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

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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Submitted on : Tuesday, November 26, 2013 - 7:15:27 PM
Last modification on : Tuesday, January 18, 2022 - 3:24:14 PM
Long-term archiving on: : Thursday, February 27, 2014 - 11:01:20 AM

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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-00870164v2⟩

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