Quantum heat current under non-perturbative and non-Markovian conditions: Applications to heat machines.

TLDR: In this article, the authors considered a quantum system strongly coupled to multiple heat baths at different temperatures and investigated the heat transport phenomena in this system using two definitions of the heat current.

Abstract: We consider a quantum system strongly coupled to multiple heat baths at different temperatures. Quantum heat transport phenomena in this system are investigated using two definitions of the heat current: one in terms of the system energy and the other in terms of the bath energy. When we consider correlations among system-bath interactions (CASBIs)—which have a purely quantum mechanical origin—the definition in terms of the bath energy becomes different. We found that CASBIs are necessary to maintain the consistency of the heat current with thermodynamic laws in the case of strong system-bath coupling. However, within the context of the quantum master equation approach, both of these definitions are identical. Through a numerical investigation, we demonstrate this point for a non-equilibrium spin-boson model and a three-level heat engine model using the reduced hierarchal equations of motion approach under the strongly coupled and non-Markovian conditions. We observe the cyclic behavior of the heat curren...