{ "cells": [ { "cell_type": "markdown", "id": "d295a8ae-fdbb-4151-bf34-92f2b74e34d8", "metadata": { "tags": [] }, "source": [ "# Environment Dynamics\n", "\n", "An example on how to compute the dynamics of a gaussian bosonic environment using the OQuPy package.\n", "\n", "- [launch binder](https://mybinder.org/v2/gh/tempoCollaboration/OQuPy/HEAD?labpath=tutorials%2Fbath_dynamics.ipynb) (runs in browser),\n", "- [download the jupyter file](https://raw.githubusercontent.com/tempoCollaboration/OQuPy/main/tutorials/bath_dynamics.ipynb), or\n", "- read through the text below and code along." ] }, { "cell_type": "markdown", "id": "12128a31", "metadata": {}, "source": [ "First let's import the necessary packages" ] }, { "cell_type": "code", "execution_count": 1, "id": "557f8f8b-10c1-4797-9092-6062dfdccf73", "metadata": { "tags": [] }, "outputs": [], "source": [ "import sys\n", "sys.path.insert(0,'..')\n", "import oqupy\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "markdown", "id": "edf53a96-c6c8-482e-aea6-ed126754652a", "metadata": { "tags": [] }, "source": [ "and define the necessary spin matrices for convenience" ] }, { "cell_type": "code", "execution_count": 2, "id": "aad71653-f73f-4c3b-8910-4e10b57bbf2e", "metadata": { "tags": [] }, "outputs": [], "source": [ "spin_down = oqupy.operators.spin_dm(\"down\")\n", "s_z = 0.5*oqupy.operators.sigma(\"z\")\n", "s_x = 0.5*oqupy.operators.sigma(\"x\")" ] }, { "cell_type": "markdown", "id": "acdfcb0f-004e-43ab-ab6a-7b3e8c3e5e3f", "metadata": {}, "source": [ "## Example - Heat transfer in a biased spin-boson model\n", "Let's try and recreate a line cut of Figure 2 from [Gribben2021] ([arXiv:2106.04212](https://arxiv.org/abs/2106.04212)). This tells us how much heat has been emitted into or absorbed from the bath by the system and how this transfer is distributed over the bath modes." ] }, { "cell_type": "markdown", "id": "90641216-6ff9-434f-b21d-6870ccb3254f", "metadata": {}, "source": [ "### 1. Hamiltonian - Biased spin-boson model\n", "The system Hamiltonian we consider is:\n", "$$H_S = \\epsilon s_z + \\Omega s_x$$\n", "describing a spin-$\\frac{1}{2}$ particle with energy splitting $\\epsilon$ and transition frequency $\\Omega$. Here $s_i = \\sigma_i/2$ where $\\sigma_i$ are the Pauli matrices.\n", "\n", "The interaction Hamiltonian is given by:\n", "$$H_I = {s_z} \\sum_k g_k \\left(a_k+a_k^\\dagger\\right),$$\n", "and the bath Hamiltonian by:\n", "$$H_B = \\sum_k \\omega_k a_k^\\dagger a_k.$$\n", "This describes a linear coupling to bosons of frequency $\\omega_k$ with strength $g_k$. These bosons are described by the ladder operators $a_k$ and $a^\\dagger_k$ which satisfy the canonical commutation relations:\n", "$$ \\left[a_k,a_{k'}^\\dagger\\right]=\\delta_{kk'},$$\n", "$$ \\left[a_k,a_{k'}\\right]=\\left[a_k^\\dagger,a_{k'}^\\dagger\\right] = 0.$$\n", "We can characterise the bath entirely by its spectral density:\n", "$$ J(\\omega) = \\sum_k |g_k|^2 \\delta(\\omega - \\omega_k) = 2 \\, \\alpha \\, \\omega \\, \\exp\\left(-\\frac{\\omega}{\\omega_\\mathrm{cutoff}}\\right) \\mathrm{,} $$\n", "where we have decided on an Ohmic spectral density with dimensionless coupling strength $\\alpha$ and high-frequency cutoff $\\omega_c$.\n", "\n", "Also, let's assume the initial density matrix of the spin is the down state\n", "$$ \\rho_S(0) = \\begin{pmatrix} 0 & 0 \\\\ 0 & 1 \\end{pmatrix} $$ and the bath is initially in thermal equilibrium at $T=\\Omega$.