Small perturbation of a disordered harmonic chain by a noise and an anharmonic potential

TL;DR

This paper investigates how small noise and anharmonic perturbations affect thermal conductivity in a disordered harmonic chain, revealing persistent localization effects unlike ordered chains.

Contribution

It demonstrates that in disordered chains, conductivity scales linearly with noise strength, contrasting with ordered chains where it diverges, highlighting localization persistence.

Findings

Conductivity scales as O(λ) with noise parameter λ.

In absence of anharmonicity, conductivity is proportional to λ.

Disordered chains show persistent localization effects.

Abstract

We study the thermal properties of a pinned disordered harmonic chain weakly perturbed by a noise and an anharmonic potential. The noise is controlled by a parameter $\lambda \rightarrow 0$, and the anharmonicity by a parameter $\lambda' \le \lambda$. Let $\kappa$ be the conductivity of the chain, defined through the Green-Kubo formula. Under suitable hypotheses, we show that $\kappa = \mathcal O (\lambda)$ and, in the absence of anharmonic potential, that $\kappa \sim \lambda$. This is in sharp contrast with the ordered chain for which $\kappa \sim 1/\lambda$, and so shows the persitence of localization effects for a non-integrable dynamics.