FinSize_Therm.ipynb

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    "# Thermodynamics of finite-size quantum systems:\n",
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/hariseldon99/StatMechCodes/blob/master/FinSize_Therm.ipynb)\n",
    "## Introduction\n",
    "This jupyter notebook numerically computes the partition function $Z(\\beta)$ for examples of systems with a finite number of single particle levels (e.g., $2-$level, $3-$level, etc.) and a finite number of non-interacting particles $N$ under Fermi-Dirac and Bose- Einstein statistics. The Maxwell-Boltzmann case is left to the reader as an exercise. This partition function will then be used to investigate the dependence of average energy, energy fluctuation and specific heat. You can change the number of particles $N$ and number of states $K$ to obtain different plots for the average energy per particle and specific heat.\n",
    "\n",
    "## Background\n",
    "\n",
    "The indistinguishability of identical particles in quantum mechanics has a profound effect on their statistical properties. To illustrate this, consider a system of $N=2$ distinguishable, non-interacting particles. Consider distributing them in $K=3$ single particle energy levels of energies $\\varepsilon(n)$. Let $n_j$ denote the state (*i.e.* quantum numbers) of particle $j$. If the particles have the same physical properties, the $n_j$'s run over the same range of values for all $j = 1, 2$. In an ideal gas in equilibrium with a temperature bath, the particles do not interact. Therefore,  the total energy of the system is the sum of the single-particle energies. The partition function of the system [1] is\n",
    "\n",
    "$$\n",
    "Z = \\sum_{n_1, n_2, \\cdots n_N} \\exp\\left\\{ -\\beta \\left[ \\varepsilon(n_1) + \\varepsilon(n_2) + \\cdots + \\varepsilon(n_N) \\right] \\right\\} \n",
    "$$\n",
    "\n",
    "This expression can be factored to obtain $Z = \\xi^N $, where $\\xi = \\sum_n e^{- \\beta\\varepsilon(n)}$. However,  if the identical particles are indistinguishable, as they are in quantum mechanics, this equation is incorrect. Consider a state of the system, described by the single particle states $|n_0, n_1, n_2\\rangle$. In the equation for $Z$, every possible permutation of the $n$s occurs once in the sum, even though each of these permutations is describing the same multi-particle state.  Thus, the number of states has been over-counted.\n",
    "\n",
    "To see this diagrammatically, consider coloring each of the $N=2$ particles *i.e.* one red, and one blue. Now, there are $N$ distinct particles in $M=3$ states. The total number of distinct configurations is $K^N = 9$. Now, contrast this with the case where the particles are indistinguishable. Suppose both particles are red, then some of the states are indistinguishable from each other. The tables below enumerate all distinct states for $2$ classical (distinguishable) and quantum bosonic (indistinguishable) particles, with identical states left blank.\n",
    "\n",
    "| Classical           \t|       \t| particles            \t|   \t|   \t|   \t| Quantum             \t|    \t| bosons           \t|\n",
    "|---------------------\t|----------------------\t|----------------------\t|---\t|---\t|---\t|---------------------\t|---------------------\t|---------------------\t|\n",
    "| $\\varepsilon_1$     \t|    $\\varepsilon_2$   \t|      $\\varepsilon_3$ \t|   \t|   \t|   \t| $\\varepsilon_1$     \t| $\\varepsilon_2$     \t| $\\varepsilon_3$     \t|\n",
    "| &#x1F534; &#x1F535; \t|                      \t|                      \t|   \t|   \t|   \t| &#x1F534; &#x1F534; \t|                     \t|                     \t|\n",
    "|                     \t| &#x1F534;  &#x1F535; \t|                      \t|   \t|   \t|   \t|                     \t| &#x1F534; &#x1F534; \t|                     \t|\n",
    "|                     \t|                      \t| &#x1F534;  &#x1F535; \t|   \t|   \t|   \t|                     \t|                     \t| &#x1F534; &#x1F534; \t|\n",
