{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# *Path Integrals - Lévy Sampling*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`Doruk Efe Gökmen -- 19/08/2018 -- Ankara`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Quantum statistical mechanics - Density matrices" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In a thermal ensemble, the probability of being in $n$th energy eigenstate is given by the Boltzmann factor $\\pi(n)\\propto e^{-\\beta E_n}$, where $\\beta=\\frac{1}{k_BT}$. Hence, e.g the probability $\\pi(x,n)$ to be in state $n$ and in position $x$ is proportional to $e^{-\\beta E_n}|\\psi_n(x)|^2$.\n", "\n", "We can consider the diagonal density matrix $\\rho(x,x,\\beta)=\\sum_n e^{\\beta E_n}\\psi_n(x)\\psi_n^*(x)$, which is the probability $\\pi(x)$ of being at position $x$. This is a special case of the more general density matrix $\\rho(x,x',\\beta)=\\sum_n e^{\\beta E_n}\\psi_n(x)\\psi_n^*(x')$, which is the central object of quantum statistical mechanics. The partition function is given by $Z(\\beta)=\\text{Tr}\\rho_u=\\int_{-\\infty}^\\infty \\rho_u(x,x,\\beta)\\text{d}x$, where $\\rho_u=e^{-\\beta \\mathcal{H}}$ is the unnormalised density matrix. It follows that $\\rho(\\beta)=\\frac{e^{-\\beta\\mathcal{H}}}{\\text{Tr}(e^{-\\beta\\mathcal{H}})}$.\n", "\n", "Properties of the density matrix:\n", "* *The convolution property*: $\\int \\rho(x,x',\\beta_1) \\rho(x',x'',\\beta_2) \\text{d}x' = \\int \\text{d}x' \\sum_{n,m} \\psi_n(x)e^{-\\beta_1 E_n} \\psi_n^*(x')\\psi_m(x')e^{-\\beta_2 E_m}\\psi_m^*(x'')$ $ = \\sum_{n,m} \\psi_n(x)e^{-\\beta_1 E_n} \\int \\text{d}x' \\psi_n^*(x')\\psi_m(x')e^{-\\beta_2 E_m}\\psi_m^*(x'') = \\sum_n \\psi_n(x)e^{-(\\beta_1+\\beta_2)E_n}\\psi_n^*(x'')=\\rho(x,x'',\\beta_1+\\beta_2)$ $\\implies \\boxed{ \\int \\rho(x,x',\\beta) \\rho(x',x'',\\beta) \\text{d}x' = \\rho(x,x'',2\\beta)}$ (note that in the discrete case, this is just matrix squaring). **So, if we have the density matrix at temperature $T=k_B/\\beta$ this equation allows us to compute the density matrix at temperature $T/2$**.\n", "\n", "* *The free density matrix* for a system of infinte size is $\\rho^\\text{free}(x,x',\\beta)=\\frac{1}{\\sqrt{2\\pi\\beta}}\\exp{\\left[-\\frac{(x-x')^2}{2\\beta}\\right]}$. Notice that in the high temperature limit ($\\beta\\rightarrow 0$) the density matrix becomes classical: $\\rho^\\text{free}\\rightarrow \\delta(x-x')$. The quantum system exihibits its peculiar properties more visibly at low temperatures.\n", "\n", "* *High temperature limit and the Trotter decomposition*. In general any Hamiltonian can be written as $\\mathcal{H}=\\mathcal{H}^\\text{free}+V(x)$. At high temperatures ($\\beta\\rightarrow 0$) we can approximate the density matrix as $\\rho(x,x',\\beta)=e^{-\\beta V(x)/2}\\rho^\\text{free}e^{-\\beta V(x')/2}$ (Trotter expansion). Hence an explicit expression for the density matrix is available without solving the Schrödinger (or more preciesly Liouville) equation for any potential." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Path integrals - Quantum Monte Carlo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Path integral representation of the kernel\n", "\n", "The kernel $K$ is the matrix element of the unitary time evolution operator $U(t_i-t_f)=e^{-i/\\hbar(t_f-t_i)\\mathcal{H}}$ in the position representation: $K(x_i,x_f;t_f-t_i)=\\langle x_f \\left| U(t_f-t_i) \\right| x_i \\rangle$. We can write $K(x_i,x_f;t_f-t_i)=\\langle x_f \\left| U^N((t_f-t_i)/N) \\right| x_i \\rangle$, that is, divide the time interval $[t_i,t_f]$ into $N$ equal intervals $[t_k,t_{k+1}]$ of length $\\epsilon$, where $\\epsilon=t_{k+1}-t_k=(t_f-t_i)/N$.\n", "\n", "Then we can insert $N-1$ resolutions of identity ($\\int_{-\\infty}^\\infty \\text{d} x_k \\left|x_k\\rangle\\langle x_k\\right|$) to obtain\n", "\n", "$K(x_i,x_f;t_f-t_i)= \\left[\\Pi_{k=1}^{N-1}\\int_{-\\infty}^\\infty dx_k \\right] \\left[\\Pi_{k=0}^{N-1} K(x_i,x_f;\\epsilon = (t_f-t_i)/N)\\right]$,\n", "\n", "where $x_f=x_N$ and $x_i=x_0$. In the continuous limit, we would have \n", "\n", "$K(x_i,x_f;t_f-t_i)= \\lim_{N\\rightarrow\\infty} \\left[\\Pi_{k=1}^{N-1}\\int_{-\\infty}^\\infty dx_k \\right] \\left[\\Pi_{k=0}^{N-1} K(x_i,x_f;\\epsilon = (t_f-t_i)/N)\\right]$. (A)\n", "\n", "Let us now consider the limit $\\epsilon\\rightarrow 0$ ($N\\rightarrow \\infty$) to obtain the short time kernel $K(x_i,x_f;\\epsilon)$ and thereby switching from discrete to the continuous limit. It is known that for small $\\epsilon$ the Trotter formula implies that to a very good approximation \n", "\n", "$K(x_i,x_f;\\epsilon = (t_f-t_i)/N) \\simeq \\langle x_{k+1} \\left| e^{-i(\\hbar\\epsilon T} e^{-i/\\hbar \\epsilon V} \\right| x_k\\rangle$,\n", "\n", "which becomes exact as $\\epsilon\\rightarrow 0$. If we insert resolution of identity $\\int \\text{d}p_k \\left| p_k \\rangle\\langle p_k \\right|$, we get\n", "\n", "$K(x_i,x_f;\\epsilon) = \\int_{-\\infty}^\\infty \\text{d}p_k \\langle x_{k+1} \\left| e^{-i(\\hbar\\epsilon T} \\left| p_k \\rangle\\langle p_k \\right| e^{-i/\\hbar \\epsilon V} \\right| x_k\\rangle = \\int_{-\\infty}^\\infty \\text{d}p_k \\langle x_{k+1} \\left| p_k \\rangle\\langle p_k \\right| x_k\\rangle e^{-i/\\hbar \\epsilon \\left(\\frac{p_k}{2m} + V(x)\\right)}$\n", "\n", "$\\implies K(x_i,x_f;\\epsilon) = \\frac{1}{2\\pi \\hbar}\\int_{-\\infty}^\\infty \\text{d}p_k e^{i/\\hbar \\epsilon \\left[p_k\\frac{x_{k+1}-x_k}{\\epsilon}-\\mathcal{H}(p_k,x_k) \\right]}$. (B)\n", "\n", "Hence, inserting (B) into (A) we get\n", "\n", "$K(x_i,x_f;t_f-t_i) = \\lim_{N\\rightarrow \\infty}\\left[\\Pi_{k=1}^{N-1}\\int_{-\\infty}^\\infty dx_k \\right] \\left \\{ \\Pi_{k=0}^{N-1} \\int_{-\\infty}^\\infty \\text{d}p_k e^{i/\\hbar \\epsilon \\left[p_k\\frac{x_{k+1}-x_k}{\\epsilon}-\\mathcal{H}(p_k,x_k) \\right]} \\right\\}$. (C)\n", "\n", "We can simplify the exponent of the integrand in the limiting case $N\\rightarrow \\infty$, \n", "\n", "$\\lim_{N\\rightarrow \\infty} \\epsilon \\sum_{k=0}^{N-1}\\left[p_k\\frac{x_{k+1}-x_k}{\\epsilon}-\\mathcal{H}(p_k,x_k) \\right] =\\int_{t_1}^{t_2}\\text{d}t[p(t)\\dot{x}(t)-\\mathcal{H}[p(t),x(t)]]$\n", "\n", "$=\\int_{t_1}^{t_2}\\text{d}t \\mathcal{L}[x(t),\\dot{x}(t)] = \\mathcal{S}[x(t);t_f,t_i]$, (D)\n", "\n", "where $\\mathcal{L}[x(t),\\dot{x}(t)] = \\frac{m}{2}\\dot{x}(t)^2-V[x(t)]$ is the Lagrangian and $\\mathcal{S}[x(t);t_f,t_i]$ is the action between times $t_f$ and $t_i$.\n", "\n", "Furthermore we can introduce the following notation for the integrals over *paths*:\n", "\n", "$\\lim_{N\\rightarrow \\infty}\\left(\\Pi_{k=1}^{N-1} \\int_{-\\infty}^\\infty \\text{d}x_k\\right)=\\int_{x(t_i)=x_i}^{x(t_f)=x_f}\\mathcal{D}[x(t)]$, (E.1)\n", "\n", "$\\lim_{N\\rightarrow \\infty}\\left(\\Pi_{k=1}^{N-1}\\int_{-\\infty}^\\infty\\frac{\\text{d}p_k}{2\\pi\\hbar}\\right) =\\int \\mathcal{D}\\left[\\frac{p(t)}{2\\pi\\hbar}\\right]$. (E.2)\n", "\n", "Using (D) and (E) in (C), we get the path integral representation of the kernel\n", "\n", "$K(x_i,x_f;t_f-t_i)= \\int_{x(t_i)=x_i}^{x(t_f)=x_f}\\mathcal{D}[x(t)] \\int \\mathcal{D}\\left[\\frac{p(t)}{2\\pi\\hbar}\\right] e^{i/\\hbar \\mathcal{S}[x(t)]}$\n", "\n", "$\\implies \\boxed{K(x_i,x_f;t_f-t_i)= \\mathcal{N} \\int_{x(t_i)=x_i}^{x(t_f)=x_f}\\mathcal{D}[x(t)] e^{i/\\hbar \\mathcal{S}[x(t)]}}$, (F)\n", "\n", "where $\\mathcal{N}$ is the normalisation factor.\n", "\n", "Here we see that each path has a phase proportional to the action. The equation (F) implies that we sum over all paths, which in fact interfere with one another. The true quantum mechanical amplitude is determined by the constructive and destructive interferences between these paths. For example, actions that are very large compared to $\\hbar$, lead to very different phases even between nearby paths that differ only slightly, and that causes destructive interference between them. Only in the extremely close vicinity of the classical path $\\bar x(t)$, where the action changes little when the phase varies, will neighbouring paths contirbute to the interference constructively. This leads to a classical deterministic path $\\bar x(t)$, and this is why the classical approximation is valid when the action is very large compared to $\\hbar$. Hence we see how the classical laws of motion arise from quantum mechanics." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Path integral representation of the partition function\n", "**Heuristic derivation of the discrete case:** Recall the convolution property of the density matrix, we can apply it repeatedly:\n", "\n", "$\\rho(x_0,x_2,\\beta) = \\int \\rho(x_0,x_2,\\beta/2) \\rho(x_2,x_1,\\beta/2) \\text{d}x_2 = \\int \\int \\int \\rho(x_0,x_3,\\beta/4) \\rho(x_3, x_2,\\beta/4) \\rho(x_2,x_4,\\beta/4) \\rho(x_4,x_1 ,\\beta/4) \\text{d}x_2 \\text{d}x_3 \\text{d}x_4 = \\cdots $ \n", "\n", "In other words: $\\rho(x_0,x_N,\\beta) = \\int\\int \\cdots \\int \\text{d}x_1 \\text{d}x_2 \\cdots \\text{d}x_{N-1}\\rho(x_0,x_1,\\beta/N)\\rho(x_1,x_2,\\beta/N)\\cdots\\rho(x_{N-1},x_N,\\beta/N)$. The variables $x_k$ in this integral is called a *path*. We can imagine the variable $x_k$ to be at position $x_k$ at given slice $k\\beta/N$ of an imaginary time variable $\\tau$ that goes from $0$ to $\\beta$ in steps of $\\Delta\\tau=\\beta/N$. Density matrices and partition functions can thus be expressed as multiple integrals over path variables, which are none other than the path integrals that were introduced in the previous subsection.\n", "\n", "Given the unnormalised density matrix $\\rho_u$, the discrete partition $Z_d(\\beta)$ function can be written as a path integral for all ***closed*** paths (because of the trace property), i.e., paths with the same beginning and end points ($x_0=x_N$), over a “time” interval $−i\\hbar\\beta$.