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

Cedric Bernardin 1 François Huveneers 2
2 CEREMADE
CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
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 λ → 0, and the anharmonicity by a parameter λ ≤ λ. Let κ be the conductivity of the chain, defined through the Green-Kubo formula. Under suitable hypotheses, we show that κ = O(λ) and, in the absence of anharmonic potential, that κ ∼ λ. This is in sharp contrast with the ordered chain for which κ ∼ 1/λ, and so shows the persistence of localization effects for a non-integrable dynamics
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Cedric Bernardin, François Huveneers. Small perturbation of a disordered harmonic chain by a noise and an anharmonic potential. Probability Theory and Related Fields, Springer Verlag, 2012, pp.1--31. ⟨10.1007/s00440-012-0458-8⟩. ⟨ensl-00870164v1⟩

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