{ "cells": [ { "cell_type": "markdown", "id": "6a6ca7ab", "metadata": {}, "source": [ "# Hierarchical Equation of Motion Examples\n", "\n", "The \"hierarchical equations of motion\" (HEOM) method is a powerful numerical approach to solve the dynamics and steady-state of a quantum system coupled to a non-Markovian and non-perturbative environment. Originally developed in the context of physical chemistry, it has also been extended and applied to problems in solid-state physics, optics, single-molecule electronics, and biological physics.\n", "\n", "QuTiP's implementation of the HEOM is described in detail in https://arxiv.org/abs/2010.10806.\n", "\n", "This collection of examples from the paper illustrates how to use QuTiP's HEOM to model and investigate the dynamics of a variety of systems coupled to bosonic or fermionic baths.\n", "\n", "## Overview of the notebooks\n", "\n", "* [Example 1a: Spin-Bath model (basic)](./heom-1a-spin-bath-model-basic.ipynb)\n", "\n", "* [Example 1b: Spin-Bath model (very strong coupling)](./heom-1b-spin-bath-model-very-strong-coupling.ipynb)\n", "\n", "* [Example 1c: Spin-Bath model (underdamped case)](./heom-1c-spin-bath-model-underdamped-sd.ipynb)\n", "\n", "* [Example 1d: Spin-Bath model, fitting of spectrum and correlation functions](./heom-1d-spin-bath-model-ohmic-fitting.ipynb)\n", "\n", "* [Example 1e: Spin-Bath model (pure dephasing)](./heom-1e-spin-bath-model-pure-dephasing.ipynb)\n", "\n", "* [Example 2: Dynamics in Fenna-Mathews-Olsen complex (FMO)](./heom-2-fmo-example.ipynb)\n", "\n", "* [Example 3: Quantum Heat Transport](./heom-3-quantum-heat-transport.ipynb)\n", "\n", "* [Example 4: Dynamical decoupling of a non-Markovian environment](./heom-4-dynamical-decoupling.ipynb)\n", "\n", "* [Example 5a: Fermionic single impurity model](./heom-5a-fermions-single-impurity-model.ipynb)\n", "\n", "* [Example 5b: Discrete boson coupled to an impurity + fermionic leads](./heom-5b-fermions-discrete-boson-model.ipynb)" ] }, { "cell_type": "code", "execution_count": null, "id": "678c987d", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "formats": "ipynb,md:myst" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 5 }