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arXiv · 1111.6383

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

Cédric Bernardin·François Huveneers
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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.

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Cédric Bernardin, François Huveneers. 2011-11-28. Small perturbation of a disordered harmonic chain by a noise and an anharmonic potential. https://arxiv.org/abs/1111.6383

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