Time-Correlated Blip Dynamics of Open Quantum Systems

TL;DR

This paper introduces an improved method combining the Stochastic Liouville-von Neumann equation with projector techniques to better simulate long-time non-Markovian quantum dynamics, especially where perturbative methods fail.

Contribution

The authors develop a novel scheme that enhances the SLN approach with projector operators, enabling systematic convergence and efficient long-time simulations of open quantum systems.

Findings

Successfully applied to two- and three-level systems

Extracted transfer rates consistent with perturbative predictions

Extended simulation capabilities to long-time regimes

Abstract

The non-Markovian dynamics of open quantum systems is still a challenging task, particularly in the non-perturbative regime at low temperatures. While the Stochastic Liouville-von Neumann equation (SLN) provides a formally exact tool to tackle this problem for both discrete and continuous degrees of freedom, its performance deteriorates for long times due to an inherently non-unitary propagator. Here we present a scheme which combines the SLN with projector operator techniques based on finite dephasing times, gaining substantial improvements in terms of memory storage and statistics. The approach allows for systematic convergence and is applicable in regions of parameter space where perturbative methods fail, up to the long time domain. Findings are applied to the coherent and incoherent quantum dynamics of two- and three-level systems. In the long time domain sequential and super-exchange transfer rates are extracted and compared to perturbative predictions.