Quantum regression beyond the Born-Markov approximation for generalized spin-boson models

Abstract

The quantum regression formula for an open quantum system consists in an infinite hierarchy of conditions for its multitime correlation functions, thus requiring full access to the total ``$\mathrm{system}+\mathrm{environment}$'' evolution, and providing a stronger requirement than completely positive (CP) divisibility. Here, we analyze CP divisibility and check the validity of quantum regression beyond the Born-Markov approximation (e.g., the weak-coupling limit) for a class of generalized spin-boson models giving rise to a multilevel amplitude-damping evolution; in all cases, it is possible to engineer the system-bath coupling in such a way that quantum regression is exactly satisfied.