Emergence of distinct relaxation behaviour and Quantum Regression Theorem in the Ultra-strong Coupling Limit

TL;DR

This paper derives a new dynamical equation for two-time correlations in the ultra-strong coupling regime of open quantum systems, revealing distinct relaxation behaviors and the emergence of the Quantum Regression Theorem after a specific time scale.

Contribution

It introduces a novel approach to describe two-time correlations in the USC regime, highlighting the emergence of the QRT and distinct relaxation behaviors, validated by numerical methods.

Findings

Distinct relaxation behaviors depend on operator types.

Quantum Regression Theorem emerges after the fastest relaxation time.

Excellent agreement with hierarchical equations of motion (HEOM).

Abstract

In the framework of open quantum systems, we derive the dynamical equation governing two-time correlation functions in the ultra-strong coupling (USC) regime between the system and its environment. Unlike the case of the standard weak-coupling regime, in the USC case, we find distinct relaxation behavior for two-time correlators depending on the types of the operators involved in the correlation function. Interestingly, the Quantum Regression Theorem (QRT) emerges after the fastest relaxation time-scale, which is governed by the system-bath coupling strength. We exemplify our findings for the dissipative spin-boson model and further find excellent agreement with the numerically exact hierarchical equations of motion (HEOM) method.