Currents and fluctuations of quantum heat transport in harmonic chains

Abstract

Heat transport in open quantum systems is particularly susceptible to the modeling of system-reservoir interactions. It thus requires us to consistently treat the coupling between a quantum system and its environment. While perturbative approaches are successfully used in fields like quantum optics and quantum information, they reveal deficiencies - typically in the context of thermodynamics, when it is essential to respect additional criteria such as fluctuation-dissipation theorems. We use a non-perturbative approach for quantum dissipative dynamics based on a stochastic Liouville-von Neumann equation to provide a very general and extremely efficient formalism for heat currents and their correlations in open harmonic chains. Specific results are derived not only for first- but also for second-order moments, which requires us to account for both real and imaginary parts of bath-bath correlation functions. Spatiotemporal patterns are compared with weak coupling calculations. The regime of stronger system-reservoir couplings gives rise to an intimate interplay between reservoir fluctuations and heat transfer far from equilibrium.