    "| &#x1F534;           \t| &#x1F535;            \t|                      \t|   \t|   \t|   \t| &#x1F534;           \t| &#x1F534;           \t|                     \t|\n",
    "| &#x1F535;           \t| &#x1F534;            \t|                      \t|   \t|   \t|   \t|                     \t|                     \t|                     \t|\n",
    "| &#x1F534;           \t|                      \t| &#x1F535;            \t|   \t|   \t|   \t| &#x1F534;           \t|                     \t| &#x1F534;           \t|\n",
    "| &#x1F535;           \t|                      \t| &#x1F534;            \t|   \t|   \t|   \t|                     \t|                     \t|                     \t|\n",
    "|                     \t| &#x1F534;            \t| &#x1F535;            \t|   \t|   \t|   \t|                     \t| &#x1F534;           \t| &#x1F534;           \t|\n",
    "|                     \t| &#x1F535;            \t| &#x1F534;            \t|   \t|   \t|   \t|                     \t|                     \t|                     \t|\n",
    "\n",
    "\n",
    "Clearly, while all $9$  distinct microstates are available for classical distinguishable particles, only $6$ are available to the quantum indistinguishable ones. This reduces the number of states to sum over while computing $Z$. In the canonical ensemble, the occupational probability $p_r$ of a state with energy $E_r$ goes as \n",
    "$$\n",
    "p_r = \\frac{1}{Z}\\;e^{-\\beta E_r}.\n",
    "$$\n",
    "\n",
    "Thus, a reduction in $Z$ leads to an *increase* in $p_r$. This explains why quantum Bosonic particles prefer to stay in the ground state (*i.e.* in a *Bose-Einstein condensate*), whose probability increases as you go from classical to quantum.\n",
    "\n",
    "The above-mentioned statistics of indistinguishability is true for Bosonic particles. However, for Fermionic particles, there is even an additional restriction given by the Pauli exclusion principle [1] *viz.* 'A single state cannot accommodate more than $1$ fermion'. Thus, the fermionic ensemble of states can be constructed from the Bosonic ensemble in the right side of the table above by removing states that have more than one particle. The table below contrasts the fermionic ensemble with the classical ensemble for the example discussed above. Clearly, the number of available microstates is reduced from $9$ to just $3$, and reduces the probability of a Bose-Einstein condensate to $0$ (however, *Fermionic condensation* can occur due to a *BCS-BEC crossover* if the fermions are interacting; interested readers may see reference [4]).\n",
    "\n",
    "| Classical           \t|       \t| particles            \t|   \t|   \t|   \t| Quantum             \t|    \t| fermions           \t|\n",
    "|---------------------\t|----------------------\t|----------------------\t|---\t|---\t|---\t|---------------------\t|---------------------\t|---------------------\t|\n",
    "| $\\varepsilon_1$     \t|    $\\varepsilon_2$   \t|      $\\varepsilon_3$ \t|   \t|   \t|   \t| $\\varepsilon_1$     \t| $\\varepsilon_2$     \t| $\\varepsilon_3$     \t|\n",
    "| &#x1F534; &#x1F535; \t|                      \t|                      \t|   \t|   \t|   \t|                    \t|                     \t|                     \t|\n",
    "|                     \t| &#x1F534;  &#x1F535; \t|                      \t|   \t|   \t|   \t|                     \t|                    \t|                     \t|\n",
    "|                     \t|                      \t| &#x1F534;  &#x1F535; \t|   \t|   \t|   \t|                     \t|                     \t|   \t|\n",
    "| &#x1F534;           \t| &#x1F535;            \t|                      \t|   \t|   \t|   \t| &#x1F534;           \t| &#x1F534;           \t|                     \t|\n",
    "| &#x1F535;           \t| &#x1F534;            \t|                      \t|   \t|   \t|   \t|                     \t|                     \t|                     \t|\n",
    "| &#x1F534;           \t|                      \t| &#x1F535;            \t|   \t|   \t|   \t| &#x1F534;           \t|                     \t| &#x1F534;           \t:|\n",
