmXdU6s\ntT2vOIF1ZtYd3hR7hKQPx6t5xxli7SApHHaET62twIKyXaJI2NXijOR63Q6sSRXKHSSdD4fWxXAu\nq8YZybk8Tqiy+yvJPbF0KAk24n4fjz30oxsexn7txTtA8qriR+k/TIxxS/3C3/gww18t3ejut5ft\nV/Xv3OjroJ44Y7hewweIOSHOKSRvYS0fTQx53FO14ozhXBZl3CUXEREp3nirFhMRkQgouYiISOaU\nXEREJHNKLiIikjklFxERyZySi4iIZE7JRUREMqfkItIgoff7O2b2sg2fP6VRx+w2sw2hY55IYcbT\nkPsimQmDOi4Ji2sIY0aRzBXSCiwLY0PVsiPds3yUccwCdgAbSXpxHyIZeBDgGZJe4a0kw+PMdPfH\nQq/wvrEeUyQLSi4iFbh7j5nNJ5laOT35U4lkXK5JOYxcPRmYXz5kiJnNTEL0x8vWdZEkmT0Njkek\nLqoWE6kgTKLVCmyusHl7+PfSHEJprWegzTAeVUsO8YjURclFpLIOkkEEd1XYdk/YtiWHONKj6laj\ngQIlGqoWE6msgwrzapjZKpJh09tG88tC28k6knaThwnzqQOXhSq49rDrbOCLoSlpRzM9QKOmEhAZ\nCyUXkco6gE1hrg0jqSJbQDLR0ozRtrW4+87QVrORZKKmXQBmtsDMHilr9N9sZoeAkeY7F2kKqhYT\nSQlvW7WSTAHcH2bye8zdLyVp17i7+m+oqqVs9j8IsxKmHEzNbijSdJRcRIabQ9Km8mWFbRuBVSfQ\nb6ViMkkt2xh/t0g0lFxEhqvY3hK0kDScT8ovHJHmo+QiMlwH8M4I2+5m5LfIsqK3vqTpKbmIlDGz\nVkbo3xLeFJsNtKe31fvrqa/Kq9Y+k8d4fJHc6G0xkSAM+dJB8uSwzMwGSAr6SSQF+kHG8KZY+N2z\ngB5glpktdffHzWweybAtA2b2hbv3hxhmAOvMbFl54394XXkOIbmF+Dbl1N9GZFTMXU/gIo0Q3jrr\nOZGxxU7guH3ufm+exxUpp2oxERHJnJKLiIhkTslFpLHUZ0V+k5RcRBprdt6ThQFrgc/zOJ7ISNSg\nLyIimdOTi4iIZE7JRUREMqfkIiIimVNyERGRzCm5iIhI5pRcREQkc/8HTMkLNp+ZhewAAAAASUVO\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11adbdc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi), c='r')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, 0., np.pi/2), c='k', lw=2)\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi) - 0.5 * fields * MU_B * 12 / GAP, c='r', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi) + 0.5 * fields * MU_B * 12 / GAP, c='r', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, 0., np.pi/2) - 0.5 * fields * MU_B * 12 / GAP, c='k', lw=2, ls='--')\n",
    "plt.plot(Bs, Es, 'o', c='r')\n",
    "#plt.plot(Bs, Es2, 'o', c='g')\n",
    "#plt.plot(Bs, Es1, 'o', c='b')\n",
    "plt.ylim([0, 1])\n",
    "plt.xlim([0,400])\n",
    "plt.title(r\"$g=12$\")\n",
    "plt.ylabel(r'$E/\\Delta$')\n",
    "plt.xlabel(r'$B$ [mT]')\n",
    "plt.savefig(\"absorption_frequency_orbital_and_zeeman_only_one_curve.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 1)"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8qaelAUuWAK1aFX6e06dPo1mzZihbVnevqoCAAHTt2hUxMTF4++23sWfPHpiZ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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11beb5358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi/2), c='b')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, 3*np.pi/4), c='g')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi), c='r')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, 0., np.pi/2), c='k', lw=2)\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi/2) - 0.5 * fields * MU_B * 2 / GAP, c='b', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, 3*np.pi/4) - 0.5 * fields * MU_B * 2 / GAP, c='g', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi) - 0.5 * fields * MU_B * 2 / GAP, c='r', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi/2) + 0.5 * fields * MU_B * 2 / GAP, c='b', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, 3*np.pi/4) + 0.5 * fields * MU_B * 2 / GAP, c='g', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, TAU, np.pi) + 0.5 * fields * MU_B * 2 / GAP, c='r', ls='--')\n",
    "plt.plot(fields, fit_orbital(fields, popt_orb, 0., np.pi/2) - 0.5 * fields * MU_B * 2 / GAP, c='k', lw=2, ls='--')\n",
    "plt.plot(Bs, Es, 'o', c='r')\n",
    "plt.plot(Bs, Es2, 'o', c='g')\n",
    "plt.plot(Bs, Es1, 'o', c='b')\n",
