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Toward the Fourier law for a weakly interacting anharmonic crystal

Olla, Stefano; Liverani, Carlangelo (2012), Toward the Fourier law for a weakly interacting anharmonic crystal, Journal of the American Mathematical Society, 25, p. 555-583. http://dx.doi.org/10.1090/S0894-0347-2011-00724-8

Type
Article accepté pour publication ou publié
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http://hal.archives-ouvertes.fr/hal-00492016/fr/
Date
2012
Nom de la revue
Journal of the American Mathematical Society
Volume
25
Éditeur
American Mathematical Society
Pages
555-583
Identifiant publication
Métadonnées
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Auteur(s)
Olla, Stefano cc
Liverani, Carlangelo
Résumé (EN)
For a system of weakly interacting anharmonic oscillators, perturbed by an energy preserving stochastic dynamics, we prove an autonomous (stochastic) evolution for the energies at large time scale (with respect to the coupling parameter). It turn out that this macroscopic evolution is given by the so called conservative (non-gradient) Ginzburg-Landau system of stochastic differential equations. The proof exploits hypocoercivity and hypoellipticity properties of the uncoupled dynamics.
Mots-clés
hypocoercivity; Weak coupling; scaling limits; Ginzburg-Landau dynamics; heat equation; hypoellipticity