    "| &#x1F535;           \t|                      \t| &#x1F534;            \t|   \t|   \t|   \t|                     \t|                     \t|                     \t:|\n",
    "|                     \t| &#x1F534;            \t| &#x1F535;            \t|   \t|   \t|   \t|                     \t| &#x1F534;           \t| &#x1F534;           \t:|\n",
    "|                     \t| &#x1F535;            \t| &#x1F534;            \t|   \t|   \t|   \t|                     \t|                     \t|                     \t:|\n",
    "\n",
    "## Description\n",
    "\n",
    "Given that a system has $N$ particles in $K$ single-particle states, we first construct the ensemble of allowed states. If the energy of the $r^{th}$ many body state in the ensemble is $E_r$, then the partition function, in the canonical ensemble, is given by [1]\n",
    "\n",
    "$$\n",
    "Z(\\beta) = \\sum_r e^{-\\beta E_r}.\n",
    "$$ \n",
    "\n",
    "The partition function, average energy, and specific heat for this ensemble are given by [1] \n",
    "$$\n",
    "Z = \\sum_r e^{-\\beta E_r},\\\\\n",
    "\\overline{E}  = -\\frac{\\partial}{\\partial \\beta}\\ln{Z},\\\\\n",
    "C_v \\equiv \\frac{1}{N}\\frac{\\partial\\overline{E}}{\\partial T} =  -\\frac{\\beta^2}{N}\\frac{\\partial\\overline{E}}{\\partial\\beta} = \\frac{\\beta^2}{N} \\frac{\\partial^2}{\\partial\\beta^2}\\ln{Z}.\n",
    "$$\n",
    "\n",
    "Note that Boltzmann constant has been set to unity.\n",
    "\n",
    "Let us first construct the Bose-Einstein ensemble. Here, all states can accommodate up to $N$ particles. The ensemble can be represented by a matrix with all the possible combinations of number totalling to $N$ with repetition. In other words, each row of the matrix is a unique Fock state in the occupation number representation.\n",
    "\n",
    "For concreteness, let's go with an example of $K = 4$ and $N=3$. For simplicity, let us set the single particle energies to that of the so-called \"Einstein Solid\" (like in Einstein's Theory of Specific Heat [1]) *i.e* the $m^{th}$ single particle energy $\\epsilon_m = m\\hbar\\omega$ . If we set $\\hbar\\omega=1$, an array of single particle energies can readily be constructed as an array of consecutive non-negative integers.\n",
    "\n",
    "In order to construct the statistical ensemble, think of placing $3$ 'dividers' into a row of $3$ identical 'particles': those dividers then divide the particles into $4$ groups (some of them may be empty), and one can read off the length of each group. So all we need to do is enumerate all of the ways by which the dividers can be placed. This can be readily done using combination tools from python [2] and has been implemented in the function 'partitions' defined in the code below. The output is a matrix of size $P\\times K$, where $P$ is the total number of states, given by\n",
    "\n",
    "$$\n",
    "P = \\frac{\\left(N+K-1\\right)!}{N!\\left(K-1\\right)!} = 15,\n",
    "$$\n",
    "\n",
    "and each $K-$ size row represents a fock state of the type $|n_1, n_2, \\dots, n_K\\rangle$ with $n_i$ particles in state $i$. This constructs a full Bose-Einstein ensemble of allowed states.and stores it in a matrix. You can experiment with this by setting different values of $N$ and $K$ and running\n",
    "\n",
    "    ensemble = partitions(N,K)\n",
    "    print(ensemble)\n",
    "\n",
    "Next, the corresponding Fermi-Dirac ensemble can be created by copying the Bose-Einstein ensemble and deleting any row (fock state) that has more than $g=2s+1$ particles for spin $s$, where $g$ is the spin degeneracy. We've set the spin to $1/2$ by default (electrons), but you can change it if you wish. Next, these ensembles are fed into the partition function (implemented in the code below by the function 'PartFn') where, for a particular inv-temperature $\\beta$ and set of single particle energies, the partition function can be computed using simple dot products on the arrays/matrices. Then, for a given range of $\\beta$'s (stored in the variable 'betas' in the code below), the partition function is computed and differentiated numerically using 'numpy.gradient' [3] to obtain arrays for the energies and specific heats.\n",