\n", "\n", "For the rest of the parameters we choose to set:\n", "\n", "* $\\epsilon = 2.0 \\Omega$\n", "* $\\omega_c = 10.0 \\Omega$\n", "* $\\alpha = 0.05$" ] }, { "cell_type": "markdown", "id": "9af12897-6c75-434f-ad92-57472749e29f", "metadata": {}, "source": [ "### 2. Building the process tensor\n", "\n", "The setting up of the system and general running of TEMPO/PT-TEMPO has been covered in detail in the previous tutorials so for now let us go right ahead and build a process tensor for this spectral density. Here we'll use much rougher convergence parameters than in the paper, the qualitative result is not really changed though." ] }, { "cell_type": "code", "execution_count": 3, "id": "46477052-8b66-4441-8529-6e8d9e2a191c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--> PT-TEMPO computation:\n", "100.0% 100 of 100 [########################################] 00:00:00\n", "Elapsed time: 0.9s\n" ] } ], "source": [ "Omega = 1\n", "alpha = 0.05\n", "w_cutoff = 10 * Omega\n", "epsilon = 2 * Omega\n", "tcut = 2.0\n", "epsrel = 1e-5\n", "final_t = 20\n", "delta_t = 0.2\n", "initial_state = spin_down\n", "corr = oqupy.PowerLawSD(alpha, 1, w_cutoff, temperature = 1)\n", "pars = oqupy.TempoParameters(dt=delta_t, epsrel=epsrel, tcut=tcut)\n", "system = oqupy.System(Omega*s_x + epsilon*s_z)\n", "bath = oqupy.Bath(s_z, corr)\n", "pt = oqupy.PtTempo(bath, 0.0, final_t, pars)\n", "pt = pt.get_process_tensor(progress_type='bar')" ] }, { "cell_type": "markdown", "id": "4b1b995d-57ae-4c33-b73e-ef74c9a187c7", "metadata": {}, "source": [ "Now as we saw previously the process tensor can readily be used to calculate system dynamics, for example let's look at how the density matrix elements evolve." ] }, { "cell_type": "code", "execution_count": 4, "id": "b9b0eab6-f1e0-4a8d-b10d-cf05f63a94fb", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--> Compute dynamics:\n", "100.0% 100 of 100 [########################################] 00:00:00\n", "Elapsed time: 0.1s\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dyns = oqupy.contractions.compute_dynamics(\n", " system=system,\n", " initial_state=initial_state,\n", " process_tensor=pt)\n", "times, states = dyns.times, dyns.states\n", "plt.plot(times, states[:,0,0].real, label=r'$\\rho_{00}$')\n", "plt.plot(times, states[:,0,1].real, label=r'$\\Re[\\rho_{01}]$')\n", "plt.plot(times, states[:,0,1].imag, label=r'$\\Im[\\rho_{01}]$')\n", "plt.xlabel(r\"$\\Omega t$\")\n", "plt.ylabel(r\"Amplitude\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "id": "095087e0-859f-45fa-a95a-3c741398ba1b", "metadata": {}, "source": [ "Already the process tensor tells us everything we could want to know about the system but actually we can infer a lot about how the bath behaves as well.\n", "\n", "### 3. Bath dynamics\n", "\n", "In [Gribben2021] ([arXiv:2106.04212](https://arxiv.org/abs/2106.04212)) we can see that for linearly coupled Gaussian environments the bath dynamics can be calculated through relatively simple transformations of system correlation functions. For example the change in energy of mode $k$ can be expressed as\n", "\n", "$$ \\omega_k\\left\\langle a_k^\\dagger (t) a_k (t)-a_k^\\dagger (0) a_k (0) \\right\\rangle = \\omega_k g_k^2 \\int_0^t dt' \\int_0^t dt'' \\left\\langle s_z(t')s_z(t'')\\right\\rangle F(\\omega_k, t', t'', T), $$\n", "with\n", "$$ F(\\omega, t', t'', T) := \\cos[\\omega (t'-t'')]-i \\sin[\\omega(t'-t'')]\\coth(\\omega /2T). $$\n", "\n", "However we typically take the continuum limit in which case the coupling to any single mode becomes infinitesimal and it makes more sense to talk about how heat is exchanged within a band of modes $(\\omega-\\delta/2,\\omega+\\delta/2)$. This gives us the expression:\n", "\n", "$$ \\Delta Q (\\omega,t) = \\int_{\\omega-\\delta/2}^{\\omega+\\delta/2}d\\omega' \\omega' J(\\omega') \\int_0^t dt' \\int_0^t dt'' \\left\\langle s_z(t')s_z(t'')\\right\\rangle F(\\omega', t', t'', T),$$\n", "$$ \\Delta Q (\\omega,t) \\approx \\omega J(\\omega)\\delta \\int_0^t dt' \\int_0^t dt'' \\left\\langle s_z(t')s_z(t'')\\right\\rangle F(\\omega', t', t'', T),$$\n", "where $\\left\\langle s_z(t')s_z(t'')\\right\\rangle = \\mathrm{Tr} [s_z(t')s_z(t'')\\rho]$ and we have approximated the integrand as constant over the bandwidth. The validity of this is reliant on the system relaxing much faster than the timescale set by $\\delta^{-1}$.