Dynamics of quantum dissipation systems interacting with Fermion and Boson grand canonical bath ensembles: Hierarchical equations of motion approach

TL;DR

This paper develops a hierarchical equations of motion framework for quantum dissipation systems interacting with Fermion and Boson baths, enabling analysis of non-Markovian effects in quantum transport and electron transfer.

Contribution

It introduces a unified hierarchical equations of motion formalism for both Fermion and Boson baths based on path-integral methods and fluctuation-dissipation theory.

Findings

Unified treatment of Fermion and Boson baths in hierarchical equations of motion

Explicit incorporation of fluctuation-dissipation relations for non-Markovian baths

Applicability to quantum transport and electron transfer problems

Abstract

A hierarchical equations of motion formalism for a quantum dissipation system in a grand canonical bath ensemble surrounding is constructed, on the basis of the calculus-on-path-integral algorithm, together with the parametrization of arbitrary non-Markovin bath that satisfies fluctuation-dissipation theorem. The influence functionals for both the Fermion or Boson bath interaction are found to be of the same path-integral expression as the canonical bath, assuming they all satisfy the Gaussian statistics. However, the equation of motion formalism are different, due to the fluctuation-dissipation theories that are distinct and used explicitly. The implications of the present work to quantum transport through molecular wires and electron transfer in complex molecular systems are discussed.