    "plt.ylim([0, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Increasing spin-orbit with respect to the best value from the fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "popt2, pcov2 = curve_fit(lambda x, z, gf: vfit_abs_pair_energy(x, z, gf, TAU, np.pi, GAP),\n",
    "                       Bs[1:], Es[1:], p0=[1.6, 40])\n",
    "popt2, pcov2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p = SimpleNamespace(z=1.1, gfactor=30, tau=TAU, phi=np.pi)\n",
    "fields = np.linspace(0., 500, 80)\n",
    "energies = []\n",
    "gaps = []\n",
    "for B in fields:\n",
    "    p.y = 0.5 * p.gfactor * MU_B * B / GAP\n",
    "    sol = find_abs_energies(p)\n",
    "    energies.append(sol)\n",
    "    gaps.append(compute_gap(p))\n",
    "ens1, ens2 = np.asarray(zip(*energies))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(fields, ens1, c='r', lw=2)\n",
    "plt.plot(fields, ens2, c='b', lw=2)\n",
    "plt.plot(fields, (ens1 + ens2)/2, c='k', ls='--', lw=1)\n",
    "plt.plot(fields, gaps, c='k', lw=2)\n",
    "plt.plot(Bs, Es, 'o', c='k', markersize=7)\n",
    "plt.xlabel(r'$B$ [mT]')\n",
    "plt.ylabel(r'$E/\\Delta$')\n",
    "#plt.savefig('fit_higher_so.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some numerical experiment. This is the range of $z=\\alpha k_F/\\Delta$ such that a Fermi-level crossing happens between 300 mT and 500 mT, at a given $g$-factor. Note: I have not done a systematic search of the interval limits, these are just estimates based on a few samples.\n",
    "\n",
    "$g = 12$ : $z \\sim 0.25-0.7$\n",
    "\n",
    "$g = 20$ : $z \\sim 0.7-0.9$\n",
    "\n",
    "$g = 30$ : $z \\sim 0.85-1$\n",
    "\n",
    "In the last two lines, the right limit of the $z$ interval basically coincides with the limit at which no Fermi-level crossing appears anymore. If one enforces the constraint that a Fermi-level crossing appears, then the agreement with the data worsens by increasing $g$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Phase dependence of the ABS levels for best fit parameters, at $B=200$ mT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p = SimpleNamespace(z=popt[0], B=100, gfactor=popt[1], tau=TAU)\n",
    "p.y = 0.5 * p.gfactor * MU_B * p.B / GAP\n",
    "phases = np.linspace(1e-4, 2*np.pi-1e-4, 100)\n",
    "p.gap = compute_gap(p)\n",
    "energies = []\n",
    "for phi in phases:\n",
    "    p.phi = phi\n",
    "    sol = find_abs_energies(p)\n",
    "    energies.append(sol)\n",
    "abs_down, abs_up = np.asarray(zip(*energies))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Fixes the value at phi=0, 2π, by continuity.\n",
    "# At phi =0, 2π, numerics fail to find zeros due to a very shallow function\n",
    "abs_down[0] = (abs_down[1] + abs_up[1])/2\n",
    "abs_up[0] = (abs_down[1] + abs_up[1])/2\n",
    "abs_down[-1] = (abs_down[1] + abs_up[1])/2\n",
    "abs_up[-1] = (abs_down[1] + abs_up[1])/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(phases, abs_down, c='r', lw=2)\n",
    "plt.plot(phases, abs_up, c='b', lw=2)\n",
    "plt.plot(phases, (abs_up+abs_down)/2, c='k', lw=1, ls='--')\n",
    "plt.axhline(p.gap, c='k', lw=2)\n",
    "plt.yticks([0, p.gap/2, p.gap], [r'$0$', r'', r'$\\Delta(B)$'])\n",
    "plt.xticks([0, np.pi, 2*np.pi], [r'$0$', r'$\\pi$', r'$2\\pi$'])\n",
    "plt.xlabel(r'$\\varphi$')\n",
    "plt.ylabel(r'$E_\\pm(\\varphi)$', labelpad=-18)\n",
    "plt.title(r'$B=%s$ mT' % p.B)\n",
    "plt.ylim(0, p.gap+0.05)\n",
    "plt.xlim(0, 2*np.pi)\n",
    "plt.savefig(\"dispersion_ABS_at_100_mT.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "p.phi = 6.35644981e-02"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sol = find_abs_energies(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p.gap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rng = np.linspace(0.855, 0.865, 100)\n",
