Heat transport through lattices of quantum harmonic oscillators in arbitrary dimensions

TL;DR

This paper analytically investigates heat transport in d-dimensional quantum harmonic oscillator lattices, examining the validity of Fourier's law and the effects of local dephasing on ballistic and diffusive regimes.

Contribution

It provides analytical solutions for heat current in quantum oscillator lattices of arbitrary dimensions, including the impact of dephasing on transport regimes.

Findings

Analytical expression for heat current in quantum harmonic lattices

Dephasing induces transition from ballistic to diffusive transport

Fourier's law validity depends on dephasing and system parameters

Abstract

In d-dimensional lattices of coupled quantum harmonic oscillators, we analyze the heat current caused by two thermal baths of different temperature, which are coupled to opposite ends of the lattice, with focus on the validity of Fourier's law of heat conduction. We provide analytical solutions of the heat current through the quantum system in the non-equilibrium steady state using the rotating-wave approximation and bath interactions described by a master equation of Lindblad form. The influence of local dephasing in the transition of ballistic to diffusive transport is investigated.