Heat Conduction in two-dimensional harmonic crystal with disorder

TL;DR

This paper investigates heat conduction in a disordered two-dimensional harmonic crystal, revealing how different stochastic heat baths influence the system size dependence of heat current through simulations and analytical methods.

Contribution

It provides new insights into the effect of disorder and noise correlations on heat conduction scaling in 2D harmonic crystals.

Findings

White noise baths yield J ~ 1/L^0.59

Correlated noise baths yield J ~ 1/L^0.51

Analytical results for correlated disorder show a=3/2, matching numerical data

Abstract

We study the problem of heat conduction in a mass-disordered two-dimensional harmonic crystal. Using two different stochastic heat baths, we perform simulations to determine the system size (L) dependence of the heat current (J). For white noise heat baths we find that J ~ 1/L^a with $ a \approx 0.59 $ while correlated noise heat baths gives $ a \approx 0.51 $. A special case with correlated disorder is studied analytically and gives a=3/2 which agrees also with results from exact numerics.