Stat Mech Recombination from various (Boltzmann, FD) kernels

Julia Recombi Example

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      "kb=8.6173324E-5 # in units of eV\n",
      "\u03b2=1/(kb*300)    # Thermodynamic Beta; units\n",
      "\n",
      "N=1000\n",
      "#pot=0.13*randn(N) # Normal distribution\n",
      "pot=0.13*sin(range(0,N)) # Sinusoidal variations\n",
      "\n",
      "function partition(f)\n",
      "    Zh=sum(f(-pot))\n",
      "    Ze=sum(f(pot))\n",
      "    \u03c1h=(1/Zh) * f(-pot)\n",
      "    \u03c1e=(1/Ze) * f(pot)\n",
      "\n",
      "    @printf \"Zh: %e Ze: %e e: %e h: %e\\n\" Zh Ze sum(\u03c1e) sum(\u03c1h)\n",
      "    # Factors of N make these values independent of number of elements in the\n",
      "    # potential, self-consistent, and equal to R=1 for a flat potential.\n",
      "    @printf \"R=N*N/(Zh*Ze): %e\\t\" N*N/(Zh*Ze)\n",
      "    @printf \"R=N*sum(\u03c1e.*\u03c1h): %e\" N*sum(\u03c1h.*\u03c1e)\n",
      "    println()\n",
      "    println()\n",
      "end\n",
      "\n",
      "println(\"Boltzmann statistics...\")\n",
      "partition( x -> exp(-\u03b2*x) )\n",
      "println(\"Fermi-Dirac statistics...\")\n",
      "partition( x -> 1./(exp(\u03b2*x) + 1.0) )\n",
      "println(\"Fermi-Dirac, chem pot = 1.0 eV...\")\n",
      "partition( x -> 1./(exp(\u03b2*(x+1.0)) + 1.0) )"
     ],
     "language": "python",
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     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Boltzmann statistics...\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Zh: 2.791863e+04 Ze: 2.791881e+04 e: 1.000000e+00 h: 1.000000e+00\n",
        "R=N*N/(Zh*Ze): 1.282948e-03\tR=N*sum(\u03c1e.*\u03c1h): 1.282948e-03\n",
        "\n",
        "Fermi-Dirac statistics...\n",
        "Zh: 4.999837e+02 Ze: 5.000163e+02 e: 1.000000e+00 h: 1.000000e+00\n",
        "R=N*N/(Zh*Ze): 4.000000e+00\tR=N*sum(\u03c1e.*\u03c1h): 2.759667e-01\n",
        "\n",
        "Fermi-Dirac, chem pot = 1.0 eV...\n",
        "Zh: 4.432327e-13 Ze: 4.432356e-13 e: 1.000000e+00 h: 1.000000e+00\n",
        "R=N*N/(Zh*Ze): 5.090185e+30\tR=N*sum(\u03c1e.*\u03c1h): 1.282948e-03\n",
        "\n"
       ]
      }
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     "prompt_number": 3
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