Emergence of distinct relaxation behavior and the quantum regression theorem in the ultrastrong-coupling limit

Abstract

In the framework of open quantum systems, we derive the dynamical equation governing two-time correlation functions in the ultrastrong-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 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 method.