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Journal Articles Probability Theory and Related Fields Year : 2012

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

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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 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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Dates and versions

ensl-00870164 , version 1 (05-10-2013)
ensl-00870164 , version 2 (26-11-2013)

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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, 2012, pp.1--31. ⟨10.1007/s00440-012-0458-8⟩. ⟨ensl-00870164v2⟩
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