Thumbnail - No thumbnail

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

Huveneers, François; Bernardin, Cédric (2013), Small perturbation of a disordered harmonic chain by a noise and an anharmonic potential, Probability Theory and Related Fields, 157, 1-2, p. 301-331. http://dx.doi.org/10.1007/s00440-012-0458-8

Type
Article accepté pour publication ou publié
Lien vers un document non conservé dans cette base
http://fr.arxiv.org/abs/1111.6383
Date
2013
Nom de la revue
Probability Theory and Related Fields
Volume
157
Numéro
1-2
Éditeur
Springer
Pages
301-331
Identifiant publication
Métadonnées
Afficher la notice complète
Auteur(s)
Huveneers, François
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Bernardin, Cédric
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
Résumé (EN)
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.
Mots-clés
Green-Kubo formula; noise; anharmonic potential; disordered harmonic chain; thermal properties