Thermal transport in out of equilibrium quantum harmonic chains

TL;DR

This paper investigates heat transport in quantum harmonic chains coupled to various environments, analyzing steady states and conditions for classical Fourier law behavior in quantum systems.

Contribution

It provides rigorous analytical conditions for steady state existence and explores how environment types influence quantum heat conduction phenomena.

Findings

Conditions for steady state existence are established.

Environmental nature critically affects heat transport behavior.

Classical Fourier law trends can emerge under specific conditions.

Abstract

We address the problem of heat transport in a chain of coupled quantum harmonic oscillators, exposed to the influences of local environments of various nature, stressing the effects that the specific nature of the environment has on the phenomenology of the transport process. We study in detail the behavior of thermodynamically relevant quantities such as heat currents and mean energies of the oscillators, establishing rigorous analytical conditions for the existence of a steady state, whose features we analyse carefully. In particular we assess the conditions that should be faced to recover trends reminiscent of the classical Fourier law of heat conduction and highlight how such a possibility depends on the environment linked to our system.