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

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

2011-11-28

arxiv.org/abs/1111.6383v1

Physics

Mathematical Physics

Scientific paper

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.

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