Realization of hierarchical equations of motion from stochastic perspectives

TL;DR

This paper rigorously derives hierarchical equations of motion for quantum dissipative systems using two stochastic approaches and demonstrates their equivalence through numerical examples.

Contribution

It introduces a unified stochastic framework for deriving HEOM and proves the equivalence of two different stochastic methods.

Findings

HEOM derived from non-Markovian quantum state diffusion.

HEOM derived from stochastic decoupling scheme.

Numerical verification of the formalism's feasibility.

Abstract

The hierarchical equations of motion (HEOM) for a generalized quantum dissipative system is rigorously constructed in the frameworks of two different stochastic dynamical descriptions, i.e., the non-Markovian quantum state diffusion approach as well as the stochastic decoupling scheme. We demonstrated that the HEOMs obtained by these two different stochastic dynamical methods are identical. Moreover, we present some numerical examples to verify the feasibility of our formalism.