Heat exchange mediated by a quantum system

TL;DR

This paper develops a quantum theoretical framework using the generalized quantum Langevin equation to analyze heat transfer between reservoirs mediated by quantum systems, addressing Fourier's law, anomalous heat currents, and thermal conductivity.

Contribution

It provides general expressions for heat current and conductance for arbitrary coupling and temperature regimes, applying these to fundamental questions in quantum heat transfer.

Findings

Derived expressions for heat current and conductance.

Explored the origin of Fourier's law in quantum systems.

Revisited the minimum thermal conductivity in scaling theory.

Abstract

We consider heat transfer between two thermal reservoirs mediated by a quantum system using the generalized quantum Langevin equation. The thermal reservoirs are treated as ensembles of oscillators within the framework of the Drude-Ullersma model. General expressions for the heat current and thermal conductance are obtained for arbitrary coupling strength between the reservoirs and the mediator and for different temperature regimes. As an application of these results we discuss the origin of Fourier's law in a chain of large, but finite subsystems coupled to each other by the quantum mediators. We also address a question of anomalously large heat current between the STM tip and substrate found in a recent experiment. The question of minimum thermal conductivity is revisited in the framework of scaling theory as a potential application of the developed approach.