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

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 $\lambda \to 0$, and the anharmonicity by a parameter ${\lambda }^{\prime }\le \lambda$. 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.

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Cited by in corpus (1)

• Diffusion in the mean for a periodic Schrödinger equation perturbed by a fluctuating potential