    "plt.plot(rng, func(rng, p))\n",
    "plt.axvline(sol[0])\n",
    "plt.axvline(sol[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-monotonicity of energy difference between contiuum and ABS: dependence on $\\tau$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p = SimpleNamespace(z=0.6, phi=np.pi)\n",
    "taus=(0.25, 0.50, 0.75, 0.99)\n",
    "ys = np.linspace(0., 2, 100)\n",
    "list_of_energies = []\n",
    "list_of_gaps = []\n",
    "for tau in taus:\n",
    "    p.tau = tau\n",
    "    gaps = []\n",
    "    energies = []\n",
    "    for y in ys:\n",
    "        p.y = y\n",
    "        sol = find_abs_energies(p)\n",
    "        energies.append(sol)\n",
    "        gaps.append(compute_gap(p))\n",
    "    list_of_energies.append(energies)\n",
    "    list_of_gaps.append(gaps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ncol = len(taus)\n",
    "cmap = cm.hot\n",
    "col_ind = np.linspace(0, 150, ncol)\n",
    "col_array = cmap(col_ind.astype(int))\n",
    "plt.figure()\n",
    "for n, (tau, levels, gaps, col) in enumerate(zip(taus, list_of_energies, list_of_gaps, col_array)):\n",
    "    ens1, ens2 = np.asarray(zip(*levels))\n",
    "    plt.plot(ys, gaps-ens2, lw = 2, c=col, label = r'$\\tau=%s$' % tau)\n",
    "    plt.legend()\n",
    "    plt.ylim(0, 1)\n",
    "    plt.yticks([0, 0.5, 1])\n",
    "    plt.ylabel(r'$E_\\textrm{gap}-E_+$')\n",
    "    plt.xlabel(r'$y$')\n",
    "    plt.title(r'$z=%s\\,,\\,\\phi=\\pi$' % p.z)\n",
    "plt.savefig(\"level_repulsion_varying_transmission.pdf\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.figure()\n",
    "for n, (tau, levels, gaps) in enumerate(zip(taus, list_of_energies, list_of_gaps)):\n",
    "    ens1, ens2 = np.asarray(zip(*levels))\n",
    "    plt.plot(ys, gaps-ens1, lw = 2, label = r'$\\tau=%s$' % tau)\n",
    "    plt.legend()\n",
    "    plt.ylim(0, 1)\n",
    "    plt.yticks([0, 0.5, 1])\n",
    "    plt.ylabel(r'$E_\\textrm{gap}-E_-$')\n",
    "    plt.xlabel(r'$y$')\n",
    "    plt.title(r'$z=%s\\,,\\,\\phi=\\pi$' % p.z)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.figure()\n",
    "for n, (tau, levels, gaps) in enumerate(zip(taus, list_of_energies, list_of_gaps)):\n",
    "    ens1, ens2 = np.asarray(zip(*levels))\n",
    "    plt.plot(ys, ens2-ens1, lw=2,  label = r'$\\tau=%s$' % tau)\n",
    "    plt.legend()\n",
    "    plt.legend()\n",
    "    plt.ylim(0, 1)\n",
    "    plt.yticks([0, 0.5, 1])\n",
    "    plt.ylabel(r'$E_+-E_-$')\n",
    "    plt.xlabel(r'$y$')\n",
    "    plt.title(r'$z=%s\\,,\\,\\phi=\\pi$' % p.z)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-monotonicity of the energy splitting between continuum and ABS: dependence on $z$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "p = SimpleNamespace(z=0.6, tau=0.95, phi=np.pi)\n",
    "zs = (0.01, 0.2, 0.4, 0.6)\n",
    "ys = np.linspace(0., 2, 100)\n",
    "list_of_energies2 = []\n",
    "list_of_gaps2 = []\n",
    "for z in zs:\n",
    "    p.z = z\n",
    "    gaps = []\n",
    "    energies = []\n",
    "    for y in ys:\n",
    "        p.y = y\n",
    "        sol = find_abs_energies(p)\n",
    "        energies.append(sol)\n",
    "        gaps.append(compute_gap(p))\n",
    "    list_of_energies2.append(energies)\n",
    "    list_of_gaps2.append(gaps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ncol = len(zs)\n",
    "cmap = cm.hot\n",
    "col_ind = np.linspace(0, 150, ncol)\n",
