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Article Dans Une Revue Probability Theory and Related Fields Année : 2013

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

Résumé

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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Dates et versions

hal-00777266 , version 3 (17-01-2013)
hal-00777266 , version 1 (05-10-2013)
hal-00777266 , version 2 (26-11-2013)

Identifiants

Citer

Cedric Bernardin, François Huveneers. Small perturbation of a disordered harmonic chain by a noise and an anharmonic potential. Probability Theory and Related Fields, 2013, 157 (1-2), pp.301-331. ⟨10.1007/s00440-012-0458-8⟩. ⟨hal-00777266v3⟩
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