Stochastic decoupling approach to the quantum dissipative dynamics: Perturbative and non-perturbative treatments

TL;DR

This paper introduces a hierarchical functional derivative method for quantum dissipative systems, enabling both perturbative and non-perturbative analysis beyond common approximations, with efficient numerical implementation.

Contribution

The paper presents a novel hierarchical functional derivative approach that extends quantum dissipative dynamics analysis beyond traditional approximations, including higher-order corrections.

Findings

Recovers the second order Nakajima-Zwanzig quantum master equation

Provides an efficient numerical scheme for complex quantum systems

Enables analysis beyond Markovian and weak-coupling regimes

Abstract

We develop a hierarchical functional derivative method to investigate the reduced dynamics of a quantum dissipative system within the framework of a stochastic decoupling description. Keeping only the lowest order truncation of the hierarchical functional derivatives, one can recover the second order Nakajima-Zwanzig quantum master equation. Taking into account the higher-order corrections, our method can be implemented as a highly efficient numerical scheme for a general quantum dissipative system beyond the usual Markovian, rotating-wave, and weak-coupling approximations.