# Heat transport along a chain of coupled quantum harmonic oscillators

## TL;DR

This paper investigates heat transport in a chain of coupled quantum harmonic oscillators connected to heat reservoirs, deriving a closed-form expression for thermal conductance and revealing infinite thermal conductivity in the thermodynamic limit.

## Contribution

It introduces a quantum approach based on a density operator evolution equation to analyze heat transport and derives a closed-form expression for conductance.

## Key findings

- Thermal conductance is finite for small interactions.
- Thermal conductivity diverges in the thermodynamic limit.
- The approach uses covariances and stationary states.

## Abstract

We study the heat transport properties of a chain of coupled quantum harmonic oscillators in contact at its ends with two heat reservoirs at distinct temperatures. Our approach is based on the use of an evolution equation for the density operator which is a canonical quantization of the classical Fokker-Planck-Kramers equation. We set up the evolution equation for the covariances and obtain the stationary covariances at the stationary states from which we determine the thermal conductance in closed form when the interparticle interaction is small. The conductance is finite in the thermodynamic limit implying an infinite thermal conductivity.