Macroscopic energy diffusion for a chain of anharmonic oscillators

Sasada, Makiko; Olla, Stefano

Sasada, Makiko; Olla, Stefano (2013), Macroscopic energy diffusion for a chain of anharmonic oscillators, Probability Theory and Related Fields, 157, 3-4, p. 721-775. http://dx.doi.org/10.1007/s00440-012-0469-5

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00626266/fr/

Date

2013

Journal name

Probability Theory and Related Fields

Volume

157

Number

3-4

Publisher

Springer

Pages

721-775

Abstract (EN)

We study the energy diffusion in a chain of anharmonic oscillators where the Hamiltonian dynamics is perturbed by a local energy conserving noise. We prove that under diffusive rescaling of space-time, energy fluctuations diffuse and evolve following an infinite dimensional linear stochastic differential equation driven by the linearized heat equation. We also give variational expressions for the thermal diffusivity and some upper and lower bounds.

Subjects / Keywords

spectral gap; non-gradient models; hydrodynamic limit; thermal conductivity; heat diffusion