    "\n",
    "The sample output below comes from $N=6$ particles in $K=4$ states. Notice that the average energy for the Fermi-Dirac case asymptotically approaches a non-zero value as $\\beta\\rightarrow\\infty$ ($T\\rightarrow 0$) while the average energy asymptotically vanishes for the Bose-Einstein case. This happens due to the Pauli exclusion principle, which prevents the population of many particles in the ground state, forcing them into higher energy states [1], unlike a Bose gas. Also note that the specific heats for both types of gases are peaked, but the peak is much sharper for the Bose gas than the Fermi gas (why?).\n",
    "\n",
    "## **Update**\n",
    "\n",
    "I have done the problem for the Maxwell-Boltzmann distribution as well. The only difference from the Bose-Einstein case is that each row (corresponding to each Fock state) of the BE ensemble matrix has a degeneracy $g_i$ associated with it. For a state $|n_1, n_2, n_3 \\dots n_K\\rangle_i$, it is simply,\n",
    "$$\n",
    "g_i = \\frac{N!}{n_0!\\times n_1! \\times \\dots n_K!}.\n",
    "$$\n",
    "So the ensemble is redefined as a python dictionary containing the ensemble matrix of fock states and the degeneracy vector, which is set to arrays of ones for the FD and BE cases.\n",
    "\n",
    "\n",
    "## References\n",
    "1. Reichl, L.E (1998), *A Modern Course in Statistical Physics (2nd ed.)*. JOHN WILEY & SONS, INC. ISBN:0-471-59520-9 .\n",
    "2. See documentation for python's [itertools combinations with replacement](https://docs.python.org/2/library/itertools.html#itertools.combinations_with_replacement)\n",
    "3. Available with the Numerical Python (https://numpy.org) package @ [numpy.gradient](https://numpy.org/doc/stable/reference/generated/numpy.gradient.html#numpy-gradient)\n",
    "4. Ueda, M. (2010), *Fundamentals and New Frontiers of Bose-Einstein Condensation*, World Sientific. ISBN: 9789812839596 ."
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    "# Python Code and Results"
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\n",
      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.special import comb, factorial\n",
    "from itertools import combinations_with_replacement as cwr\n",
    "import matplotlib.pyplot as plt\n",
    "#from matplotlib import rc\n",
    "#rc('font',**{'family':'sans-serif','sans-serif':['Bitstream Vera Sans']})\n",
    "#rc('text', usetex=True)\n",
    "fs = 13\n",
    "\n",
    "##Spin of the fermions\n",
    "s = 1./2.\n",
    "g = int(2*s + 1)\n",
    "##Number of particles\n",
    "n=6\n",
    "##Number of single particle energy levels\n",
    "k=8\n",
    "##Single particle energy levels\n",
    "sp_energies = np.arange(k)\n",
    "##Range of inverse temperatures\n",
    "betas = np.linspace(1e-4, 6.0, 10000)\n",
    "\n",
    "def partitions(n, b):\n",
    "    '''\n",
    "    Returns a matrix of configurations of n objects with b partitions\n",
    "    '''\n",
    "    ncr = int(comb(n+b-1, b-1))\n",
    "    partition_array = np.empty((ncr, b), dtype=int)\n",
    "    masks = np.identity(b, dtype=int)\n",
    "    for i, c in enumerate(cwr(masks, n)): \n",
    "        partition_array[i,:] = sum(c)\n",
    "    return partition_array\n",
    "\n",
    "def PartFn(beta, ensemble, sp_energies):\n",
    "    '''\n",
    "    Returns the partition function at inv temp beta for an ensemble matrix\n",
    "    with given single particle energies \n",
    "    '''\n",
    "    emat = ensemble[\"matrix\"]\n",
    "    d = ensemble[\"degeneracy\"]\n",
    "    many_body_energies = np.dot(emat, sp_energies)\n",
    "    Z = np.sum(np.exp(-beta * d * many_body_energies))\n",
    "    return Z\n",
    "\n",
    "##This is the full Bose-Einstein ensemble\n",
    "##Each row is a fock state\n",
    "ens_bemat = partitions(n,k)\n",
