Thermal conductivity of nonlinear waves in disordered chains

TL;DR

This paper investigates how nonlinear waves affect thermal conductivity in disordered chains, revealing temperature-dependent behaviors and regimes of wave spreading that influence heat transport.

Contribution

It provides computational evidence that cubic nonlinearity restores finite thermal conductivity in disordered chains and characterizes its temperature dependence.

Findings

Thermal conductivity exhibits a $ ext{T}^4$ dependence at low temperatures.

Intermediate temperatures show a $ ext{T}^2$ dependence.

Disorder causes Anderson localization, which nonlinearity can overcome.

Abstract

We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity $\kappa(T)$. We find indications for an asymptotic low-temperature $\kappa \sim T^4$ and intermediate temperature $\kappa \sim T^2$ laws. These findings are in accord with theoretical studies of wave packet spreading, where a regime of strong chaos is found to be intermediate, followed by an asymptotic regime of weak chaos (EPL 91 (2010) 30001).