\n", "\n", "$Z_d(\\beta)= \\text{Tr}(e^{-\\beta \\mathcal{H}}) = \\text{Tr}(\\rho_u(x_0,x_N,\\beta) )=\\int \\text{d}x_0 \\rho_u (x_0,x_N=x_0,\\beta) $ $ = \\int \\int\\int \\cdots \\int \\text{d}x_0 \\text{d}x_1 \\text{d}x_2 \\cdots \\text{d}x_{N-1}\\rho_u(x_0,x_1,\\beta/N)\\rho_u(x_1,x_2,\\beta/N)\\cdots\\rho_u(x_{N-1},x_N,\\beta/N)\\rho_u(x_{N-1},x_0,\\beta/N)$. \n", "\n", "The integrand is the probabilistic weight $\\Phi\\left[\\{x_i\\}\\right]$ of the discrete path consisting of points $\\{x_i\\}$. The continuous case can be obtained by taking the limit $N\\rightarrow \\infty$. By defining\n", "\n", "$\\Phi[x(\\tau)] = \\lim_{N\\rightarrow \\infty} \\rho_u(x_0,x_1,\\beta/N)\\cdots \\rho_u(x_{N-1},x_N,\\beta/N)$, (G)\n", "\n", "(note that this is the probability weight of a particular continuous path), and by using (E.1), we can express the continuous partition function $Z(\\beta)$ as\n", "\n", "$Z(\\beta) = \\int_{x(0)}^{x(\\hbar \\beta)=x(0)}\\mathcal{D}[x(\\tau)] \\Phi[x(\\tau)]$. (H)\n", "\n", "But what is $\\Phi[x(\\tau)]$?\n", "\n", "**Derivation of the continuous case:** Again we start from $Z(\\beta)= \\text{Tr}(e^{-\\beta \\mathcal{H}})$. The main point of the argument that follows is the operational resemblance between the unitary time evolution operator $U(t)=e^{-(i/\\hbar) t\\mathcal{H}}$ and the unnormalised density matrix $e^{-\\beta \\mathcal{H}}$: the former is used to define the kernel which reads $K(x,x';t)=\\langle x \\left| e^{-(i/\\hbar) t\\mathcal{H}} \\right| x' \\rangle$; and the latter is used in defining the density matrix which reads $\\rho(x,x';\\beta)=\\langle x \\left| e^{-\\beta \\mathcal{H}} \\right| x' \\rangle$. If we regard $\\beta$ as the analytic continuation of the real time $t$ to the imaginary values: $t\\rightarrow i \\tau \\rightarrow i \\hbar \\beta$, and $t=t_i-t_f$, we get the cousin of the partition function that lives in the imaginary spacetime (i.e. Minkowskian rather than Euclidian, but this has nothing to do with relativity, or has it?)\n", "\n", "$Z\\left[\\beta\\rightarrow -\\frac{i}{\\hbar}(t_f-t_i)\\right]=\\text{Tr}\\left[U(t_f-t_i)\\right]=\\int_{-\\infty}^\\infty \\text{d}x \\langle x \\left| U(t_f-t_i) \\right| x \\rangle$\n", "\n", "$=\\int_{-\\infty}^\\infty \\text{d}x K(x,x;t_f-t_i)$\n", "\n", "$=\\int_{-\\infty}^\\infty \\text{d}x \\mathcal{N} \\int_{x(t_i)=x}^{x(t_f)=x}\\mathcal{D}[x(t)] e^{i/\\hbar \\int_{t_i}^{t_f}\\text{d}t \\mathcal{L}[x(t),\\dot{x}(t)]} $ (using (F)) \n", "\n", "$=\\mathcal{N} \\int_{x(t_f)=x(t_i)}\\mathcal{D}[x(t)] e^{i/\\hbar \\int_{t_i}^{t_f}\\text{d}t \\mathcal{L}[x(t),\\dot{x}(t)]} = \\mathcal{N} \\int_{x(t_f)=x(t_i)}\\mathcal{D}[x(t)] e^{i/\\hbar \\int_{t_i}^{t_f}\\text{d}t \\left[\\frac{m}{2}\\dot{x}(t)^2-V[x(t)]\\right]}$,\n", "\n", "which means that one is integrating not over all paths but over all *closed* paths (loops) at $x$. We are now ready to get the path integral representation of the real partition function by making the transformations $t\\rightarrow i\\tau$ so that $t_i\\rightarrow 0$ and $t_f\\rightarrow -i\\hbar \\beta$ (also note that $\\dot{x(t)}=\\frac{\\partial x(t)}{\\partial t}\\rightarrow -i \\frac{\\partial x(\\tau)} {\\partial \\tau} = -i x'(\\tau) \\implies \\dot{x}(t)^2 \\rightarrow -x'(\\tau)^2$):\n", "\n", "$\\implies Z(\\beta)=\\mathcal{N} \\int_{x(\\hbar \\beta)=x(0)}\\mathcal{D}[x(\\tau)] e^{-\\frac{1}{\\hbar} \\int_{0}^{\\beta \\hbar}\\text{d}\\tau\\left( \\frac{m}{2}x'(\\tau)^2+V[x(\\tau)]\\right)}$\n", "\n", "$\\implies \\boxed{ Z(\\beta)=\\mathcal{N} \\int_{x(\\hbar \\beta)=x(0)}\\mathcal{D}[x(\\tau)] e^{-\\frac{1}{\\hbar} \\int_{0}^{\\beta \\hbar}\\text{d}\\tau \\mathcal{H}[p(\\tau),x(\\tau)]} }$. (I)\n", "\n", "Notice that by comparing (H) and (I) we get an expression for the probabilistic weight $\\Phi[x(\\tau)]$ of a particular path $x(\\tau)$, that is \n", "\n", "$\\Phi[x(\\tau)] = \\lim_{N\\rightarrow \\infty} \\rho_u(x_0,x_1;\\beta/N)\\cdots \\rho_u(x_{N-1},x_N;\\beta/N) = \\exp{\\left\\{ e^{-\\frac{1}{\\hbar} \\int_{0}^{\\beta \\hbar}\\text{d}\\tau \\mathcal{H}[p(\\tau),x(\\tau)]}\\right\\}}$ (J), which is very intuitive, considering the definition of the unnormalised density matrix $\\rho_u$. This is an intriguing result, since we were able to obtain the complete statistical description of a quantum mechanical system without the appearance of complex numbers. \n", "\n", "Because of this reason, using (J) it is easy to see why some paths contribute very little to the path integral: those are paths for which the exponent is very large due to high energy, and thus the integrand is negligibly small. *Furthermore, it is unnecessary to consider whether or not nearby paths cancel each other's contributions, for in the present case they do not interfere (since no complex numbers involved) i.e. all contributions add together with some being large and others small.*\n", "\n", "#### Path integral Monte Carlo\n", "\n", "In the algorithm, so called the *naïve path integral (Markov-chain) Monte Carlo*, we move from one path configuration consisting of $\\{x_i\\}$ to another one consisting of $\\{x'_i\\}$ by choosing a single position $x_k$ and by making a little displacement $\\Delta x$ that can be positive or negative. We compute the weight before ($\\Phi[\\{x_i\\}]$) this move and after ($\\Phi[\\{x'_i\\}]$) the move and accept the move with the Metropolis acceptance rate (reject with certainty if the new weight is greater than the old one, smaller the new weight is, the higher the acceptance rate). Defining $\\epsilon \\equiv \\beta/N$, we can approximate $\\Phi[\\{x_i\\}]$ by making a Trotter decomposition *only around the point $x_k$*:\n", "\n", "$\\Phi\\left[\\{x_i\\}\\right]\\approx \\cdots \\rho^\\text{free}(x_{k-1},x_k;\\epsilon) e^{-\\frac{1}{2}\\epsilon V(x_k)} e^{-\\frac{1}{2}\\epsilon V(x_k)} \\rho^\\text{free}(x_{k},x_{k+1};\\epsilon)\\cdots$.\n", "\n", "Therefore, the acceptance ratio $\\frac{\\Phi\\left[\\{x'_i\\}\\right]}{\\Phi\\left[\\{x_i\\}\\right]}$ can be approximated as\n", "\n", "\n", "$\\frac{\\Phi\\left[\\{x'_i\\}\\right]}{\\Phi\\left[\\{x_i\\}\\right]}\\approx\\frac{\\rho^\\text{free}(x_{k-1},x'_k;\\epsilon) e^{-\\epsilon V(x'_k)}\\rho^\\text{free}(x'_k,x_{k+1};\\epsilon)}{\\rho^\\text{free}(x_{k-1},x_k;\\epsilon) e^{-\\epsilon V(x_k)} \\rho^\\text{free}(x_k,x_{k+1};\\epsilon)}$.\n", "\n", "This is implemented in the following program." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab qt\n", "import math, random, pylab, os\n", "\n", "# Exact quantum position distribution:\n", "def p_quant(x, beta):\n", " p_q = sqrt(tanh(beta / 2.0) / pi) * exp(- x**2.0 * tanh(beta / 2.0))\n", " return p_q\n", "\n", "def rho_free(x, y, beta): # free off-diagonal density matrix\n", " return math.exp(-(x - y) ** 2 / (2.0 * beta))\n", "\n", "output_dir = 'snapshots_naive_harmonic_path'\n", "if not os.path.exists(output_dir): os.makedirs(output_dir)\n", "\n", "fig = pylab.figure(figsize=(6, 10))\n", "def show_path(x, k, x_old, Accepted, hist_data, step, fig):\n", " pylab.clf()\n", " path = x + [x[0]] #Final position is the same as the initial position. \n", " #Note that this notation appends the first element of x as a new element to x \n", " y_axis = range(len(x) + 1) #construct the imaginary time axis\n", " \n", " ax = fig.add_subplot(2, 1, 1)\n", " #Plot the paths\n", " if Accepted:\n", " old_path = x[:] #save the updated path as the old path\n", " old_path[k] = x_old #revert the update to get the actual old path\n", " old_path = old_path + [old_path[0]] #final position is the initial position\n", " ax.plot(old_path, y_axis, 'ko--', label='old path')\n", " if not Accepted and step !=0:\n", " old_path = x[:]\n", " old_path[k] = x_old \n", " old_path = old_path + [old_path[0]]\n", " ax.plot(old_path, y_axis, 'ro-', label='rejection', linewidth=3)\n", " ax.plot(path, y_axis, 'bo-', label='new path') #plot the new path\n", " ax.legend()\n", " ax.set_xlim(-2.5, 2.5)\n", " ax.set_ylabel('$\\\\tau$', fontsize=14)\n", " ax.set_title('Naive path integral Monte Carlo, step %i' % step)\n", " ax.grid()\n", " \n", " #Plot the histogram\n", " ax = fig.add_subplot(2, 1, 2)\n", " x = [a / 10.0 for a in range(-100, 100)]\n", " y = [p_quant(a, beta) for a in x]\n", " ax.plot(x, y, c='gray', linewidth=1.0, label='Exact quantum distribution')\n", " ax.hist(hist_data, 10, histtype='step', normed = 'True', label='Path integral Monte Carlo') #histogram of the sample\n", " ax.set_title('Position distribution at $T=%.2f$' % T)\n", " ax.set_xlim(-2.5, 2.5) #restrict the range over which the histogram is shown\n", " ax.set_xlabel('$x$', fontsize = 14)\n", " ax.set_ylabel('$\\pi(x)=e^{-\\\\beta E_n}|\\psi_n(x)|^2$', fontsize = 14)\n", " ax.legend(fontsize = 6)\n", " ax.grid()\n", " \n", " pylab.pause(0.2)\n", " pylab.savefig(output_dir + '/snapshot_%05i.png' % step)\n", "\n", "beta = 4.0 # inverse temperature\n", "T = 1 / beta\n", "N = 8 # number of (imagimary time) slices\n", "dtau = beta / N\n", "delta = 1.0 # maximum displacement on one slice\n", "n_steps = 4 # number of Monte Carlo steps\n", "hist_data = []\n", "x = [random.uniform(-1.0, 1.0) for k in range(N)] # initial path (a position for each time)\n", "show_path(x, 0, 0.0, False, hist_data, 0, fig) #show the initial path\n", "\n", "for step in range(n_steps):\n", " #print 'step',step\n", " k = random.randint(0, N - 1) # randomly choose slice\n", " knext, kprev = (k + 1) % N, (k - 1) % N # next/previous slices\n", " x_old = x[k]\n", " x_new = x[k] + random.uniform(-delta, delta) # new position at slice k\n", " #calculate the weight before and after the move\n", " old_weight = (rho_free(x[knext], x_old, dtau) *\n", " rho_free(x_old, x[kprev], dtau) *\n", " math.exp(-0.5 * dtau * x_old ** 2))\n", " new_weight = (rho_free(x[knext], x_new, dtau) *\n", " rho_free(x_new, x[kprev], dtau) *\n", " math.exp(-0.5 * dtau * x_new ** 2))\n", " if random.uniform(0.0, 1.0) < new_weight / old_weight: #accept with metropolis acceptance rate\n", " x[k] = x_new\n", " Accepted = True\n", " else:\n", " Accepted = False\n", " show_path(x, k, x_old, Accepted, hist_data, step + 1, fig) \n", " hist_data.append(x[k]) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![caption](path_integral.gif)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the above program satisfies the detailed balance condition, is aperiodic and irreducible. However it is very slow, as it takes very long to explore all of the available configuration space." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To make progress, let us now move back by two steps: consider the free particle instead of the harmonic potential, and instead of sampling $x_k$ with random $k$ at each step, keep $k$ fixed: we modify the position $x_k$ between the fixed positions $x_{k\\pm 1}$ with the Metropolis algorithm." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The distribution of the position $x_k$ between fixed values of $x_{k\\pm 1}$ is a gaussian. This is not a coincidence. Because $\\pi^\\text{free}(x_k|x_{k-1},x_{k+1})\\propto \\rho^\\text{free}(x_{k-1},x_k;\\epsilon) \\rho^\\text{free}(x_{k},x_{k+1};\\epsilon)\\propto \\exp{\\left[\\frac{(x_k-\\langle x_k \\rangle)^2}{2\\sigma^2}\\right]}$, i.e. the product of two gaussians is also a gaussian. Here we have the mean $\\langle x_k \\rangle = \\frac{x_{k-1} + x_{k+1}}{2}$, and the variance $\\sigma=\\frac{\\epsilon}{2}$.\n", "\n", "On the other hand, since we can derive that the distribution is a gaussian $\\pi(x) = \\sqrt{\\tanh(\\beta / 2) / \\pi} \\exp[-x^2 * \\tanh(\\beta/2)]$, we do not need to use the Metropolis algorithm. We can use direct sampling of the gaussian with the above mean and variance instead! However, instead of doing that, let us generalise the problem further.\n", "\n", "Consider a position $x_k$ between $x'$ and $x''$ with corresponding intervals $\\epsilon'$ and $\\epsilon''$ (not necessarily equal), respectively. Then $\\pi^\\text{free}(x_k|x',x'')\\propto \\rho^\\text{free}(x',x_k;\\epsilon') \\rho^\\text{free}(x_{k},x'';\\epsilon'')\\propto \\exp{\\left[\\frac{(x_k-\\langle x_k \\rangle)^2}{2\\sigma^2}\\right]}$ with the mean $\\langle x_k \\rangle = \\frac{\\epsilon''x' + \\epsilon'x''}{\\epsilon'+\\epsilon''}$, and the variance $\\sigma=\\left(\\frac{1}{\\epsilon'} + \\frac{1}{\\epsilon''}\\right)^{-1}$. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%pylab inline\n", "import math, random, pylab\n", "\n", "def rho_free(x, y, beta):\n", " return math.exp(-(x - y) ** 2 / (2.0 * beta))\n", "\n", "dtau_prime = 0.1\n", "dtau_dprime = 0.2\n", "x_prime = 0.0\n", "x_dprime = 1.0\n", "delta = 1.0 # maximum displacement of xk\n", "n_steps = 100000 # number of Monte Carlo steps\n", "data_hist = []\n", "xk = 0.0 # initial value of xk\n", "for step in xrange(n_steps):\n", " xk_new = xk + random.uniform(-delta, delta)\n", " old_weight = (rho_free(x_dprime, xk, dtau_dprime) *\n", " rho_free(xk, x_prime, dtau_prime))\n", " new_weight = (rho_free(x_dprime, xk_new, dtau_dprime) * \n", " rho_free(xk_new, x_prime, dtau_prime))\n", " if random.random() < new_weight / old_weight:\n", " xk = xk_new\n", " data_hist.append(xk)\n", "\n", "def pi_analytic(xk, x_prime, x_dprime, dtau_prime, dtau_dprime):\n", " mean = (dtau_dprime * x_prime + dtau_prime * x_dprime) / (dtau_prime + dtau_dprime)\n", " sigma = 1.0 / math.sqrt(1.0 / dtau_prime + 1.0 / dtau_dprime)\n", " return math.exp(-(xk - mean) ** 2 / (2.0 * sigma ** 2)) / math.sqrt(2.0 * math.pi) / sigma\n", "\n", "pylab.title('Distribution on slice k', fontsize=18)\n", "histo, bin_edges, dummy = pylab.hist(data_hist, bins=100, normed=True)\n", "bin_centers = 0.5 * (bin_edges[1:] + bin_edges[:-1])\n", "pylab.plot(bin_centers, [pi_analytic(x, x_prime, x_dprime, dtau_prime, dtau_dprime) for x in bin_centers], 'r-', lw=3)\n", "pylab.xlabel('$x_k$', fontsize=18)\n", "pylab.ylabel('$\\pi(x_k)$', fontsize=18)\n", "pylab.savefig('plot-path_slice.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Lévy sampling of quantum paths" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\pi(x_k | x', x'')$ gives the statistical weight of all paths that start at x' that pass through $x_k$ and that end up at $x''$. Let's apply this idea for $x_k = x_1 x' = x_0$ and $x'' = x_N$. We can sample the position $x_1$, given $x_0$ and $x_N $. Between the freshly sampled value of $x_1$ and $x_N$ we can then sample the value of $x_2$ and then of $x_3\\cdots$ and eventually the entire path. Here we use $\\pi^\\text{free}(x_k|x',x'')\\propto \\exp{\\left[\\frac{(x_k-\\langle x_k \\rangle)^2}{2\\sigma^2}\\right]}$ with the mean $\\langle x_k \\rangle = \\frac{\\epsilon''x' + \\epsilon'x''}{\\epsilon'+\\epsilon''}$, and the variance $\\sigma=\\left(\\frac{1}{\\epsilon'} + \\frac{1}{\\epsilon''}\\right)^{-1}$ in order to apply this condition." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math, random, pylab, os\n", "\n", "fig = pylab.figure(figsize=(6, 10))\n", "def show_path(x,step,title):\n", " path = x[:] #Final position is the same as the initial position. \n", " #Note that this notation appends the first element of x as a new element to x \n", " y_axis = range(len(x)) #construct the imaginary time axis\n", " #Plot the paths\n", " pylab.plot(path, y_axis, 'ko-')\n", " pylab.xlabel('$x$', fontsize = 14)\n", " pylab.ylabel('$\\\\tau$', fontsize=14)\n", " pylab.title(title, fontsize=14)\n", " pylab.xlim([-1,2])\n", " pylab.grid()\n", " pylab.savefig(output_dir + '/snapshot_%05i.png' % step)\n", " pylab.clf()\n", " \n", "output_dir = 'snapshots_Levy_harmonic_path'\n", "if not os.path.exists(output_dir): os.makedirs(output_dir)\n", "\n", "beta = 1.0\n", "N = 4\n", "dtau = beta / N\n", "nsteps = 100 # number of paths to be generated\n", "xstart, xend = 0.0, 1.0 # initial and final points\n", "for step in range(nsteps):\n", " title = 'Levy sampling quantum path, step %i' % step\n", " x = [xstart] #initialise the path\n", " for k in range(1, N): # loop over internal slices\n", " dtau_prime = (N - k) * dtau #current \"time\" step\n", " x_mean = (dtau_prime * x[k - 1] + dtau * xend) / \\\n", " (dtau + dtau_prime) #current mean is calculated from the above formula\n", " sigma = math.sqrt(1.0 / (1.0 / dtau + 1.0 / dtau_prime)) #current variance calculated similarly\n", " x.append(random.gauss(x_mean, sigma)) #generate a gaussian random variable using above parameters\n", " x.append(xend)\n", " show_path(x,step,title)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![Levy sampling of the paths of a free particle](path_levy_free.gif)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that without the condition that the path will finish at $x_N$, this is simply a random walk." ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math, random\n", "\n", "beta = 4.0\n", "N = 8\n", "sigma = math.sqrt(beta / N)\n", "x = [0.0]\n", "title = 'Random walk'\n", "for k in range(N - 1):\n", " x.append(random.gauss(x[-1], sigma))\n", "fig = pylab.figure(figsize=(6, 10))\n", "show_path(x,title)" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math, random\n", "\n", "beta = 1.0\n", "N = 8\n", "sigma = math.sqrt(beta / N)\n", "xend = 1.0\n", "Upsilon = [0.0]\n", "title = 'Trivial quantum path algorithm'\n", "for k in range(N):\n", " Upsilon.append(random.gauss(Upsilon[-1], sigma))\n", "x = [0.0] + [Upsilon[k] + (xend - Upsilon[-1]) * \\\n", " k / float(N) for k in range(1, N + 1)]\n", "fig = pylab.figure(figsize=(6, 10))\n", "show_path(x,title)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the harmonic oscillator density matrix is also a gaussian (see e.g. Feynman), we can use the Lévy sampling here." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%pylab inline \n", "import math, random, pylab\n", "\n", "beta = 2.0\n", "N = 20\n", "dtau = beta / N\n", "nsteps = 1\n", "xstart, xend = 2.0, 1.0\n", "fig = pylab.figure(figsize=(6, 10))\n", "for step in range(nsteps):\n", " pylab.clf()\n", " x = [xstart]\n", " for k in range(1, N):\n", " dtau_prime = (N - k) * dtau\n", " Ups1 = 1.0 / math.tanh(dtau) + \\\n", " 1.0 / math.tanh(dtau_prime)\n", " Ups2 = x[k - 1] / math.sinh(dtau) + \\\n", " xend / math.sinh(dtau_prime)\n", " x.append(random.gauss(Ups2 / Ups1, \\\n", " 1.0 / math.sqrt(Ups1)))\n", " x.append(xend)\n", " # graphics\n", " pylab.plot(x, [j * dtau for j in range(N + 1)], 'k-o')\n", " pylab.xlabel('$x$', fontsize=18)\n", " pylab.ylabel('$\\\\tau$', fontsize=18)\n", " pylab.title('Harmonic Levy path %i' % step)\n", " #pylab.xlim(-2.0, 4.0)\n", " pylab.grid()\n", " pylab.show()\n", " pylab.pause(0.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can easily generalise this to the multidimensional case. We have no problem understanding that a three-dimensional harmonic oscillator quantum path can be sampled by independent Lévy constructions in x, y and z. The following is a 2D implementation." ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib qt\n", "import math, random, os\n", "import matplotlib as mpl\n", "from mpl_toolkits.mplot3d import Axes3D\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "def levy_harmonic_1d(start, end, dtau):\n", " x = [start]\n", " for k in range(1, N):\n", " dtau_prime = (N - k) * dtau\n", " Ups1 = 1.0 / math.tanh(dtau) + \\\n", " 1.0 / math.tanh(dtau_prime)\n", " Ups2 = x[k - 1] / math.sinh(dtau) + \\\n", " end / math.sinh(dtau_prime)\n", " x.append(random.gauss(Ups2 / Ups1, \\\n", " 1.0 / math.sqrt(Ups1)))\n", " x.append(end)\n", " return x\n", "\n", "def show_path_2d(x,y,title):\n", " plt.gca(projection='3d')\n", " plt.plot(x, y, [j * dtau for j in range(N + 1)], 'k-o')\n", " plt.title(title)\n", " plt.xlabel('$x$')\n", " plt.ylabel('$y$')\n", " plt.gca(projection='3d').set_zlabel('$\\\\tau$')\n", " plt.grid()\n", " plt.show()\n", " plt.pause(0.1)\n", " plt.clf()\n", "\n", "output_dir = 'snapshots_Levy_2d_harmonic_path'\n", "if not os.path.exists(output_dir): os.makedirs(output_dir)\n", " \n", "beta = 1.0\n", "N = 20\n", "nsteps = 50\n", "dtau = beta / float(N)\n", "[xstart, ystart, zstart] = [1.0, -2.0, 1.5]\n", "[xend, yend, zend] = [-2.5, 0.0, -0.5]\n", "\n", "for step in range(nsteps):\n", " plt.clf()\n", " title = '2D quantum path %.i th step' % step\n", " x = levy_harmonic_1d(xstart, xend, dtau)\n", " y = levy_harmonic_1d(ystart, yend, dtau)\n", " #z = levy_harmonic_1d(zstart, zend, dtau)\n", " #for i in range(N + 1):\n", " # print 'slice %2i: ' % i, x[i], y[i], z[i]\n", " show_path_2d(x,y,title)\n", " plt.savefig(output_dir + '/snapshot_%05i.png' % step)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![caption](Levy_2d_path.gif)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Path sampling methods implemented\n", "\n", "#### Preliminaries\n", "\n", "***P.1.a*** The following program proposes uniformly distributed configurations in the heliport square (-1 to 1 in $x$, and -1 to 1 in $y$), then accepts these configurations with the mixed harmonic and quartic weight $\\pi(x,y)=\\exp[-0.5 (x^2 + y^2) - \\alpha (x^4 + y^4)]$, for $\\alpha = 0.5$. Also produces a two-dimensional histogram to visualise the data. Note that this is a pure *rejection-sampling* algorithm." ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import random, math, pylab\n", "\n", "alpha = 0.5\n", "nsamples = 1000000\n", "samples_x = []\n", "samples_y = []\n", "for sample in xrange(nsamples):\n", " while True:\n", " x = random.uniform(-1.0, 1.0)\n", " y = random.uniform(-1.0, 1.0)\n", " p = math.exp(-0.5 * (x ** 2 + y ** 2) - alpha * (x ** 4 + y ** 4))\n", " if random.uniform(0.0, 1.0) < p:\n", " break\n", " samples_x.append(x)\n", " samples_y.append(y)\n", "\n", "pylab.hexbin(samples_x, samples_y, gridsize=50, bins=1000)\n", "pylab.axis([-1.0, 1.0, -1.0, 1.0])\n", "cb = pylab.colorbar()\n", "pylab.xlabel('x')\n", "pylab.ylabel('y')\n", "pylab.title('A1_1')\n", "pylab.savefig('plot_A1_1.png')\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***P.1.b*** The same algorithm can be implemented by proposing the random variables with gaussian distribution with a cutoff to restrict into the region $[-1,1]$. Then the algorithm becomes partly rejection-free for the harmonic part of $\\pi(x,y)$. Note that the two programs do not agree for negative values of alpha." ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import random, math, pylab\n", "\n", "def gauss_cut():\n", " while True:\n", " x = random.gauss(0.0, 1.0)\n", " if abs(x) <= 1.0:\n", " return x\n", "\n", "alpha = 0.5\n", "nsamples = 1000000\n", "samples_x = []\n", "samples_y = []\n", "for sample in xrange(nsamples):\n", " while True:\n", " x = gauss_cut()\n", " y = gauss_cut()\n", " p = math.exp(- alpha * (x ** 4 + y ** 4))\n", " if random.uniform(0.0, 1.0) < p:\n", " break\n", " samples_x.append(x)\n", " samples_y.append(y)\n", "\n", "pylab.hexbin(samples_x, samples_y, gridsize=50, bins=1000)\n", "pylab.axis([-1.0, 1.0, -1.0, 1.0])\n", "cb = pylab.colorbar()\n", "pylab.xlabel('x')\n", "pylab.ylabel('y')\n", "pylab.title('A1_2')\n", "pylab.savefig('plot_A1_2.png')\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***P.2.a*** We can break $\\pi(x,y)$ into a product of one dimensional distributions, propose uniform random variables between -1, 1. Note that although a direct-sampling approach is used in the coordinate that is changed, this is now a *Markov-chain sampling* algorithm because the outcome of the move depends on the present configuration." ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import random, math, pylab\n", "\n", "alpha = 0.5\n", "nsteps = 1000000\n", "samples_x = []\n", "samples_y = []\n", "x, y = 0.0, 0.0\n", "for step in range(nsteps):\n", " if step % 2 == 0:\n", " while True:\n", " x = random.uniform(-1.0, 1.0)\n", " p = math.exp(-0.5 * x ** 2 - alpha * x ** 4)\n", " if random.uniform(0.0, 1.0) < p:\n", " break\n", " else:\n", " while True:\n", " y = random.uniform(-1.0, 1.0)\n", " p = math.exp(-0.5 * y ** 2 - alpha * y ** 4)\n", " if random.uniform(0.0, 1.0) < p:\n", " break\n", " samples_x.append(x)\n", " samples_y.append(y)\n", "\n", "pylab.hexbin(samples_x, samples_y, gridsize=50, bins=1000)\n", "pylab.axis([-1.0, 1.0, -1.0, 1.0])\n", "cb = pylab.colorbar()\n", "pylab.xlabel('x')\n", "pylab.ylabel('y')\n", "pylab.title('A2_1')\n", "pylab.savefig('plot_A2_1.png')\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***P.2.a*** Propose gaussian variables as in P.1.b." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import random, math, pylab\n", "\n", "def gauss_cut():\n", " while True:\n", " x = random.gauss(0.0, 1.0)\n", " if abs(x) <= 1.0:\n", " return x\n", "\n", "alpha = 0.5\n", "nsteps = 1000000\n", "samples_x = []\n", "samples_y = []\n", "x, y = 0.0, 0.0\n", "for step in range(nsteps):\n", " if step % 2 == 0:\n", " while True:\n", " x = gauss_cut()\n", " p = math.exp(-alpha * x ** 4)\n", " if random.uniform(0.0, 1.0) < p:\n", " break\n", " else:\n", " while True:\n", " y = gauss_cut()\n", " p = math.exp(-alpha * y ** 4)\n", " if random.uniform(0.0, 1.0) < p:\n", " break\n", " samples_x.append(x)\n", " samples_y.append(y)\n", "\n", "pylab.hexbin(samples_x, samples_y, gridsize=50, bins=1000)\n", "pylab.axis([-1.0, 1.0, -1.0, 1.0])\n", "cb = pylab.colorbar()\n", "pylab.xlabel('x')\n", "pylab.ylabel('y')\n", "pylab.title('A2_2')\n", "pylab.savefig('plot_A2_2.png')\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***P.3.a*** Full-fledged Markov-chain Monte Carlo sampling using Metropolis algorithm:" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import random, math, pylab\n", "\n", "alpha = 0.5\n", "nsteps = 1000000\n", "samples_x = []\n", "samples_y = []\n", "x, y = 0.0, 0.0\n", "for step in range(nsteps):\n", " xnew = random.uniform(-1.0, 1.0)\n", " ynew = random.uniform(-1.0, 1.0)\n", " exp_new = - 0.5 * (xnew ** 2 + ynew ** 2) - alpha * (xnew ** 4 + ynew ** 4)\n", " exp_old = - 0.5 * (x ** 2 + y ** 2) - alpha * (x ** 4 + y ** 4)\n", " #Use the Metropolis algorithm:\n", " if random.uniform(0.0, 1.0) < math.exp(exp_new - exp_old): #the transition rate pi(x_old->x_new)\n", " x = xnew\n", " y = ynew\n", " samples_x.append(x)\n", " samples_y.append(y)\n", "\n", "pylab.hexbin(samples_x, samples_y, gridsize=50, bins=1000)\n", "pylab.axis([-1.0, 1.0, -1.0, 1.0])\n", "cb = pylab.colorbar()\n", "pylab.xlabel('x')\n", "pylab.ylabel('y')\n", "pylab.title('A3_1')\n", "pylab.savefig('plot_A3_1.png')\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***P.3.b*** Again, we can improve the above program by proposing gaussian random variables instead of uniform random variables, hence the Metropolis acceptance rate simplifies." ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import random, math, pylab\n", "\n", "def gauss_cut():\n", " while True:\n", " x = random.gauss(0.0, 1.0)\n", " if abs(x) <= 1.0:\n", " return x\n", "\n", "alpha = 0.5\n", "nsteps = 1000000\n", "samples_x = []\n", "samples_y = []\n", "x, y = 0.0, 0.0\n", "for step in range(nsteps):\n", " xnew = gauss_cut()\n", " ynew = gauss_cut()\n", " exp_new = - alpha * (xnew ** 4 + ynew ** 4)\n", " exp_old = - alpha * (x ** 4 + y ** 4)\n", " #Use the Metropolis algorithm:\n", " if random.uniform(0.0, 1.0) < math.exp(exp_new - exp_old): #the transition rate pi(x_old->x_new)\n", " x = xnew\n", " y = ynew\n", " samples_x.append(x)\n", " samples_y.append(y)\n", "\n", "pylab.hexbin(samples_x, samples_y, gridsize=50, bins=1000)\n", "pylab.axis([-1.0, 1.0, -1.0, 1.0])\n", "cb = pylab.colorbar()\n", "pylab.xlabel('x')\n", "pylab.ylabel('y')\n", "pylab.title('A3_2')\n", "pylab.savefig('plot_A3_2.png')\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Harmonic oscillator\n", "\n", "##### Naive sampling\n", "\n", "The naive algorithm uses the Trotter decomposition formula, hence it is only correct in the limit $\\beta/N \\rightarrow 0$. Although it is slow, it provides a good approximation and constitutes an intuitive starting point. " ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math, random, pylab, os\n", "\n", "def show_path(x, step, title):\n", " fig = pylab.figure(figsize=(6, 10))\n", " pylab.clf()\n", " path = x[:] #Final position is the same as the initial position. \n", " #Note that this notation appends the first element of x as a new element to x \n", " y_axis = range(len(x)) #construct the imaginary time axis\n", " #Plot the paths\n", " pylab.plot(path, y_axis, 'ko-')\n", " pylab.xlabel('$x$', fontsize = 14)\n", " pylab.ylabel('$\\\\tau$', fontsize=14)\n", " pylab.title(title, fontsize=14)\n", " pylab.grid()\n", " pylab.savefig('snapshot_%i.png' % step)\n", "\n", "def rho_free(x, y, beta):\n", " return math.exp(-(x - y) ** 2 / (2.0 * beta))\n", "\n", "beta = 20.0\n", "N = 80\n", "dtau = beta / N\n", "delta = 1.0\n", "n_steps = 4000000\n", "x = [5.0] * N\n", "#show_path(x, 1, 'initial configuration')\n", "data = []\n", "for step in range(n_steps):\n", " k = random.randint(0, N - 1)\n", " knext, kprev = (k + 1) % N, (k - 1) % N\n", " x_new = x[k] + random.uniform(-delta, delta)\n", " old_weight = (rho_free(x[knext], x[k], dtau) *\n", " rho_free(x[k], x[kprev], dtau) *\n", " math.exp(-0.5 * dtau * x[k] ** 2))\n", " new_weight = (rho_free(x[knext], x_new, dtau) *\n", " rho_free(x_new, x[kprev], dtau) *\n", " math.exp(-0.5 * dtau * x_new ** 2))\n", " if random.uniform(0.0, 1.0) < new_weight / old_weight:\n", " x[k] = x_new\n", " if step % N == 0:\n", " k = random.randint(0, N - 1)\n", " data.append(x[k])\n", " \n", "#Write the final path configuration on a file:\n", "filename = 'naive_harmonic_path_configuration_N%i.txt' % N\n", "f = open(filename, 'w')\n", "for i in range(N):\n", " f.write(str(x[i])+ '\\n')\n", "f.close()\n", "\n", "show_path(x, step, 'Naive harmonic path final configuration, N = %i' %N)\n", "pylab.show()\n", "\n", "pylab.clf()\n", "fig = pylab.figure(figsize=(7, 5))\n", "pylab.hist(data, normed=True, bins=100, label='QMC')\n", "list_x = [0.1 * a for a in range (-30, 31)]\n", "list_y = [math.sqrt(math.tanh(beta / 2.0)) / math.sqrt(math.pi) * \\\n", " math.exp(-x ** 2 * math.tanh(beta / 2.0)) for x in list_x]\n", "pylab.plot(list_x, list_y, label='analytic')\n", "pylab.legend()\n", "pylab.xlabel('$x$')\n", "pylab.ylabel('$\\\\pi(x)$ (normalized)')\n", "pylab.title('naive_harmonic_path (beta=%s, N=%i)' % (beta, N))\n", "pylab.xlim(-2, 2)\n", "pylab.savefig('plot_B1_beta%s.png' % beta)\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Lévy sampling\n", "\n", "The Lévy algorithm for the harmonic oscillator paths is exact, it uses no approximation." ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math, random, pylab, os\n", "\n", "def show_path(x, step, title):\n", " fig = pylab.figure(figsize=(6, 10))\n", " pylab.clf()\n", " path = x[:] #Final position is the same as the initial position. \n", " #Note that this notation appends the first element of x as a new element to x \n", " y_axis = range(len(x)) #construct the imaginary time axis\n", " #Plot the paths\n", " pylab.plot(path, y_axis, 'ko-')\n", " pylab.xlabel('$x$', fontsize = 14)\n", " pylab.ylabel('$\\\\tau$', fontsize=14)\n", " pylab.title(title, fontsize=14)\n", " pylab.grid()\n", " pylab.savefig('levy_snapshot_%i.png' % step)\n", " \n", "def levy_harmonic_path(xstart, xend, dtau, N):\n", " x = [xstart]\n", " for k in range(1, N):\n", " dtau_prime = (N - k) * dtau\n", " Ups1 = 1.0 / math.tanh(dtau) + \\\n", " 1.0 / math.tanh(dtau_prime)\n", " Ups2 = x[k - 1] / math.sinh(dtau) + \\\n", " xend / math.sinh(dtau_prime)\n", " x.append(random.gauss(Ups2 / Ups1, \\\n", " 1.0 / math.sqrt(Ups1)))\n", " return x\n", "\n", "beta = 20.0\n", "N = 80\n", "dtau = beta / N\n", "delta = 1.0\n", "n_steps = 40000\n", "x = [5.0] * N\n", "data = []\n", "for step in range(n_steps):\n", " Ncut = N/2\n", " x = x[Ncut:] + x[:Ncut] #slices the x data from the middle and swaps the two parts, hence x[0] changes\n", " x = levy_harmonic_path(x[0], x[0], dtau, N)\n", " k = random.randint(0, N - 1) \n", " data.append(x[k])\n", " \n", "#Write the final path configuration on a file:\n", "filename = 'levy_harmonic_path_configuration_levy_N%i.txt' % N\n", "f = open(filename, 'w')\n", "for i in range(N):\n", " f.write(str(x[i])+ '\\n')\n", "f.close()\n", "\n", "show_path(x, step, 'Levy harmonic final configuration, N = %i' %N)\n", "pylab.show()\n", "\n", "pylab.clf()\n", "fig = pylab.figure(figsize=(7, 5))\n", "pylab.hist(data, normed=True, bins=100, label='QMC')\n", "list_x = [0.1 * a for a in range (-30, 31)]\n", "list_y = [math.sqrt(math.tanh(beta / 2.0)) / math.sqrt(math.pi) * \\\n", " math.exp(-x ** 2 * math.tanh(beta / 2.0)) for x in list_x]\n", "pylab.plot(list_x, list_y, label='analytic')\n", "pylab.legend()\n", "pylab.xlabel('$x$')\n", "pylab.ylabel('$\\\\pi(x)$ (normalized)')\n", "pylab.title('levy_harmonic_path (beta=%s, N=%i)' % (beta, N))\n", "pylab.xlim(-2, 2)\n", "pylab.savefig('plot_B2_beta%s.png' % beta)\n", "pylab.show()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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+rFmzhnPOOcftGFExZcoUpk+fzhtvvJFv+8zu9yUiS1W1fqT7si5TY4wxUde/f38+/PBDZs+enfvGLrGCaIwxJupGjhzpdoRc2TFEY4wxBiuIxhhjDGAF0RhjjAHsGKIx8U8VMvZBkRIRPc1GnhpzNGshGhNvVOGP9bDkVZjyT3imBjxVCf7XAD64B75/H/bZ0mjmxKSnp9OlSxeqV6/OWWedRb9+/Th8+DDz5s1DRHj55ZePbLt8+XJEhOHDhx+5b/jw4dSsWZPzzjuP2rVr8/rrr7vxNiJiLURjCjpV2LkBNi6AjV86P/ducx4rXgGqtoCy1WHLEvj2XVgS+qAqVxNSm0NqM8pwkJ2UdO89mOOWXUv+ROSlF0BVufLKK+nbty/Tp08nEAjQu3dv7r//frp27cr555/PpEmTuPXWWwFnsu7atWsfef6YMWOYO3cu33zzDSVLlmT37t1MmzYtX99HNFhBNKag2vsrfPYY/PQ57Nni3FesPFR1ihypLaBsNQif7zHgh20rnML585ew4m1YPI5lRWFtsDJzgg0Y5b8Cn/3XN8fw2WefUbRoUW655RbAmbf0ueee48wzz6Rt27ZUqVKFPXv28Ntvv1G+fHnmzJlD+/btjzz/ySef5PPPP6dkSedLWKlSpbjppptceS+RsP8VxhREP30G7/eGw3uhxuV/FcBTqx9dALPyJkGl+s6l2f9BwAdblzNszHiaer7nX0nvc4lnBf19/dmkp8Xu/Zi4smrVKurVq3fUfSVLliQ1NZX169cD0K1bNyZPnkydOnWoW7cuRYoUAZy1D/fu3Uu1atVinvtEWUE0piAJ+OHzJ2DBc1CuBtw0E8pnP41XngbFeJOhckNGB7YzOtCFywLfMCx5LB+kPMhAXy9mBY89R6VJTDmtNBE+1efVV19Njx49WLt2LT179mTRokXHfG48sEE1xhQUu9NZ/J8msOBZ3vG3pObmB0h9dkO+vsRHwYZ0yHiKn7Qio1Je4ImklylCxpHHUwfMyvZiEkutWrXIOk90ZhdpjRo1AKhQoQLJycnMnTv3qNXsS5YsSbFixdiwIX//dmPBCqIxBcHa2TCmGefIJu7KuJOB/l4cokhUXipdy9E94xHG+DtxXdKnTEsZRDXZEpXXMvGpdevWHDhw4MjI0EAgwL333ku/fv2OWtV+yJAh/Pe//8Xr9R71/IEDB3LnnXeyZ88ewCmmY8eOjd0bOE7WZWqMm/wZ8MmjkDYaKlxAx103sVFPP2qTaLTQ/CQx1N+TtOA5PJP8IjNTHmaQ7xbeC7bI99cy8UdEmDp1KnfeeSePPfYY27dvp0ePHjz00EPMmzfvyHZNmzbN9vl9+/Zl3759NGjQgOTkZJKTk7n33ntjlP742fJPxrhl5wbnPMKty6Hh7XDpY6Q+/MkJ7TKnIfXHKqrl+ZPnk0fRxLua9wLNGeS7hQMUzdN+Tf4riMs/LVq0iJ49e/L+++//bbCN22z5J2Pi3erpMO1O8Higx1twTkfXovzOKVzne5D+wancnfQ+F6asp6/vX/yolV3LZAqWpk2b8ssvv7gdI+rsGKIxsbZuLky+2RlF2meBq8UwUxAPzweu4lrfQ5SQg7yV8iRn8IfbsYyJKWshGhNl4d2VZ8tm3ksZTInTa8GN06FIcReT/V1a8Fyuy3iQ91Ie5eWU4XTLeJT9nJT7E40pBKwgGhMjZdnNKylPc4AilOg5KSrFMD8G4KzTSvTz3cWrycMYkTyK23335EMyE4l4PpcvlvJ7DIwVRGNioAgZvJTyHGXZw9UZj/DdUyuAFW7HytH8YG0G+2/iseTXeEDfATq5HSlhFC1alB07dlC2bFkrisegquzYsYOiRYvmvnEeWUE0JuqUocnjqO/5kb4Zd/OdnuV2oDx5I3Ap1WQrtyfNgqUToF7Bn4uyMKhUqRLp6els324rluSmaNGiVKpUKd/2ZwXRmCjr551GV+9Chvmu5sNgI7fjROQx/w1UlV+5eNY9UKaqs7KGiark5GSqVq3qdoyEZKNMjYmm79/nvuTJvBdoxuhAF7fTRCyAl36+u6DsP2DSDc46jMYUUlYQjYmW9KUwrS+Lg2cz0NcLiM/jQXs5mWbpfdhxMMCGFzpQe8Akm9/UFEpWEI2Jhl2b4Z1roPhp3J5xDxkku53ohKRreXpn3ENF+YMXk0eQjN/tSMbkOyuIxuS3w/vgnZ7gPwTXvltoVqpfqjV4wNebpt7VDEl6FeJ42kdjsmMF0Zj8FAzA+73g91XQ/VUoX9PtRPlqWrAZI/1X0DPpc/hqlNtxjMlXNsrUmOOQ0zG0jW2XwQ+zof1w+EebGKeKjWf93ThLtnL5Rw9z8wd7mB+sfdTjNhG4iVfWQjQmn9SSn2HBs3Dh9dCwl9txokbxcK+vL+v1DJ5KHk8xDrodyZh8YQXRmHyQhJ9hyWOhWDm47Am340TdIYowwNeL09nJfUnvuh3HmHxhBdGYfHCr90NqeX5xukpPKu12nJhYpmfzeqAtN3k/po6sczuOMScsZscQRaQd8DzgBcar6tAsj98MPA1sCd31P1UdH6t8xuQkt3PuzpRf+b+kKcwJNKDP614gcc7Re9rfg0u9S3gqeTydMp7AZ8MSTByLSQtRRLzAKOBy4Fygp4icm82mk1T1wtDFiqGJA8qTSS+TQRKP+G52O0zM7eckHvb9k5qezdzunel2HGNOSKy6TBsC61V1g6pmABOB+JvHypgsunu/4CLvKob6r+V3TnE7jis+C9ZlZqAx/ZOmUk225P4EYwqoWBXEisDmsNvpofuyukpEvhWRKSJSOTbRjDk+p7Kbh5Le4utgTd4JXOJ2HFf9x3cTBynCk8kvQzDodhxjjkusCmJ2kzhmneZiJpCqqhcAnwATst2RSG8RWSIiS2x5FOOmR5MncBKHedB3K5rg49P+oBRP+K+jkWctLHvN7TjGHJdY/S9OB8JbfJWAreEbqOoOVT0cujkOqJfdjlR1rKrWV9X65cqVi0pYY3LTyrOMTt40Rvq78pNm19mReCYHLmZhoBbMfRT2bM39CcYUMLEqiIuB6iJSVURSgGuAGeEbiMjpYTc7A2tilM2YiBTjII8nv8LaYGVeCthK8n8RBvpvg0AGzP6322GMiVhMCqKq+oF+wEc4he5dVV0lIkNEpHNos7tEZJWIrATuAm6ORTZjIvXvpElU4E8G+HrZaQZZbNLT4JIHYe0HsHpG7k8wpgCJ2f9mVZ0NzM5y3yNh1wcCA2OVx5jjUVd+5EbvXCYELmWF/sPtOAVStZlVmZ6SSvlJ/Wlz+BB7KGbzm5q4kNgjAYyJQDJ+hiaPYytlGe6/2u04BVYALw/4elGGPQxIesftOMbkmRVEY/Kor3cGZ3u28LDvn+znJLfjFGirtCrjA+25NukzGokNBzDxwQqiMXlQTbZwZ9I0pgeaMi94odtx4sII/1X8EizPU8njwHfI7TjG5MoKojF58GDS2xwihSG+G9yOEjcOUYSH/LdyludXWDzO7TjG5MoKojG5aCRraO1dzmh/F3ZQyu04cWVB8HzmBWrD/OFwcJfbcYw5JiuIxhyLKgOS32GbluG1wGVup4lL//VfA4d2w8IRbkcx5pisIBpzLGtmUseznmf93ThMittp4tIaPRMuuBrSXrQZbEyBZgXRmJwE/PDpEH4MVuT9QHO308S3Sx4CDcK8oblva4xLrCAak5MVb8KOdQzzX0MAr9tp4tspZ0KD22D5G7D9R7fTGJMtm3fKmOxkHIDPn4LKjflkXV2308S91AGzOIULmF+kCAtfuIM+vv8DsBlsTIFiLURjsvP1i7DvV2gzmOxXLzOR+pOSvOTvSDvvYuqKtRJNwWMtRGNCUgfMAqA0e5lf5Gm+Dtaj14s7XU5VuLwcuJybkj7mgeSJ9MgY5HYcY45iLURjsrgzaTrFOMQwfw+3oxQ6BynKCP9VNPKspZVnudtxjDmKFURjwlRkOzd6P2ZK4GLWaSW34xRKkwIt2RCswANJEyEYcDuOMUdYQTQmzD3JU1CEEf6r3I5SaPlJ4ml/D2p40mHlRLfjGHOEFURjQmrKJrp6FvBaoB3bKOt2nELtw2BDVgSrwedPgO+g23GMAawgGnPE/UkT2ctJjPZ3cjtKAhBnSrc9W+Abm/jbFAxWEI0B2LiAVt4VjPZ3YQ/F3U6TEL4K1oJ/tIEvn7GJv02BYKddmISUeYqFQ5ma8igVxCbwjrk2g2FMc2fi7zaD3c1iEp61EE3Cu8yz2CbwdkuF823ib1NgWEE0Cc1LgPuTJtkE3i5JHTCLZoubctjnZ+Kwvlla7sbElhVEk9C6ehdQzbON4f6rbQJvl6RrOd4KtKGbdz5V5De345gEZgXRJCwPQe7wTmdV8Ew+DtZ3O05Ce9HfiQBe+npnuB3FJDAriCZhdfSkcZbnV0b6u2ITeLtrO6cwMdCSq7zzYddmt+OYBGUF0SQkIcidSdP4IViJj6x1WCCM8Xd2riwc4W4Qk7DstAtTqOU0SOMyzxJqeNK5K6Mfat8LC4RtlGVKoAXXLnsDmt8HJU93O5JJMPZJYBKQ0j9pGhuCFfgg2NjtMCbMi4HOEPTDopFuRzEJyAqiSTitPMs5z7OR0YEuBO2/QIGyWU9zzktc8grs2+52HJNg7NPAJBindbg5WI5pgYvcDmOy0/xe8B+CtFFuJzEJxgqiSSjNPN9Tx7OeFwOd8dsh9ILp1OpQq6sz6feBnW6nMQnECqJJKP2TprJVyzAl0MLtKOZYWtwHGfvg6zFuJzEJxAqiSRgNZQ2NPGt5yd+JDJLdjmOO5bRaULOjUxAP7XY7jUkQVhBNwuifNJXtWoqJgUvcjmLyosV9TjG09RJNjFhBNAmhjqyjufd7xvo72IoW8eKMOlD9UvhqFBze53YakwCsIJqE0C9pGju1OG8F2rgdxUSixf1wcCcsfdXtJCYBxKwgikg7EflBRNaLyIBjbNdNRFREbD4tky9qyc+09i5nvL89ByjqdhwTicoN4KyWsPAF8B10O40p5CIuiCJSTEQiWicntP0o4HLgXKCniJybzXYlgLuAryPNZUxO+idNY7eezBuBS92OYo5Hi3/D/t9h2etuJzGFXK4nYomIB7gGuA5oABwGiojIdmA2MFZV1+Wym4bAelXdENrnRKALsDrLdo8Bw4D7InkTxuTkbNlMO+9invdfyV5OdjuOyYPs5p+dlFKTRgufh3o3Q1KR2IcyCSEvLcTPgWrAQKCCqlZW1fJAcyANGCoi1+eyj4pA+Jou6aH7jhCROkBlVf0gr+GNyU2/pGns06K84m/ndhRzAkb6u8KeLQx8dCCpA2YduRiTn/IyVUcbVfVlvVNVdwLvAe+JSG4ndWW32JweedBphT4H3JxbGBHpDfQGqFKlSm6bm0T2xzo6etJ4KdCR3RR3O405AQuC57EiWI07vDOYHLjYZhkyUZGXv6r+Ijkvnqqqz2ZXMLNIByqH3a4EbA27XQI4D5gXeq0KwAwR6ayqS7K83lhgLED9+vUVY3Ly5bMcJpnx/vZuJzEnTHjB35VXUobTxbOI94I205DJf3npMi0RutQH+uJ0dVYE+uAMkMmLxUB1EakqIik4xyRnZD6oqrtV9VRVTVXVVJyu2L8VQ2PybNcm+HYSbwdas4NSbqcx+eCzYB2+D6ZyR9J0hKDbcUwhlGsLUVX/AyAiHwN1VXVv6PZgYHJeXkRV/SLSD/gI8AKvqOoqERkCLFHVGcfegzG5Cz+m9GjSBK7zwjhrHRYiwhh/J/6XMpK2nqV8HGzgdiBTyETSEV8FyAi7nQGk5vXJqjobZ1Rq+H2P5LBtywhyGXOU0uylh3ce0wMX8Stl3Y5j8tGHwYb8EixPn6SZfJxhpyqb/BXJeYhvAN+IyGAReRTnXEE7McgUODd5P+ZkOcyYQCe3o5h8FsDLuEAH6nrW01DWuh3HFDJ5Loiq+gRwC/AnsAu4RVWfjFYwY47HSRzipqSPmBuox09aMfcnmLgzOXAxf2hJ+iTNdDuKKWTyXBDFGf55LlBKVZ8HdohIw6glM+Y4XO39gjKyjzH+jm5HMVFymBRe819GK+8K+G2V23FMIRJJl+looAnQM3R7L850bMYUCEn46ZU0i8UV5UNxAAAgAElEQVTBs1mqNdyOY6LojUBb9msRWPi821FMIRJJQWykqncChwBU9U+wdXRMwdHBk0Yl+YMxfjt2WNjtpjjvBFrBd1OcU2yMyQeRFERfaJJuBRCRcmAnA5kCQpU+SR/wY7AinwXruJ3GxMDL/vYg4qyXaEw+iKQgvgBMBcqLyBPAAsAG1ZiCYf0nnOPZxEv+Tqgt85kQtlEWzr/aWQXjwE6345hCIJJRpm8B9wNPAduAK1Q1TyfmGxN1C0awVcswI9jU7SQmli66G3wH4JuxbicxhUBEM+Sq6lrATv4xBUv6EvhlAS/7r8dnkz4nlvI14ezL4euXoGl/SCnmdiITxyI57eJTEWmf5T77Wmbct+A5KFraGWRhEkrqgFlc9V1DOLiTR/8z0JaEMickkoMtVYEHQrPUZLK5k4y7/lgHa2dBw14coKjbaYwLlmoNFgfPplfSLJLwux3HxLFICuIuoDVwmojMFBFbQsC4b+HzzgrqDW93O4lx0Rh/JyrJH3TwpLkdxcSxSAqiqKpfVe/AWRh4AVA+OrGMyYM92+DbSVDneihezu00xkWfBevwY7AifZI+ALVlUs3xiaQgvph5RVVfA27CWc7JGHekjYagH5r0czuJcZni4SV/J87xbIL1n7gdx8SpXAuiiCwIXX1GRPZkXoAvgO5RTWdMTg7ugiWvQq2uUKaq22lMATAj2JStWgYWjHA7iolTuRZEVW0W+llCVUuGXUqoasnoRzQmG0tegYy9znloxgA+kpzZa35Z4JyKY0yE7KQtE3dqDJjKgiIjWBM8nxufTwfS3Y5kCoh3Aq0YVOID51Sca95yO46JM3npMt0b6ibdm81lTyxCGhPuSu+XlJPdtgCw+ZsDFIUGtzmn4vyxzu04Js7kpcu0RFgXadaLdZma2AoG6OWdxbfBqiwK1nI7jSmIGvVxTsWxpaFMhCKaBVlEThGRhiLSIvMSrWDGZGvtB5zl+TW0xJO4ncYURMXLwYXXOafk7P3V7TQmjkQyddttwHycUy3+E/o5ODqxjMmGKiwYwcbgacwJNnQ7jSnImvZzTslJezH3bY0JiWRQzd1AAyBNVS8RkZo4hdGY2Ni4ALYuY1zgnwRtiSeTg8z5TP+X3JAWC17iok/PYy8ns3FoB5eTmYIukk+VQ6p6CEBEioRWvqgRnVjGZGPh81CsHFMC1lNvcjfG35GScpCe3k/djmLiRCQFMV1ESgPTgLkiMh3YGp1YxmTx6/ewfi40up3DpLidxsSB7/UsFgRqcWvSh6TgczuOiQORLBDcVVV3qepgYBDwMnBFtIIZc5RFL0ByMWdIvTF5NCbQmdNkF128C92OYuLAcR2IUdUvVHWGqmbkdyBj/mbXJvhuCtS7GU46xe00Jo4sCJ7H98FU+nhnQjDodhxTwEUyyrS+iEwVkWUi8m3mJZrhjAHgq9EgAk3ucDuJiTvCS/6OVPNsgx8/dDuMKeAiaSG+BbwKXAV0CrsYEz0HdsKyCXB+dyhVye00Jg7NDjZiU7CcM+m3LQ1ljiGSgrg91E36s6r+knmJWjJjABaPB98BaHqX20lMnArgZVygA6R/A5tsAWGTs0gK4qMiMl5EeorIlZmXqCUzJuMAfD0Gql8Gp53rdhoTxyYHLoaTy8JCWxrK5CySE/NvAWoCyUDm0WkF3s/vUMYAsOItOLADmv3L7SQmzh2iCDS8HeY9Cb+vgfLnuB3JFECRFMTaqnp+1JIYEy7gh0UjoVIDqNLE7TSmMGjYy2khLnwButqUbubvIukyTRMR67cysbFmOuz6BS76lzPC1JgTdXIZqHsjfPcu7N7idhpTAEVSEJsBK0Tkh9ApF9/ZaRcmKkKTeFO2OtRo73YaU0ikDphFs/nn4A8EGff0fUfmPDUmU566TEVEgNsBG1Vqom/DPPj1W+g8Ejw2ibfJP+lajpnBJvT0fsZIv020ZY6Wp08bVVXgufDTLSI97UJE2oVal+tFZEA2j/cJtTpXiMgC655NYAtHQPEKcEEPt5OYQuglfyeKyyGu937idhRTwEQyqCZNRBqo6uJIX0REvMAooC2QDiwWkRmqujpss7dVdUxo+87As0C7SF/LxK/UAbOoJT8zq8g8nvL15KWH7QPL5L+1WoV5gdrckjQHfIcguajbkUwBEUl/1CU4RfGn4ziG2BBYr6obQvOfTgS6hG+gqnvCbhbDOaXDJJg+STPZoyfxdqC121FMITYm0IlysgdWvu12FFOARNJCvPwEXqcisDnsdjrQKOtGInIncA+QArTKbkci0hvoDVClSpUTiGQKmiryG+09XzMu0JG9nOx2HFOIpQXPYUXwLC5cNBLq3gQer9uRTAEQyfJPvwCl+WsO09IRHEPMbtz831qAqjpKVasBDwAP55BjrKrWV9X65cqVy+PLm3jQ2/sBfry84reechNtwhh/Z9i5AVZPdzuMKSDy3EIUkbuBXvw1M82bIjJWVUfm4enpQOWw25U49uLCEwE7czaR7P2V7t4veC/Qgt+xJZ5M9H0crM9PwdM5/O5g2r+ZQvj39o1DO7gXzLgmkmOItwKNVPURVX0EaIxTIPNiMVBdRKqKSApwDTAjfAMRqR52swOwLoJsJt4tGkkSAV4M2AIqJjaCeBjt78K5nl+4xLPC7TimAIikIAoQCLsdIPuu0L9RVT/QD/gIWAO8q6qrRGRIaEQpQD8RWSUiK3COI94UQTYTzw7shCWvMiPYlM16mttpTAKZHmxKup5Kv6Rp2Dg+E8mgmleBr0Vkauj2FcDLeX2yqs4GZme575Gw63dHkMUUJmkvgm8/o/1dct/WmHzkJ4kx/k48nvwqTTyr+SpYy+1IxkWRDKp5FmfFi53An8AtqmprqZgTc2gPfPMS1OzIOrUFgE3sTQ5czO9amju8Nrgm0UU0L5aqLlPVF1T1eVVdHq1QJoEseRkO7Ybm97qdxCSow6Qwzt+e5t7vqS3r3Y5jXJTngigiRUTkWhF5UEQeybxEM5wp5HwH4atRUK0VVKzrdhqTwN4OtGaXFqNfkrUSE1kkLcTpOLPL+IH9YRdjjs+y12H/dmh+n9tJTILbz0m86m9HW+9Sasgmt+MYl0QyqKaSqtoZ0yZ/+DOchVqrNIHUi9xOYwyvBS6jV9Is7kiaAfR1O45xQSQtxEUicn7UkpjE8u0k2JNuxw5NgbGb4rwZaENHz1ew4ye34xgXRLpA8FJbINicsGAAFjwHp9eGf7RxO40xR7zsb4+fJOfv0yScWE3ubcxfVk2FnT/B1a+D5GluB2NiYjulmRhoyU0rJ0LLAVDKTgVKJLm2EEWcT6zsFgfOnNw7cxtjcqUKXz4Lp54NNW2aNlPwjPV3BBQW5WWaZlOY5KXL9HMR6S8iR621JCIpItJKRCZg06yZvPpxDvy+CprdA56IToM1Jia2UA4u6AFLJ8C+7W7HMTGUl0+kdjjzlr4jIltFZLWIbMCZfLsn8JyqvhbFjKawUIX5w6F0FTi/m9tpjMlZs/8D/yFIG+V2EhNDuR5DVNVDwGhgtIgkA6cCB1V1V7TDmULm5/mwZQkP+f7JWw997HYaY3J2anWodQV8Mx4u+hecVNrtRCYGIp26zaeq26wYmuPy5XAoXoEpgRZuJzEmd83vhYy98M04t5OYGLGDOCY2Ni92WohN+3GYFLfTGJO7CudD9csgbTQc3ud2GhMDVhBNbHw5HE46Berd4nYSY/KuxX1wcCcsfc3tJCYGIi6IIlJMRLzRCGMKqW3fOqNLG98BRYq7ncaYvKvcEFKbO6dg+A66ncZEWV7OQ/SEVrmYJSK/A2uBbaHV7Z8WkerRj2ni2rynoEgpaNjL7STGRO7i+2Hfr7DkVbeTmCjL03mIQDVgIFBBVSuranmgOZAGDBWR66OY0cSzLUvhh9nQtL/TZWpMvKnawrkseBYybIGfwiwvU7e1UVVf1jtVdSfwHvBe6HQMY/7u8yfhpDLQuI/bSYzJs9QBs466XVda8X6R+c6I02b/cimVibZcW4iZxVBERuQ0RVt2BdMYNqXB+k/goruhSAm30xhz3Jbp2c5E9AtHwKE9bscxURLJoJp9wAwRKQYgIpeKyMLoxDKFwmePQ7HyduzQFA6XPAQH/4Svx7idxERJnguiqj4MvAPME5EFwL3AgGgFM3Fuwxew8Utofg+kFHM7jTEnrmJdqNEBFv3PKYym0MlzQRSR1kAvYD9QDrhLVb+MVjATx1Th8yegxBl23qEpXC55EA7vdoqiKXQiWQ/xIWCQqi4QkfOBSSJyj6p+FqVsJo6ED0K42LOSCSlf85DvnzyRXNTFVMbkswrnQa2uTrdp4zugWFm3E5l8FMl6iK1UdUHo+nc4CwY/Fr6NMaDckzSZzcFyvBto6XYYY/Jfy4HgO+AMsDGFynGvhwjswDkH0dZDNEe09SyltmcDLwS64ouoA8KYOFGuBpzf3TkFY+9vbqcx+ehE10PsjK2HaEKEIPckTeHn4Gm8H2judhxjoufiByCQ4ZysbwqNPK+HKCJvAIew9RBNDi73fMM5nk3cnXEHAWy6W1O4ZD1Zf2hSc7qmjadI0/5QqpJLqUx+iqRPaxnQBfhRVf0AInK2qv4YlWQmrngI8n9J7/FjsCIzg02P3J/1Q8SYwmKkvytXer+E+cOhkx1PLAwiOTG/DDAK2Cwi34nIu8Ds6MQy8aazZxHVPVt4zt+NoK0qZhLAFsoxMdAKlr8Bf250O47JB5F8cm1S1UtU9XScEabjgJujksrEl4CPu5PeY3XwTOYEG7idxpiYGeXvAuKFL552O4rJB5EUxFIi0lRESqlquqrOzTwNwyS4le9Q1fMbz/i7odY6NAnkN8pAg9tg5dvwx3q345gTFMmnV3HgPuAbEdkoIh+KiH0tSnT+DPjiaVYEq/FpsK7baYyJuXrzzuNAMJlpz/cndcAsO24exyIpiE1U9UpVrQHUxJm55tvoxDJxY/nrsHsTz/q7ATY/g0k8OyjFhMCldPZ8RXVJdzuOOQGRTO79U9j1Q6q6TFXfyOvzRaSdiPwgIutF5G+TgovIPaFzHL8VkU9F5My87tu4JOOAM8KuShPmBy9wO40xrnnJ35H9FOXepMluRzEnICYHfETEizNC9XLgXKCniJybZbPlQH1VvQCYAgyLRTZzAhaNhL3boPUjWOvQJLJdlGCsvwPtvItpKGvcjmOOU6xGQDQE1qvqBlXNACbinNN4hKp+rqoHQjfTADvTtSDbs9WZy/HcLnBm09y3N6aQGxfowFYtw8PJb0Iw6HYccxxiVRArApvDbqeH7svJrcCHUU1kTsynj0HQD23+43YSYwqEQxThv75ruMDzM3w70e045jjEqiBm15+m2W4ocj1QH8h2BKuI9BaRJSKyZPv27fkY0eTZ1uXOMPPGfaFMVbfTGFNgzAg2ZUWwGnw6BDL2ux3HRChWBTEdqBx2uxKwNetGItIGZ/RqZ1U9nN2OVHWsqtZX1frlypWLSlhzDKp8PaYPf2hJzvv0fBtmbkwYxcMQ3w3OsfWFz7sdx0QoVgVxMVBdRKqKSApwDTAjfAMRqQO8hFMMf49RLhOp1dNp5FnLM/7u7ONkt9MYU+As07PhvKtg4Quw207DiCcxKYihycD7AR8Ba4B3VXWViAwRkc6hzZ7GOfl/soisEJEZOezOuMV3COY+wppgZSYFLnE7jTEFV5vBgMIndow9nsRsBVdVnU2WycBV9ZGw621ilcUcp6/HwK5feNw/0CbwNuZYSleBJnfCl89Aoz5QqZ7biUwe2KeayZt9252T8M9ux8Lg+W6nMabga/Z/UPw0+GggaLZjCE0BYwXR5M3nT4D/IFz6uNtJjIkPRUpAq4dh89ew6n2305g8sIJocvfbKlg2ARr0glOru53GmPhx4XVQ4XyY+yj4DrqdxuTCCqI5NlX46EEoUhIuvt/tNMbEF48XLnsKdm+Gr0a5ncbkwgqiObYfP4IN86DlQDi5jNtpjIk/VZtDzY6w4DnY+5vbacwxWEE0OQv44OOHoWx1aHCr22mMiV9th4D/MHz2mNtJzDHE7LQLE4cWvww71kHPSeBNdjuNMfGrbDVodDvBRaPomHYOqzX1yEMbh3ZwL5c5irUQTfYO7IR5T8FZLeHsy9xOY0z8a/FvdlGMQUlvksNUzsZlVhBN9uYNhcN74LInQWytQ2NO2EmledbfnSbe1VzmWeJ2GpMNK4jm77YshcXjoN4tcFott9MYU2i8E2jF2mBlHk2eQHEO5P4EE1N2DNEczZ8B0/tD8dM4f0ET9i6wlSyMiVTOK8B4GeDrxfspj/JA0kQG+f8Z01zm2KyFaI628Hn4fRV0eJa9tpqFMfluhf6DVwPtuCHpExrIWrfjmDBWEM1ftv8A84dBra5Qs73baYwptIb7u7M5WI6hyeOcVWRMgWAF0TiCQZhxFySfDJcPczuNMYXaQYryoP9Wqnm2OV9CTYFgBdE4lrwMm9Og3VAoXt7tNMYUel8GL2Cyv4VzmOLX79yOYwDROF6WpH79+rpkiQ1fPmG7NrPvufosC1bnRt8AwE6zMCYWSrGPlWUfhpJnwG2fgtfGOeYHEVmqqvUjfZ61EBOdKsy6B0F50H8bVgyNiZ3dFIf2w2DbCkgb7XachGcFMdF9NwXWfcxw/9Wkazm30xiTeM69Amp0gM+fhJ0b3E6T0KwgJrL9O2DOA1CxPhMCNj2bMa4QgQ7DnfmCZ97t9NoYV1hBTGRzBsChPdDlfwTtT8EY95Q8w1kR4+f5sPwNt9MkLDuCm6h+/Bi+excuHgDlzwGsq8YYN2TOaiOcyjsp53Du9Aco+Y+2UPJ0l5MlHmsWJKLDe+GD/4NyNaH5PW6nMcYAiocBvttIwQez73M7TkKygpiIPvkP7NkCnUdCUhG30xhjQjbq6YzwXwVrP4DV092Ok3CsICaaTWmweDw06gOVG7qdxhiTxbhABzi9Nsy6z1mX1MSMHUNMJAd2wnu9oHRlaPWw22mMMdkI4KX9xh5MSxnEvKe60dt3D5nnB28c2sHdcIWcFcREoQrT7yRj1xa6ZQzm20e/cDuRMSYHqzWVof5reST5DW4NfsjLAZtsPxasyzRRfPU/+GE2T/qv41ut5nYaY0wuXgm0Y06gAQOS3qGOrHM7TkKwgpgINn8DnwyGczrzmp2Ab0ycEO739WablmFkykhKsc/tQIWeFcTC7sBOmHwLlKoEXf6HzVVqTPzYQzHu9N1NOXbxTPKLzjJtJmqsIBZmwSBMvR32/w7dJ0DRUm4nMsZE6Ds9iyf819HGuxy+Gul2nELNCmJhtuh5WPcxXPYknHGh22mMMcfp9cClfBBo5JxDvCnN7TiFlo0yLax++Qo+fQxqXQkNbnM7jTHmhAgDfb04TzZS5OWetD/8JH9SErBTMfKTtRALo/1/wJRb4JRU6PS8M5u+MSau7eVk7vTdTRn28lzyiwh2PDG/WQuxsAkG4f3ecGAn7Q/0Z/XgL91OZIzJJ6s0lSH+G3gi+RX6BmcyOtDF7UiFirUQC5sFz8BPn8LlQ1mtqW6nMcbks7cCrZkZaMy9Se/SUNa4HadQiVlBFJF2IvKDiKwXkQHZPN5CRJaJiF9EusUqV6Hy85fOqtvndYN6t7idxhgTFcJA3238oqcxMmUk7NvudqBCIyYFUUS8wCjgcuBcoKeInJtls03AzcDbschU6Oz9Dd67FcqcBZ1G2HFDYwqxfaHjiaXYD+/3goDf7UiFQqxaiA2B9aq6QVUzgInAUZ3fqrpRVb8FO1IcsUN74K2rnHUOu0+AIiXcTmSMibI1eiaD/LfAhs9h1v858xWbExKrQTUVgc1ht9OBRjF67cLNfxgmXYdv22pu893HFyN+AX5xO5UxJgYmB1rydOtSMP9pKF4BWj3kdqS4FquCmF3/3XF9nRGR3kBvgCpVqpxIpviXORPNz/P5t+8OvgjWdjuRMSbWLnkI9v0G84dB8fLQsJfbieJWrLpM04HKYbcrAVuPZ0eqOlZV66tq/XLlyuVLuLikCnMegFVT4dLHmRZs5nYiY4wLUgfOptqitswN1CM469/0ffARUgfMcjtWXIpVQVwMVBeRqiKSAlwDzIjRaxdOXz4D34yFJv2gaX+30xhjXBTASz9ff5ZqdUYkj6KJZ5XbkeJSTAqiqvqBfsBHwBrgXVVdJSJDRKQzgIg0EJF0oDvwkojYv2hOlr0Onz0GF/SAto+5ncYYUwAcJoXbMu5jo1ZgbPKzsO1btyPFnZidh6iqs1X1bFWtpqpPhO57RFVnhK4vVtVKqlpMVcuqaq1YZYsra2fDzLuhWmvoMgo8NreCMcaxm+LclPEAezgZ3uoGO392O1JcsU/TeLIpzZmj9PQL4erXwZvsdiJjTAHzK2W5MWMABDLgzSvtxP0I2Fym8eL3NfB2DzZklKbbht7sfPQLtxMZYwqon7QiXPsuTOgMb3eHm2ba+cl5YC3EeLA7Hd68CpKKcqNvIDtDy74YY0yOKjeE7q85xxIn3QD+DLcTFXhWEAuw1AGzaDjgTdY9cyl7du+k3Y5/ka4JfKqJMSYyNdpB55HObDbv97KimAvrMi3AqskWJqT8l9Ls458Z/2atJvhEBMaYyNW5Dg7+CR8/BId2Q483rPs0B6JxPP9d/fr1dcmSJW7HiI7N3/Dn+K748XJzxv2s0qpuJzLGxLFu3i8YnjIeKpwH101xZrUppERkqarWj/R51mVaEP3wIUzozC4txpUZg60YGmNO2JTAxXDtJPhjHbzcFnb85HakAscKYkGzdAJMvBbKn0O3jMFs1tPcTmSMKSyqt4WbPnBWxnm5LWxZ6naiAsUKYkGhCl8Mg5l3QbVWcNNMdlDK7VTGmMKmUj3458eQUhxe6wjrPnE7UYFhg2oKgmAAZt0LS1+F2tdC5xfspHtjTL4Ln/S7HA/wasowarx5Ncld/wcXXutisoLBCqLbfAfhvdtg7QfQ7B5o/Yitdm+MibrtlOaajIcZk/wczab15b+Tv+DFQCcyV+vbOLSDuwFdYF2mbjqwE16/AtbOgsuHQZtHrRgaY2JmHydzi+8Bpgea8kDyRAYnTcBD0O1YrrEWolu2Locpt8LuzdyR0Z/ZUyvBVFvDzBgTWz6S+JfvDn7X0vRKms2Z8hv/9vVxO5YrrIUYa8EALHgOxrdxuktvnM7sYGO3UxljEpji4Qn/9Tzsu4WmntV8WOQB+PFjt2PFnBXEWNqdDq93gU8GQ80O0HchnNnU7VTGGAPAm4G2dMp4nD+0lDMp+Ox/O1/cE4R1mcbKqqnOOoYBP3QZ7YzosuOFxpgC5ketzBUZj/FDy8WQNgp+ng9XjYcK57sdLeqsIEZJ5vDmYhxkcNIEuifNZ0WwGhfePRnKVnM5nTHG5OwwKdDuSfhHK5h2B4xrBW0GQ6O+pD744d+2LywjUq3LNIrqyDpmpwzkSu+XPO/vSreMR60YGmPixz/aQN9Fzs+PHoQ3r6Q8f7qdKmqshRgNAT/9ve9zd9L7/EoZemQMYonWBI4+MdYYYwq8YqfCNW87E4fMeZA5RRYzwNeLj4MN3E6W76wg5refPoe5g7g3+TumBi7iEd8t7OVkt1MZY0xE/v7l/TSqyRBGJI9ibMpzzAk04L/+a/hZT3clXzRYQcwvv34Pcx+Bnz6F0lW4I+MuO53CGFOo/KQVuTJjCLd7Z9InaSatU5bxdqAV7GsIxeN/8XJbD/FE7dnKu8P60M07n72cxEh/V14PXEoGNhepMabwOpXd3J30Hj29n5FUpBg0uxsa3wkp7veIHe96iFYQj9ehPbBwBHw1msM+HxMClzHK34XdFHcnjzHGuKCabOHTC+bBD7OgxBnQ6iGo3RM8XtcyHW9BtC7TSAV8sPQ1mDcUDvwB53Wj9dJmpGvhXX3aGGNy8pNWhJ5vw8aFMHcQTL8TvhoNlw5xRqfGEWsh5lXGfvhuCix6AXashzObwaWPQcW6NnLUGGMAUDp4vub+pImc6fmdBYFajA904IvgBWjoLL9YnLNoLcR8llnkqso2rvd+QnfvF5SUA6wJVmG4/14+/aEu/LANsGJojDEOYVawMXMz6nG99xP6Js3gNe8wfgmW581AGyYHLnY74DFZCzE7AT+9Bz3O9d5PaOH9jgz1MifYkNf9bVmiNchcL8wYY0zOkvFzmWcxNyTNpZFnLYc0mZmBJrwRaMu3+tckJfndarRBNflh3++wbAIseQ32pLNVy/C2vzWTApewndL59zrGGJNgasgmbvDOpat3AcXkMCuDZ/FGoC0zA02cqeKycbyF0gri8Tq8l77/eZr23q+5zLOYFAkwP3A+bwba8GmwLgHcGylljDGFTXEO0NW7gBu8cznbs4VdWoypgWZ8FGzA4mCNoz5zrSBG4FgFMbuBLkd+uXu2wg+z4YcPnZncAxns1OJMDTTnrUBrNugZ0YxtjDEGpbFnDdd759LWs4wi4mOXFuOzYB0+CdRlfvACvh/a/bj2bINqjkk5RzbBvP86hXDbCufuMmdBw95cPe8UlurZ1ho0xpiYEdKC55IWPJeTOURzz7e09S6jlWcZV3oXcFiT4I13oMblUKM9lKoY/USFsoWoysUPvkJdWUc9z4+09K6kkvwBCFRq4PyCa3aAU88GETttwhjz/+3de4xUZxnH8e+PRUBt09JuuAm2IuuFagzbQnoxhrS2VtIUjRrxn1LFEDRNNPqHNCTVUJOKJjU2agy2TVpDamNtFRuaFqXVf+R+LW5hATHgYhHaoNhIgXn84xzScXZmd2Z2OZfd3yeZ7Jk570yeZ9+z+8w55z3vsYLo4Dzd6uXWjm0sndQDrx1KVkz9CLz35uR/+PSBp4ob3YdMz5yGvu1wZDMc3ZI83jgJwOmYwJ8rs1lfuZYN57s5wWU5R21mZs04/MACOLH/rVNcf98GlXPJyolXv1UcZ8yFyR+CjmTKzNFZELsmx8gNmIMAAAbfSURBVNZvdMHxvRCV5MXO98H0udy7ZQLbK130xnQqvu2jmVnpjedN9n1lSrrjsxmObIHT/0hWjn07TJsDM+ai2+4fhQVx+rh48Ivz2BFd7KjMYkdllucSNTMbNYJpnKR7TC/dY3qZM+YA1+ivjF/5erEH1Ui6HfgR0AE8HBHfq1k/HngcuBY4CXw+Ig4P9Jl7zl/FXWfvvTgBm5lZwYk+OumrdPJs5QYgmQwAPtXWp2VyLFFSB/AT4JPAbOALkmbXNFsCvB4Rs4AfAquyiM3MzEaOs0PYz8vq5No84EBEHIqIN4FfAgtr2iwEHkuXnwJukeQ50szMLBNZFcR3AUeqnh9NX6vbJiLOAaeAKzOJzszMRr2sziHW29OrHc3TTBskLQWWpk/P/G3VHS8PMba8dQIn8g5iiJxD/soePziHohgJOby/nTdlVRCPAjOqnk8H+hq0OSppLHAZ8FrtB0XEamA1gKSt7YwkKhLnUAxlz6Hs8YNzKIqRkkM778vqkOkWoEvSeySNAxYBa2varAUWp8ufBTZEma8JMTOzUslkDzEizkm6B3ie5LKLRyNir6SVwNaIWAs8AvxC0gGSPcNFWcRmZmYGGV6HGBHrgHU1r91XtfxfoNWpzVcPQ2h5cw7FUPYcyh4/OIeiGLU5lHqmGjMzs+HiST7NzMwoWUGU9ANJr0jaLekZSZc3aHe7pH2SDkhannWcA5H0OUl7JVUkNRzJJemwpD2SdrY7YupiaSGHIvfDFZLWS+pNf05s0O582gc7JdUOBMvcYL9TSeMlPZmu3yTp6uyjHFgTOdwt6Z9Vv/cv5xFnI5IelXRcUt1LvpR4KM1vt6TurGMcTBM5zJd0qqoP7qvXLi+SZkh6UVJP+r/oa3XatN4PEVGaB3AbMDZdXgWsqtOmAzgIzATGAbuA2XnHXhXfB0mukXkJuG6AdoeBzrzjbTeHEvTD94Hl6fLyettSuu503rG28jsFvgr8LF1eBDyZd9xt5HA38OO8Yx0gh48B3cDLDdYvAJ4jubb6emBT3jG3kcN84Nm84xwg/qlAd7p8KbC/znbUcj+Uag8xIl6IZBYbgI0k1zPWamaauNxERE9E7Ms7jqFoModC9wP/P1XgY7Q7G3C2RsIUiEXfLgYVEX+izjXSVRYCj0diI3C5pKnZRNecJnIotIg4FhHb0+V/Az30n/2s5X4oVUGs8SWS6l+rmWniyiCAFyRtS2fnKZui98PkiDgGyR8XMKlBuwmStkraKCnvojkSpkBsdrv4THqY6ylJM+qsL7Kib/vNukHSLknPSbom72AaSU8LzAE21axquR8yu+yiWZJ+D0yps2pFRPw2bbMCOAesqfcRdV7LdChtMzk04aaI6JM0CVgv6ZX0W10mhiGHQvdDCx/z7rQfZgIbJO2JiIPDE2HLhm0KxBw1E9/vgCci4oykZSR7vDdf9MiGT9H7oBnbgasi4rSkBcBvgK6cY+pH0iXAr4GvR8S/alfXecuA/VC4ghgRHx9ovaTFwB3ALZEeKK7RzDRxF9VgOTT5GX3pz+OSniE51JRZQRyGHArdD5JelTQ1Io6lh1GON/iMC/1wSNJLJN9E8yqIwzYFYo4GzSEiTlY9/TnluxVc7tv+UFUXl4hYJ+mnkjojojBznEp6G0kxXBMRT9dp0nI/lOqQqZKbDH8LuDMi3mjQrJlp4gpN0jslXXphmWQwUdkmMS96P1RPFbgY6LfXK2mikhtXI6kTuAn4S2YR9jcSpkAcNIea8zx3kpwfKpO1wF3pKMfrgVMXDs+XhaQpF849S5pHUitODvyu7KSxPQL0RMSDDZq13g95jxZqcWTRAZJjwjvTx4XRdNOAdTWji/aTfJNfkXfcNTl8muSbyxngVeD52hxIRuDtSh97y5hDCfrhSuAPQG/684r09euAh9PlG4E9aT/sAZYUIO5+v1NgJcmXRIAJwK/Sv5XNwMy8Y24jhwfS7X4X8CLwgbxjron/CeAYcDb9O1gCLAOWpetFckP0g+l203A0eYFzuKeqDzYCN+Ydc038HyU5/Lm7qh4sGGo/eKYaMzMzSnbI1MzM7GJxQTQzM8MF0czMDHBBNDMzA1wQzczMABdEMzMzwAXRzMwMcEE0K7X0nnC3psvflfRQ3jGZlVXh5jI1s5Z8G1iZTgI/h2SqMzNrg2eqMSs5SX8ELgHmR3JvODNrgw+ZmpWYpA+T3D38jIuh2dC4IJqVVHpXiDUkdwb/j6RP5BySWam5IJqVkKR3AE8D34yIHuB+4Du5BmVWcj6HaGZmhvcQzczMABdEMzMzwAXRzMwMcEE0MzMDXBDNzMwAF0QzMzPABdHMzAxwQTQzMwPgf1y/6NF0KLCyAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math, random, pylab, os\n", "\n", "def show_path(x, step, title):\n", " fig = pylab.figure(figsize=(6, 10))\n", " pylab.clf()\n", " path = x[:] #Final position is the same as the initial position. \n", " #Note that this notation appends the first element of x as a new element to x \n", " y_axis = range(len(x)) #construct the imaginary time axis\n", " #Plot the paths\n", " pylab.plot(path, y_axis, 'ko-')\n", " pylab.xlabel('$x$', fontsize = 14)\n", " pylab.ylabel('$\\\\tau$', fontsize=14)\n", " pylab.title(title, fontsize=14)\n", " pylab.grid()\n", " pylab.savefig('levy_snapshot_%i.png' % step)\n", " \n", "def levy_harmonic_path(xstart, xend, dtau, N):\n", " x = [xstart]\n", " for k in range(1, N):\n", " dtau_prime = (N - k) * dtau\n", " Ups1 = 1.0 / math.tanh(dtau) + \\\n", " 1.0 / math.tanh(dtau_prime)\n", " Ups2 = x[k - 1] / math.sinh(dtau) + \\\n", " xend / math.sinh(dtau_prime)\n", " x.append(random.gauss(Ups2 / Ups1, \\\n", " 1.0 / math.sqrt(Ups1)))\n", " return x\n", "\n", "beta = 20.0\n", "N = 80\n", "dtau = beta / N\n", "delta = 1.0\n", "n_steps = 40000\n", "x = [5.0] * N\n", "data = []\n", "for step in range(n_steps):\n", " sigma = 1.0 / math.sqrt( 2.0 * math.tanh( beta / 2.0))\n", " x[0] = random.gauss(0.0, sigma)\n", " x = levy_harmonic_path(x[0], x[0], dtau, N)\n", " k = random.randint(0, N - 1) \n", " data.append(x[k])\n", " \n", "##Write the final path configuration on a file:\n", "#filename = 'levy_path_configuration_levy_2_N%i.txt' % N\n", "#f = open(filename, 'w')\n", "#for i in range(N):\n", "# f.write(str(x[i])+ '\\n')\n", "#f.close()\n", "\n", "show_path(x, step, 'Levy harmonic final configuration, N = %i' %N)\n", "pylab.show()\n", "\n", "pylab.clf()\n", "fig = pylab.figure(figsize=(7, 5))\n", "pylab.hist(data, normed=True, bins=100, label='QMC')\n", "list_x = [0.1 * a for a in range (-30, 31)]\n", "list_y = [math.sqrt(math.tanh(beta / 2.0)) / math.sqrt(math.pi) * \\\n", " math.exp(-x ** 2 * math.tanh(beta / 2.0)) for x in list_x]\n", "pylab.plot(list_x, list_y, label='analytic')\n", "pylab.legend()\n", "pylab.xlabel('$x$')\n", "pylab.ylabel('$\\\\pi(x)$ (normalized)')\n", "pylab.title('levy_harmonic_path (beta=%s, N=%i)' % (beta, N))\n", "pylab.xlim(-2, 2)\n", "pylab.savefig('plot_B2_2_beta%s.png' % beta)\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Anharmonic oscillator\n", "\n", "Using the approach introduced in the preliminaries of this section, we can sample the x points by free particle Lévy sampling. This allows us to avoid using the free density matrix ratios in the Metropolis acceptance rate; we only use the Trotter approximation corresponding to the potential, which is anharmonic in this case. Note that the following algorithm can be applied for any potential." ] }, { "cell_type": "code", "execution_count": 107, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math, random, pylab, os\n", "\n", "def show_path(x, step, title):\n", " fig = pylab.figure(figsize=(6, 10))\n", " pylab.clf()\n", " path = x[:] #Final position is the same as the initial position. \n", " #Note that this notation appends the first element of x as a new element to x \n", " y_axis = range(len(x)) #construct the imaginary time axis\n", " #Plot the paths\n", " pylab.plot(path, y_axis, 'ko-')\n", " pylab.xlabel('$x$', fontsize = 14)\n", " pylab.ylabel('$\\\\tau$', fontsize=14)\n", " pylab.title(title, fontsize=14)\n", " pylab.grid()\n", " pylab.savefig('levy_snapshot_%i.png' % step)\n", "\n", "def V(x, cubic, quartic):\n", " pot = x**2 / 2 + cubic * x**3 + quartic * x**4\n", " return pot\n", "\n", "def levy_free_path(xstart, xend, dtau, N):\n", " x = [xstart]\n", " for k in range(1, N):\n", " dtau_prime = (N - k) * dtau\n", " x_mean = (dtau_prime * x[k - 1] + dtau * xend) / (dtau + dtau_prime)\n", " sigma = math.sqrt(1.0 / (1.0 / dtau + 1.0 / dtau_prime))\n", " x.append(random.gauss(x_mean, sigma))\n", " return x\n", "\n", "beta = 20.0\n", "N = 100\n", "dtau = beta / N\n", "delta = 1.0\n", "n_steps = 10000\n", "x = [1.0] * N\n", "cubic, quartic = -1, 1\n", "data = []\n", "for step in range(n_steps):\n", " x_old = x[:]\n", " Ncut = 11 #pick a prime number ?\n", " x = x[Ncut:] + x[:Ncut] #slices the x data from Ncut'th element and swaps the two parts, hence x[0] changes\n", " x_new = levy_free_path(x[0], x[Ncut], dtau, Ncut) + x[Ncut:] #sample x points using free Levy sampling\n", " #This is why the free density matrix part is not necessary in the Metropolis acceptance rate\n", " #Metropolis algorithm\n", " if random.uniform(0,1) < math.exp(sum(-V(a, cubic, quartic) * dtau for a in x_new)) \\\n", " / math.exp(sum(-V(a, cubic, quartic) * dtau for a in x_old)): \n", " x = x_new[:]\n", " k = random.randint(0, N - 1) \n", " data.append(x[k])\n", " \n", "#Write the final path configuration on a file:\n", "filename = 'levy_anharmonic_path_configuration_levy_N%i.txt' % N\n", "f = open(filename, 'w')\n", "for i in range(N):\n", " f.write(str(x[i])+ '\\n')\n", "f.close()\n", "\n", "show_path(x, step, 'Levy anharmonic final configuration, N = %i' %N)\n", "pylab.show()\n", "\n", "pylab.clf()\n", "fig = pylab.figure(figsize=(7, 5))\n", "T = 1 / beta\n", "list_x = [0.1 * a for a in range (-30, 31)]\n", "y = [V(a, cubic, quartic) for a in list_x]\n", "pylab.plot(list_x, y, c='gray', linewidth=4.0, label='Anharmonic potential')\n", "pylab.hist(data, normed=True, bins=100, label='QMC')\n", "pylab.legend()\n", "pylab.xlabel('$x$')\n", "pylab.ylabel('$\\\\pi(x)$ (normalized)')\n", "pylab.title('levy_anharmonic_path (beta=%s, N=%i, cubic=%.1f, quartic=%.1f)' % (beta, N, cubic, quartic))\n", "pylab.xlim(-2, 2)\n", "pylab.ylim(0, 0.9)\n", "pylab.grid()\n", "pylab.savefig('plot_C1_beta%s.png' % beta)\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we can improve the performance of this program for even further for the special case of anharmonic potential. Since tha anharmonic potential contains the harmonic potential, we can sample the x[i] by harmonic Lévy sampling, and use the modified Metropolis acceptance rate (analogously to what is done in P.3.b)." ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math, random, pylab, os\n", "\n", "def show_path(x, step, title):\n", " fig = pylab.figure(figsize=(6, 10))\n", " pylab.clf()\n", " path = x[:] #Final position is the same as the initial position. \n", " #Note that this notation appends the first element of x as a new element to x \n", " y_axis = range(len(x)) #construct the imaginary time axis\n", " #Plot the paths\n", " pylab.plot(path, y_axis, 'ko-')\n", " pylab.xlabel('$x$', fontsize = 14)\n", " pylab.ylabel('$\\\\tau$', fontsize=14)\n", " pylab.title(title, fontsize=14)\n", " pylab.grid()\n", " pylab.savefig('levy_snapshot_%i.png' % step)\n", " \n", "def V_harm(x):\n", " pot = x**2 / 2\n", " return pot\n", "\n", "def V_anharm(x, cubic, quartic):\n", " pot = x**2 / 2 + cubic * x**3 + quartic * x**4\n", " return pot\n", "\n", "def levy_harmonic_path(xstart, xend, dtau, N):\n", " x = [xstart]\n", " for k in range(1, N):\n", " dtau_prime = (N - k) * dtau\n", " Ups1 = 1.0 / math.tanh(dtau) + \\\n", " 1.0 / math.tanh(dtau_prime)\n", " Ups2 = x[k - 1] / math.sinh(dtau) + \\\n", " xend / math.sinh(dtau_prime)\n", " x.append(random.gauss(Ups2 / Ups1, \\\n", " 1.0 / math.sqrt(Ups1)))\n", " return x\n", "\n", "beta = 20.0\n", "N = 100\n", "dtau = beta / N\n", "delta = 1.0\n", "n_steps = 10000\n", "x = [1.0] * N\n", "cubic, quartic = -1, 1\n", "data = []\n", "for step in range(n_steps):\n", " x_old = x[:]\n", " Ncut = 11 #pick a prime number ?\n", " x = x[Ncut:] + x[:Ncut] #slices the x data from Ncut'th element and swaps the two parts, hence x[0] changes\n", " x_new = levy_harmonic_path(x[0], x[Ncut], dtau, Ncut) + x[Ncut:] #sample x points using harmonic Levy sampling\n", " #This is why the free and harmonic density matrix part is not necessary in the Metropolis acceptance rate\n", " #Metropolis algorithm\n", " if random.uniform(0,1) < math.exp(sum(-(V_anharm(a, cubic, quartic) - V_harm(a)) * dtau for a in x_new)) \\\n", " / math.exp(sum(-(V_anharm(a, cubic, quartic) - V_harm(a)) * dtau for a in x_old)): \n", " x = x_new[:]\n", " k = random.randint(0, N - 1) \n", " data.append(x[k])\n", " \n", "#Write the final path configuration on a file:\n", "filename = 'improved_levy_anharmonic_path_configuration_levy_N%i.txt' % N\n", "f = open(filename, 'w')\n", "for i in range(N):\n", " f.write(str(x[i])+ '\\n')\n", "f.close()\n", "\n", "show_path(x, step, 'Levy anharmonic final configuration, N = %i' %N)\n", "pylab.show()\n", "\n", "pylab.clf()\n", "fig = pylab.figure(figsize=(7, 5))\n", "T = 1 / beta\n", "list_x = [0.1 * a for a in range (-30, 31)]\n", "y = [V(a, cubic, quartic) for a in list_x]\n", "pylab.plot(list_x, y, c='gray', linewidth=4.0, label='Anharmonic potential')\n", "pylab.hist(data, normed=True, bins=100, label='QMC')\n", "pylab.legend()\n", "pylab.xlabel('$x$')\n", "pylab.ylabel('$\\\\pi(x)$ (normalized)')\n", "pylab.title('levy_anharmonic_path_improved (beta=%s, N=%i, cubic=%.1f, quartic=%.1f)' % (beta, N, cubic, quartic))\n", "pylab.xlim(-2, 2)\n", "pylab.ylim(0, 0.9)\n", "pylab.savefig('plot_C2_beta%s.png' % beta)\n", "pylab.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Mexican hat\n", "\n" ] }, { "cell_type": "code", "execution_count": 181, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math, random, pylab, os\n", "\n", "def show_path(x, step, title):\n", " fig = pylab.figure(figsize=(5, 10))\n", " pylab.clf()\n", " path = x[:] #Final position is the same as the initial position. \n", " #Note that this notation appends the first element of x as a new element to x \n", " y_axis = range(len(x)) #construct the imaginary time axis\n", " #Plot the paths\n", " pylab.plot(path, y_axis, 'k-')\n", " pylab.xlabel('$x$', fontsize = 14)\n", " pylab.ylabel('$\\\\tau$', fontsize=14)\n", " pylab.title(title, fontsize=14)\n", " #pylab.xlim(-6, 6)\n", " pylab.grid()\n", " pylab.savefig('levy_snapshot_%i.png' % step)\n", "\n", "def V(x, barrier):\n", " if x < -5.0: return (x + 5.0) ** 2 #barrier on the left hand side\n", " elif x > 5.0: return (x - 5.0) ** 2 #barrier on the left hand side\n", " elif x <= -1.0: return 0.0 #0 potential in between the left wall and the bump barrier\n", " elif x < 1.0: return numpy.exp(-1.0 / (1.0 - x ** 2)) * numpy.exp(barrier) * barrier #gaussian bump barrier\n", " else: return 0.0 #0 potential elsewhere\n", " \n", "def levy_free_path(xstart, xend, dtau, N):\n", " x = [xstart]\n", " for k in range(1, N):\n", " dtau_prime = (N - k) * dtau\n", " x_mean = (dtau_prime * x[k - 1] + dtau * xend) / (dtau + dtau_prime)\n", " sigma = math.sqrt(1.0 / (1.0 / dtau + 1.0 / dtau_prime))\n", " x.append(random.gauss(x_mean, sigma))\n", " return x\n", "\n", "beta = 5.0\n", "N = 500\n", "dtau = beta / N\n", "delta = 1.0\n", "n_steps = 10000\n", "x = [1.0] * N\n", "barrier = 1.0\n", "data = []\n", "for step in range(n_steps):\n", " x_old = x[:]\n", " Ncut = 11 #pick a prime number ?\n", " x = x[Ncut:] + x[:Ncut] #slices the x data from Ncut'th element and swaps the two parts, hence x[0] changes\n", " x_new = levy_free_path(x[0], x[Ncut], dtau, Ncut) + x[Ncut:] #sample x points using free Levy sampling\n", " #This is why the free density matrix part is not necessary in the Metropolis acceptance rate\n", " #Metropolis algorithm\n", " if random.uniform(0,1) < math.exp(sum(-V(a, barrier) * dtau for a in x_new)) \\\n", " / math.exp(sum(-V(a, barrier) * dtau for a in x_old)): \n", " x = x_new[:]\n", " k = random.randint(0, N - 1) \n", " data.append(x[k])\n", " \n", "#Write the final path configuration on a file:\n", "filename = 'mexicanhat_path_configuration_levy_N%i.txt' % N\n", "f = open(filename, 'w')\n", "for i in range(N):\n", " f.write(str(x[i])+ '\\n')\n", "f.close()\n", "\n", "show_path(x, step, 'Levy mexican hat final configuration, N = %i' %N)\n", "pylab.show()\n", "\n", "pylab.clf()\n", "fig = pylab.figure(figsize=(10, 5))\n", "T = 1 / beta\n", "list_x = [0.1 * a for a in range (-90, 91)]\n", "y = [V(a, barrier) for a in list_x]\n", "pylab.plot(list_x, y, c='gray', linewidth=4.0, label='Mexican hat potential')\n", "pylab.hist(data, normed=True, bins=100, label='QMC')\n", "pylab.legend()\n", "pylab.xlabel('$x$')\n", "pylab.ylabel('$\\\\pi(x)$ (normalized)')\n", "pylab.title('levy_mexicanhat_path (beta=%s, N=%i, cubic=%.1f, quartic=%.1f)' % (beta, N, cubic, quartic))\n", "pylab.xlim(-6, 6)\n", "pylab.ylim(0, 1.5)\n", "pylab.grid()\n", "pylab.savefig('plot_mexicanhat_beta%s.png' % beta)\n", "pylab.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%pylab qt\n", "import math, random, pylab, os\n", "\n", "output_dir = 'snapshots_Levy_mexicanhat_path'\n", "if not os.path.exists(output_dir): os.makedirs(output_dir)\n", " \n", "fig = pylab.figure(figsize=(5, 10))\n", "\n", "def show_path(x, hist_data, beta, barrier, step, fig):\n", " pylab.clf()\n", " path = x[:] \n", " #Note that this notation appends the first element of x as a new element to x \n", " y_axis = range(len(x)) #construct the imaginary time axis\n", " ax = fig.add_subplot(2, 1, 1)\n", " #Plot the path\n", " ax.plot(path, y_axis, 'k-', label='path')\n", " #ax.legend()\n", " ax.set_xlim(-6, 6)\n", " ax.set_ylabel('$\\\\tau$', fontsize=14)\n", " ax.set_title('Levy path integral Monte Carlo, step %i \\n beta=%s, N=%i, barrier height$\\sim$%.1f' % (step, beta, N, barrier))\n", " ax.grid()\n", " \n", " #Plot the histogram\n", " T = 1.0 / beta\n", " ax = fig.add_subplot(2, 1, 2)\n", " list_x = [0.1 * a for a in range (-90, 91)]\n", " y = [V(a, barrier) for a in list_x]\n", " temp = [T] * 2\n", " pylab.plot([-6,6], temp, '-', color=plt.cm.cool(step), linewidth=2.0, label='Thermal energy:$k_B T$')\n", " pylab.plot(list_x, y, c='gray', linewidth=4.0, label='Mexican hat potential')\n", " ax.hist(hist_data, 10, histtype='step', normed = 'True', label='Position distribution') #histogram of the sample\n", " ax.set_xlim(-6, 6) #restrict the range over which the histogram is shown\n", " ax.set_ylim(0, 1.5)\n", " ax.set_xlabel('$x$', fontsize = 14)\n", " ax.set_ylabel('$\\pi(x)$', fontsize = 14)\n", " ax.legend(fontsize = 9)\n", " ax.grid()\n", " \n", " pylab.pause(0.2)\n", " pylab.savefig(output_dir + '/snapshot_%05i.png' % step)\n", "\n", "def V(x, barrier):\n", " if x < -5.0: return (x + 5.0) ** 2 #barrier on the left hand side\n", " elif x > 5.0: return (x - 5.0) ** 2 #barrier on the left hand side\n", " elif x <= -1.0: return 0.0 #0 potential in between the left wall and the bump barrier\n", " elif x < 1.0: return numpy.exp(-1.0 / (1.0 - x ** 2)) * numpy.exp(barrier) * barrier #gaussian bump barrier\n", " else: return 0.0 #0 potential elsewhere\n", " \n", "def levy_free_path(xstart, xend, dtau, N):\n", " x = [xstart]\n", " for k in range(1, N):\n", " dtau_prime = (N - k) * dtau\n", " x_mean = (dtau_prime * x[k - 1] + dtau * xend) / (dtau + dtau_prime)\n", " sigma = math.sqrt(1.0 / (1.0 / dtau + 1.0 / dtau_prime))\n", " x.append(random.gauss(x_mean, sigma))\n", " return x\n", "\n", "beta = 256.0\n", "N = 100\n", "dtau = beta / N\n", "delta = 1.0\n", "n_steps = 10000\n", "x = [1.0] * N\n", "barrier = 0.5\n", "data = []\n", "for step in range(n_steps):\n", " x_old = x[:]\n", " Ncut = 11 #pick a prime number ?\n", " x = x[Ncut:] + x[:Ncut] #slices the x data from Ncut'th element and swaps the two parts, hence x[0] changes\n", " x_new = levy_free_path(x[0], x[Ncut], dtau, Ncut) + x[Ncut:] #sample x points using free Levy sampling\n", " #This is why the free density matrix part is not necessary in the Metropolis acceptance rate\n", " #Metropolis algorithm\n", " if random.uniform(0,1) < math.exp(sum(-V(a, barrier) * dtau for a in x_new)) \\\n", " / math.exp(sum(-V(a, barrier) * dtau for a in x_old)): \n", " x = x_new[:]\n", " k = random.randint(0, N - 1) \n", " data.append(x[k])\n", " show_path(x, data, beta, barrier, step, fig)\n", " if step % 30 == 0:\n", " beta /= 2 #increase the temperature by twice at each 50 steps" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![caption](mexicanhat.gif)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 2 }