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  "name": ""
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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Fixed Charge approximation\n",
      "\n",
      "This notebook briefly compares the fixed charge approximation to the exact, grand canonical system. For the fixed charge approximation we rescrict the Hilbert space to states where there are exactly two electrons (more generally, a fixed number of electrons) per cell. The chemical potential is zero, $\\mu = 0$. Hence the approximation is valid as long as there actually are two electrons on each cell in the grand canonical system and as long as the energetically next highest charge sectors are sufficiently gapped (compared with the temperature).\n",
      "\n",
      "Below we plot, for a two cell system, the energy histogram and the particle number per cell over temperature. The fixed charge system indeed reproduces the low energy part of the spectrum exactly. The particle numbers agree, as long as the temperature ($T < 10$) is much smaller than the energy gap ($\\Delta E \\sim 30$)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "import qca\n",
      "print(qca.__version__)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "8.2.0\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s_g = qca.QcaGrandCanonical()\n",
      "s_f = qca.QcaFixedCharge()\n",
      "\n",
      "# Wire geometry\n",
      "N = 2\n",
      "V1 = 100.0\n",
      "boa = 2.0\n",
      "P_0 = 1\n",
      "\n",
      "# Other parameters\n",
      "V_0 = 1000\n",
      "mu=250\n",
      "\n",
      "# Set the systems up\n",
      "s_f.l = qca.Wire(N,V1,boa,P_0)\n",
      "s_g.l = qca.Wire(N,V1,boa,P_0)\n",
      "s_f.V_0 = V_0\n",
      "s_g.V_0 = V_0\n",
      "s_f.mu = mu\n",
      "s_g.mu = mu\n",
      "\n",
      "# Takes about half an hour!\n",
      "s_f.init()\n",
      "s_f.run()\n",
      "s_g.init()\n",
      "s_g.run()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Are we in the right charge sector?\n",
      "T = 1.0\n",
      "s_g.T = T\n",
      "s_f.T = T\n",
      "s_g.run(True)\n",
      "s_f.run(True)\n",
      "print('Particle number for cell 1 and 2 in the grand canonical system: {:.2f}, {:.2f}'\n",
      "        .format(s_g.results['N'][0][4],s_g.results['N'][1][4]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Particle number for cell 1 and 2 in the grand canonical system: 2.00, 2.00\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create and plot an energy histogram\n",
      "Es_g = np.array(s_g.energies())\n",
      "Es_f = np.array(s_f.energies())\n",
      "Emin = np.concatenate((Es_g, Es_f)).min()\n",
      "Es_g -= Emin\n",
      "Es_f -= Emin\n",
      "Emin = 0\n",
      "#Emax = np.concatenate((Es_g, Es_f)).max()\n",
      "\n",
      "Emax = 100\n",
      "bins = np.linspace(Emin,Emax,10000)\n",
      "h_f,_ = np.histogram(Es_f,bins)\n",
      "h_g,_ = np.histogram(Es_g,bins)\n",
      "bins = bins[:-1]\n",
      "\n",
      "# Particle number over temperature\n",
      "Ns_g = []\n",
      "Ns_f = []\n",
      "for T in np.linspace(0.1,50,50):\n",
      "    s_g.T = T\n",
      "    s_f.T = T\n",
      "    s_g.run(True)\n",
      "    s_f.run(True)\n",
      "    Ns_g.append([T, s_g.results['N'][0][4],s_g.results['N'][1][4]])\n",
      "    Ns_f.append([T, s_f.results['N'][0][4],s_f.results['N'][12][4]])\n",
      "Ns_g = np.array(Ns_g)\n",
      "Ns_f = np.array(Ns_f)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "NameError",
       "evalue": "name 's_fresults' is not defined",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-5-cddbf0a132fe>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     23\u001b[0m     \u001b[0ms_f\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     24\u001b[0m     \u001b[0mNs_g\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ms_g\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mresults\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'N'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0ms_g\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mresults\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'N'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 25\u001b[1;33m     \u001b[0mNs_f\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ms_fresults\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'N'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0ms_f\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mresults\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'N'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m12\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     26\u001b[0m \u001b[0mNs_g\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mNs_g\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     27\u001b[0m \u001b[0mNs_f\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mNs_f\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mNameError\u001b[0m: name 's_fresults' is not defined"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(10,5))\n",
      "p = fig.add_subplot(1,2,1)\n",
      "p.plot(bins,h_g,'-',label='Grand')\n",
      "p.plot(bins,-h_f,'-',label='Fixed')\n",
      "p.set_xlim(0,50)\n",
      "p.set_ylim(-20,30)\n",
      "p.set_xlabel('energy')\n",
      "p.set_ylabel('state count')\n",
      "p.legend(loc='upper left')\n",
      "p.get_yaxis().set_ticklabels([20,10,0,10,20,30])\n",
      "p.text(0.02,0.02,'(a)', \n",
      "        fontsize='12', \n",
      "        horizontalalignment='left', \n",
      "        verticalalignment='bottom', \n",
      "        transform=p.transAxes)\n",
      "\n",
      "p = fig.add_subplot(1,2,2)\n",
      "p.plot(Ns_g[:,0],Ns_g[:,1],label='Grand. Cell 1',color='blue')\n",
      "p.plot(Ns_g[:,0],Ns_g[:,2],label='Grand. Cell 2',color='red')\n",
      "p.plot(Ns_f[:,0],Ns_f[:,1],label='Fixed. Cell 1,2',color='green')\n",
      "p.set_xlabel('temperature')\n",
      "p.set_ylabel('particle number')\n",
      "p.legend(loc='upper left')\n",
      "p.text(0.02,0.02,'(b)', \n",
      "        fontsize='12', \n",
      "        horizontalalignment='left', \n",
      "        verticalalignment='bottom', \n",
      "        transform=p.transAxes)\n",
      "\n",
      "fig.savefig('../plots/chapter02/fixed_charge_approximation.pdf')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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KCvQDfjuUggJYswbmz9fd+U2dCo89Bi4uSkdmteLi4oiLi6vQOiTpqgA/Pz/++usvnJ2d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\nSUVORK5CYII=\n"
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}