Hierarchical quantum master equation with semiclassical Drude dissipation

TL;DR

This paper introduces a nonperturbative hierarchical quantum master equation for quantum dissipation, improving upon traditional methods by incorporating an advanced semiclassical Drude bath treatment, applicable to various condensed phase dynamics.

Contribution

The paper develops a novel hierarchical quantum master equation with an improved semiclassical Drude bath approach, extending the validity and accuracy over conventional stochastic Liouville equations.

Findings

Effective for two-level electron transfer models

Provides a simple modification to existing theories

Includes a criterion for performance estimation

Abstract

We propose a nonperturbative quantum dissipation theory, in term of hierarchical quantum master equation. It may be used with a great degree of confidence to various dynamics systems in condensed phases. The theoretical development is rooted in an improved semiclassical treatment of Drude bath, beyond the conventional high temperature approximations. It leads to the new theory a simple modification but important improvement over the conventional stochastic Liouville equation theory, without extra numerical cost. Its broad range of validity and applicability is extensively demonstrated with two--level electron transfer model systems, where the new theory can be considered as the modified Zusman equation. We also present a criterion, which depends only on the system--bath coupling strength, characteristic bath memory time, and temperature, to estimate the performance of the hierarchical quantum master equation.