    "col_array = cmap(col_ind.astype(int))\n",
    "plt.figure()\n",
    "for n, (z, levels, gaps, col) in enumerate(zip(zs, list_of_energies2, list_of_gaps2, col_array)):\n",
    "    ens1, ens2 = np.asarray(zip(*levels))\n",
    "    plt.plot(ys, gaps-ens2, lw = 2, c=col, label = r'$z=%s$' % z)\n",
    "    plt.plot(ys, gaps, ls='--', c=col)\n",
    "    plt.legend()\n",
    "    plt.ylim(0, 1)\n",
    "    plt.yticks([0, 0.5, 1])\n",
    "    plt.ylabel(r'$E_\\textrm{gap}-E_+$')\n",
    "    plt.xlabel(r'$y$')\n",
    "    plt.title(r'$\\tau=%s\\,,\\,\\phi=\\pi$' % p.tau)\n",
    "plt.savefig(\"level_replusion_varying_z.pdf\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p.z = zs[1]\n",
    "ens1, ens2 = np.asarray(zip(*list_of_energies2[1]))\n",
    "gaps = list_of_gaps2[1]\n",
    "plt.figure()\n",
    "plt.plot(ys, gaps, c='k', lw=2, label=r'$E_\\textrm{gap}$')\n",
    "plt.plot(ys, ens2, c='b', lw=2, label=r'$E_+$')\n",
    "plt.plot(ys, gaps-ens2, c='k', ls='--', lw=1, label=r'$E_\\textrm{gap}-E_+$')\n",
    "plt.xlabel(r'$y$')\n",
    "plt.yticks([0, 0.5, 1])\n",
    "plt.title(r'$z=%s\\,,\\,\\phi=\\pi$' % zs[1])\n",
    "plt.ylabel(r'$E$')\n",
    "plt.legend()\n",
    "plt.axvline(yc(p, +1), c='r', ls='--')\n",
    "plt.savefig(\"level_repulsion_example_at_small_z.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting of ABS levels at large $y$, as a function of $\\tau$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p = SimpleNamespace(y=6, z=0.6, phi=np.pi)\n",
    "taus = np.linspace(1e-4, 1 - 1e-4, 200)\n",
    "splittings = []\n",
    "for tau in taus:\n",
    "    p.tau = tau\n",
    "    en1, en2 = find_abs_energies(p)\n",
    "    splittings.append(en2 - en1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "12 * MU_B * 300 / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(taus, splittings, c='k', lw=2)\n",
    "plt.title(r'$y=%s,\\; z=%s$' % (p.y, p.z))\n",
    "plt.yticks([0, 0.01])\n",
    "plt.xlabel(r'$\\tau$')\n",
    "plt.ylabel(r'$E_+-E_-$')\n",
    "plt.savefig(\"ABS_splitting_at_large_y.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit for dev_1_103_117.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#GAP_103 = 167\n",
    "#TAU_103 = 0.67\n",
    "#minima_103= [(0,97),(1,95),(4,97),(10,96),(20,97),(40,94),(100,89),\n",
    "# (125,87),(150,80),(160,78),(175,76),(185,74),(200,69),(225,65),(240,59),(250,61),(200,71),(225,67),(250,65),]\n",
    "#Bs_103, Es_103 = np.asarray(zip(*minima_103))\n",
    "#Es /= GAP_103\n",
    "#popt_103, pcov_103 = curve_fit(lambda x, z, gf: vfit_abs_pair_energy(x, z, gf, TAU_103, np.pi, GAP_103),\n",
    "#                       Bs_103, Es_103, p0=[1.5, 12])\n",
    "#popt_103, pcov_103"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#plt.plot(Bs_103, Es_103,'.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit for dev_2_166.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Discarding sign change detections: too close to each other.\n",
      "No sign changes: 0\n",
      "Discarding sign change detections: too close to each other.\n",
      "No sign changes: 0\n",
      "Discarding sign change detections: too close to each other.\n",
      "No sign changes: 0\n",
      "Discarding sign change detections: too close to each other.\n",
      "No sign changes: 0\n",
      "Discarding sign change detections: too close to each other.\n",
      "No sign changes: 0\n",
      "Discarding sign change detections: too close to each other.\n",
      "No sign changes: 0\n",
      "Discarding sign change detections: too close to each other.\n",
      "No sign changes: 0\n",