\n", "\n", "To be compatible with PT-TEMPO we must now discretise this expression according into timesteps, a rough discretisation can be expressed as:\n", "$$\\Delta Q (\\omega,t_N) \\approx \\omega J(\\omega)\\delta \\sum_{k=0}^{N-1} \\sum_{k'=0}^{N-1} \\left\\langle s_z(t_k)s_z(t_{k'})\\right\\rangle F(\\omega,t_k,t_{k'},T) \\, dt^2.$$\n", "Here $dt$ is the same timestep set as the convergence parameter in PT-TEMPO and we have defined timesteps $t_k = k dt$. In practice this discretisation breaks down at large $\\omega$, the actual implementation does something slightly more sophisticated which will be detailed elsewhere.\n", "\n", "To calculate this in OQuPy we begin by initialising a `TwoTimeBathCorrelations` object from the `bath_dynamics` module:" ] }, { "cell_type": "code", "execution_count": 5, "id": "51429960-28a3-47b8-8eb2-f92611294daa", "metadata": {}, "outputs": [], "source": [ "bath_corr = oqupy.bath_dynamics.TwoTimeBathCorrelations(system, bath, pt, initial_state)" ] }, { "cell_type": "markdown", "id": "a6111f16-bd3f-4645-875e-197f8af44394", "metadata": {}, "source": [ "As inputs this requires everything necessary to calculate the system correlation functions:\n", "* `system`: the system Hamiltonian.\n", "* `bath`: characterises bath containing information about its spectral density and temperature.\n", "* `process_tensor`: the process tensor which when combined with the system Hamiltonian can be used to calculate any system correlation function.\n", "* `initial_state`: the initial system density matrix which must be either built into the process tensor or input here.\n", "\n", "We can now use the method `occupation` to calculate the energy dynamics of a particular mode by multiplying the output by its frequency, in this case let's look at `w = Omega` and a bandwidth of `delta = 0.1 * Omega`:" ] }, { "cell_type": "code", "execution_count": 6, "id": "58c0cbf3-b214-4070-99e4-b3b18b844a8e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--> Compute correlations:\n", "100.0% 100 of 100 [########################################] 00:00:07\n", "Elapsed time: 7.9s\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\Delta Q ( \\\\Omega, t)$')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "w = Omega\n", "delta = 0.1 * Omega\n", "tlist, occ = bath_corr.occupation(w, delta, change_only = True)\n", "energy = w * occ\n", "plt.plot(tlist,energy)\n", "plt.xlabel(r'$\\Omega t$')\n", "plt.ylabel(r'$\\Delta Q ( \\Omega, t)$')" ] }, { "cell_type": "markdown", "id": "3d876074-7492-4f05-b2fb-70372946ba2b", "metadata": {}, "source": [ "...that took quite a while. From the expression for $\\Delta Q$ is would seem that to calculate the change in energy of the bath up to time $t_N$ requires the $N^2$ two-time system correlation functions. In fact we only need the $N(N+1)/2$ time-ordered correlation functions due to $\\left\\langle s_z(t_{k'})s_z(t_{k})\\right\\rangle = \\left\\langle s_z(t_{k})s_z(t_{k'})\\right\\rangle^*$. However, this can still be quite time-consuming to calculate, but let's see what happens if we want the energy of another mode now, let's say `w = 2 * Omega`" ] }, { "cell_type": "code", "execution_count": 7, "id": "c86048d1-2212-4fc6-8ef0-632ea2639670", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\Delta Q (2 \\\\Omega, t)$')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "w = 2 * Omega\n", "delta = 0.1 * Omega\n", "tlist, occ = bath_corr.occupation(w, delta, change_only = True)\n", "energy = w * occ\n", "plt.plot(tlist, energy)\n", "plt.xlabel(r'$\\Omega t$')\n", "plt.ylabel(r'$\\Delta Q (2 \\Omega, t)$')" ] }, { "cell_type": "markdown", "id": "9325b043-269f-4a6b-a1f6-b74037aa6d1c", "metadata": {}, "source": [ "Much quicker! This is because the same set of system correlation functions can be used to compute any bath correlation function $\\langle \\alpha_2(t_2)\\alpha_1(t_1)\\rangle$ where $\\alpha_2, \\alpha_1 \\in \\{a_k^\\dagger,a_k\\} $ and $t_1,t_2 < t_N$. So now we see the logic of having a bath_dynamics object, it allows us to conveniently store the calculated system correlation functions and re-use them as we like :)\n", "\n", "### 4. Recreating Figure 2\n", "\n", "Now we have all the tools necessary to recreate the study of total heat exchanged as a function of $\\epsilon$. However, this would take a while as we would need a new set of correlation functions for each $\\epsilon$. Here we will just look at the case where $\\epsilon = 2\\Omega$. We are only interested in the total heat exchanged over the process so simply look at the final value of $\\Delta Q$." ] }, { "cell_type": "code", "execution_count": 8, "id": "96b8d7aa-c279-4107-85c5-8ebfb01476ce", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Heat Exchanged$/\\\\Omega$')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "heat_list = []\n", "freq_list = np.arange(1, 10, 0.1)\n", "for w in freq_list:\n", " tlist, occ = bath_corr.occupation(w, 0.1, True)\n", " heat_list.append(w * occ[-1])\n", "plt.plot(freq_list, heat_list)\n", "plt.xlabel(r\"Mode Frequency$/\\Omega$\")\n", "plt.ylabel(r\"Heat Exchanged$/\\Omega$\")" ] }, { "cell_type": "markdown", "id": "ca545275-50dd-4c67-912c-b746cba6779a", "metadata": {}, "source": [ "This is highly oscillatory, perhaps unsurprising from the dynamics we generated but still it would be nice to smooth this out. We expect the result to eventually equilibrate but with such a small bandwidth this will take a while, instead we simply period-average the result. The period at which each mode oscillates is $T(\\omega)=2\\pi/\\omega$ so we average over the last $n$ timesteps where $(n+1) dt \\geq T(\\omega) > n dt$." ] }, { "cell_type": "code", "execution_count": 9, "id": "3ce24ca0-866a-45b6-89d0-8ed8e4994c56", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Heat Exchanged$/\\\\Omega$')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "heat_list = []\n", "freq_list = np.arange(0.05, 10, 0.1)\n", "for w in freq_list:\n", " tlist, occ = bath_corr.occupation(w, 0.1, True)\n", " sel = tlist > (tlist[-1] - 2 * np.pi/w)\n", " energy = occ * w\n", " period_averaged_energy = np.mean(energy[sel])\n", " heat_list.append(period_averaged_energy)\n", "plt.plot(freq_list, heat_list)\n", "plt.xlabel(r\"Mode Frequency$/\\Omega$\")\n", "plt.ylabel(r\"Heat Exchanged$/\\Omega$\")" ] }, { "cell_type": "markdown", "id": "37980eff-caf4-4bd2-bed7-cca871611f81", "metadata": {}, "source": [ "Here, as in the paper, we see heat is absorbed by the system from the band of the modes in the vicinity of $\\tilde{\\Omega}=\\sqrt{\\Omega^2+\\epsilon^2}$. This seems sensible as in a Markovian theory the system would sample the environment purely at its eigensplitting $\\tilde{\\Omega}$." ] }, { "cell_type": "markdown", "id": "8793c039-6a4c-4d4d-9289-1e0ffeff96a7", "metadata": {}, "source": [ "-------------------------------------------------" ] } ], "metadata": { "interpreter": { "hash": "56674a1249193ed385a20db9ba6c6497b0cb98d98f01f014399e91d8567384eb" }, "kernelspec": { "display_name": "oqupyPR", "language": "python", "name": "oqupypr" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.15" } }, "nbformat": 4, "nbformat_minor": 5 }