Exact open quantum system dynamics using the Hierarchy of Pure States (HOPS)

Abstract

We show that the general and numerically exact Hierarchy of Pure States method (HOPS) is very well applicable to calculate the reduced dynamics of an open quantum system. In particular we focus on environments with a sub-Ohmic spectral density (SD) resulting in an algebraic decay of the bath correlation function (BCF). The universal applicability of HOPS, reaching from weak to strong coupling for zero and non-zero temperature, is demonstrated by solving the spin-boson model for which we find perfect agreement with other methods, each one suitable for a special regime of parameters. The challenges arising in the strong coupling regime are not only reflected in the computational effort needed for the HOPS method to converge but also in the necessity for an importance sampling mechanism, accounted for by the non-linear variant of HOPS. In order to include non-zero temperature effects in the strong coupling regime we found that it is highly favorable for the HOPS method to use the zero temperature BCF and include temperature via a stochastic Hermitian contribution to the system Hamiltonian.

This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in the Journal of Chemical Theory and Computation, copyright \c{opyright} American Chemical Society after peer review. To access the final edited and published work see http://pubs.acs.org/doi/abs/10.1021/acs.jctc.7b00751

References in corpus (7)

• Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
• Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems
• Analytic Representations of Bath Correlation Functions for Ohmic and Superohmic Spectral Densities Using Simple Poles
• Non-perturbative stochastic method for driven spin-boson model
• Hierarchical equations for open system dynamics in fermionic and bosonic environments
• Time-Dependent Transport Through Quantum-Impurity Systems with Kondo Resonance
• Consistent perturbative treatment of the subohmic spin-boson model yielding arbitrarily small $T_2/T_1$ decoherence time ratios

Cited by in corpus (8)

• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Control relaxation via dephasing: an exact quantum state diffusion study
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion
• Simulating optical linear absorption for mesoscale molecular aggregates: an adaptive hierarchy of pure states approach
• Dynamics of a strongly coupled quantum heat engine -- computing bath observables from the hierarchy of pure states
• A new approach for open quantum systems based on a phonon number representation of a harmonic oscillator bath
• Temperature Controlled Open Quantum System Dynamics using Time-dependent Variational Method
• Information Loss Pathways in a Numerically Exact Simulation of a non-Markovian Open Quantum System