    "r, c = ens_bemat.shape\n",
    "d = np.ones(r)\n",
    "ens_be = {\"matrix\": ens_bemat, \"degeneracy\":d}\n",
    "\n",
    "##This is the full Fermi-Dirac ensemble\n",
    "##Copy the BE ensemble into the FD ensemble and exclude rows \n",
    "##with more than 'g' particles in a state\n",
    "ens_fdmat = partitions(n,k)\n",
    "ens_fdmat = ens_fdmat[np.prod(ens_fdmat<=g, axis=1).astype(bool)]\n",
    "r, c = ens_fdmat.shape\n",
    "d = np.ones(r)\n",
    "ens_fd = {\"matrix\": ens_fdmat, \"degeneracy\":d}\n",
    "\n",
    "##This is the full Maxwell-Boltzmann ensemble\n",
    "##Copy the BE ensemble into the MB ensemble\n",
    "ens_mbmat = partitions(n,k)\n",
    "#The degeneracy of the Maxwell-Boltzmann ensemble\n",
    "# for each state N!/prod(n_i!)\n",
    "d = factorial(n)/np.array([np.prod(factorial(row)) for row in ens_mbmat])\n",
    "ens_mb = {\"matrix\": ens_mbmat, \"degeneracy\":d}\n",
    "\n",
    "#Compute the many body ground state. This is the monimum of the many body energies\n",
    "eg_be = np.amin(np.dot(ens_be[\"matrix\"], sp_energies))\n",
    "eg_fd = np.amin(np.dot(ens_fd[\"matrix\"], sp_energies))\n",
    "\n",
    "\n",
    "zvals_be = np.array([PartFn(b, ens_be, sp_energies) for b in betas])\n",
    "energies_be = - np.gradient(np.log(zvals_be), betas)\n",
    "cv_be = -betas**2 * np.gradient(energies_be, betas)/n\n",
    "\n",
    "zvals_fd = np.array([PartFn(b, ens_fd, sp_energies) for b in betas])\n",
    "energies_fd = - np.gradient(np.log(zvals_fd), betas)\n",
    "cv_fd = -betas**2 * np.gradient(energies_fd, betas)/n\n",
    "\n",
    "zvals_mb = np.array([PartFn(b, ens_mb, sp_energies) for b in betas])\n",
    "energies_mb = - np.gradient(np.log(zvals_mb), betas)\n",
    "cv_mb = -betas**2 * np.gradient(energies_mb, betas)/n\n",
    "\n",
    "fig, axs = plt.subplots(1, 2,figsize=(16, 8))\n",
    "fig.suptitle('Thermodynamics of Quantum System with N = %ld and K = %ld' % (n,k), fontsize=fs)\n",
    "\n",
    "for ax in axs:\n",
    "    ax.tick_params(direction='in', length=12, width=3, labelsize=fs)\n",
    "    ax.set_xlabel(r\"$\\beta$\", fontsize=fs)\n",
    "    \n",
    "axs[0].plot(betas, energies_be/n, label=r\"Bose-Einstein Ensemble,  $E_g = %1.2lf$\" % eg_be)\n",
    "axs[0].plot(betas, energies_fd/n, label=r\"Fermi-Dirac Ensemble $E_g = %1.2lf$\" % eg_fd)\n",
    "axs[0].plot(betas, energies_mb/n, label=r\"Maxwell-Boltzmann Ensemble\")\n",
    "axs[0].set_ylim(-0.4, np.amax(energies_fd/n)*1.05)\n",
    "\n",
    "axs[0].set_ylabel(r\"$\\overline{E}$\", fontsize=fs)\n",
    "axs[0].legend(fontsize=fs)\n",
    "\n",
    "axs[1].plot(betas, cv_be, label=\"Bose-Einstein Ensemble\")\n",
    "axs[1].plot(betas, cv_fd, label=\"Fermi-Dirac Ensemble\")\n",
    "axs[1].plot(betas, cv_mb, label=r\"Maxwell-Boltzmann Ensemble\")\n",
    "axs[1].set_ylabel(r\"$C_V$\", fontsize=fs)\n",
    "axs[1].legend(fontsize=fs)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises:\n",
    "* Run the code above by loading it into [Jupyter](https://jupyter.org/), clicking on the code cell and pressing 'Shift-Enter'. Make suitable changes to the code and run it for $N=2$, $K=2$. Compute analytical formulae for the partition function for the Bose-Einstein and Fermi-Dirac cases and plot the results $\\overline{E}$ and $C_V$ in the graphs above. Compare the analytical and numerical results.\n",
    "\n",
    "* Start a new code cell below and plot the specific heat for as function of inverse temperature $\\beta$ for several numbers of bosons in $8$ single particle states. Plot specific heats for, say, $N= 5, 8, 10, 20, 30$. What happens to the peak in the specific heat curve as $N$ increases? What do you think will happen to the peak in the thermodynamic limit?\n",
    "\n",
    "* The above code was for an Einstein Solid, where single particle energy levels are integers. Change this to model the energy levels of a particle in a box and re-run for $N=6$, $K=4$. Compare with the Einstein Solid.  "
   ]
  }
 ],
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