Heat transport in quantum harmonic chains with Redfield baths

TL;DR

This paper presents an explicit solution method for heat transport in quantum harmonic chains coupled to thermal baths, revealing classical and universal heat current behaviors in different regimes.

Contribution

It introduces an analytic solution to the Redfield master equation for quadratic bosonic systems, including disordered chains, with insights into heat transport properties.

Findings

Analytic solution for Redfield master equation in harmonic chains

Vanishing temperature gradient and constant heat current in homogeneous chains

Universal heat current scaling in disordered gapped chains

Abstract

We provide an explicit method for solving general markovian master equations for quadratic bosonic Hamiltonians with linear bath operators. As an example we consider a one-dimensional quantum harmonic oscillator chain coupled to thermal reservoirs at both ends of the chain. We derive an analytic solution of the Redfield master equation for homogeneous harmonic chain and recover classical results, namely, vanishing temperature gradient and constant heat current in the thermodynamic limit. In the case of the disordered gapped chains we observe universal heat current scaling independent of the bath spectral function, the system-bath coupling strength, and the boundary conditions.