Thermal Conductivity for a Noisy Disordered Harmonic Chain

TL;DR

This paper investigates the thermal conductivity of a disordered harmonic chain with noise, establishing finite bounds and convergence of the Green-Kubo formula, thus confirming positive finite thermal conductivity in the system.

Contribution

It provides rigorous bounds and convergence results for the Green-Kubo formula in a disordered harmonic chain with noise, advancing understanding of thermal transport in such systems.

Findings

Finite positive bounds for thermal conductivity

Convergence of the homogenized Green-Kubo formula

Uniform bounds independent of volume

Abstract

We consider a $d$-dimensional disordered harmonic chain (DHC) perturbed by an energy conservative noise. We obtain uniform in the volume upper and lower bounds for the thermal conductivity defined through the Green-Kubo formula. These bounds indicate a positive finite conductivity. We prove also that the infinite volume homogenized Green-Kubo formula converges.