      "Discarding sign change detections: too close to each other.\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n",
      "No sign changes: 0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([ 2.38617781,  2.00356668]),\n",
       " array([[  1.17094002e+16,   9.41972822e+15],\n",
       "        [  9.41972822e+15,   7.57778501e+15]]))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GAP_166 =130\n",
    "TAU_166 =0.57\n",
    "minima_166 = [(1,84),(28,86),(69,84),(109,78),(133,76),(178,71),(191,69),(213,63)]\n",
    "Bs_166, Es_166 = np.asarray(zip(*minima_166))\n",
    "Es /= GAP_166\n",
    "popt_166, pcov_166 = curve_fit(lambda x, z, gf: vfit_abs_pair_energy(x, z, gf, TAU_166, np.pi, GAP_166),\n",
    "                       Bs_166, Es_166, p0=[1.5, 12])\n",
    "popt_166, pcov_166"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10a56da50>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a127890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Bs_166, Es_166,'.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p = SimpleNamespace(z=popt_166[0], gfactor=popt_166[1], tau=TAU_166, phi=np.pi)\n",
    "fields = np.linspace(0., 300, 80)\n",
    "energies = []\n",
    "gaps = []\n",
    "for B in fields:\n",
    "    p.y = 0.5 * p.gfactor * MU_B * B / GAP_166\n",
    "    sol = find_abs_energies(p)\n",
    "    energies.append(sol)\n",
    "    gaps.append(compute_gap(p))\n",
    "ens1, ens2 = np.asarray(zip(*energies))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(fields, ens1, c='r', lw=2)\n",
    "plt.plot(fields, ens2, c='b', lw=2)\n",
    "plt.plot(fields, (ens1 + ens2)/2, c='k', ls='--', lw=1)\n",
    "plt.plot(fields, gaps, c='k', lw=2)\n",
    "#plt.plot(Bs, Es, 'o', c='k', markersize=7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit for dev_2_162.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'Bs_162' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-17-daf6df023fd8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mEs\u001b[0m \u001b[0;34m/=\u001b[0m \u001b[0mGAP_162\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m popt_162, pcov_162 = curve_fit(lambda x, z, gf: vfit_abs_pair_energy(x, z, gf, TAU_162, np.pi, GAP_162),\n\u001b[0;32m----> 7\u001b[0;31m                        Bs_162, Es_162, p0=[1.5, 12])\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0mpopt_162\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpcov_162\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'Bs_162' is not defined"
     ]
    }
   ],
   "source": [
    "GAP_162 = 123\n",
    "TAU_162 = 0.73\n",
    "minima_162 = [(13,64),(26,65),(42,66),(54,65),(67,64),(91,64),(108,63),(118,62),(145,61),(158,58),(171,58),(198,56),\n",
    "              (210,52),(224,52),(251,49)]\n",
    "Es /= GAP_162\n",
    "popt_162, pcov_162 = curve_fit(lambda x, z, gf: vfit_abs_pair_energy(x, z, gf, TAU_162, np.pi, GAP_162),\n",
    "                       Bs_162, Es_162, p0=[1.5, 12])\n",
    "popt_162, pcov_162"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit for dev_2_156.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "GAP_156 = 147\n",
    "TAU_156 = 0.52\n",
    "minima_156 = [(8,104),(22,102),(40,103),(64,96),(103,95),(120,93),(134,89),(146,89),(171,83),(202,77),(215,74),\n",
    "              (242,62),(263,56)]\n",
    "Es /= GAP_156\n",
    "popt_156, pcov_156 = curve_fit(lambda x, z, gf: vfit_abs_pair_energy(x, z, gf, TAU_156, np.pi, GAP_156),\n",
    "                       Bs_156, Es_156, p0=[1.5, 12])\n",
    "popt_156, pcov_156"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}