Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach

TL;DR

This paper introduces an exact hierarchical equations of motion framework for simulating quantum systems interacting with complex environments, enabling accurate analysis at any temperature or external field condition.

Contribution

It develops a nonperturbative, residue-corrected hierarchical equations of motion formalism based on path-integral calculus for arbitrary quantum dissipation systems.

Findings

Provides an exact, efficient method for quantum dissipation analysis.

Incorporates residue correction for practical truncation.

Applicable to systems with arbitrary bath environments.

Abstract

A nonperturbative theory is developed, aiming at an exact and efficient evaluation of a general quantum system interacting with arbitrary bath environment at any temperature and in the presence of arbitrary time-dependent external fields. An exact hierarchical equations of motion formalism is constructed on the basis of calculus-on-path-integral algorithm, via the auxiliary influence generating functionals related to the interaction bath correlation functions in a parametrization expansion form. The corresponding continued-fraction Green's functions formalism for quantum dissipation is also presented. Proposed further is the principle of residue correction, not just for truncating the infinite hierarchy, but also for incorporating the small residue dissipation that may arise from the practical difference between the true and the parametrized bath correlation functions. The final residue-corrected hierarchical equations of motion can therefore be used practically for the evaluation of arbitrary dissipative quantum systems.