Macroscopic energy diffusion for a chain of anharmonic oscillators

Stefano Olla (1, 2) , Makiko Sasada (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 MICMAC - Methods and engineering of multiscale computing from atom to continuum
3 Departement of Mathematics

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.

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

Domaines: Physique mathématique [math-ph]; Probabilités [math.PR]; Mécanique statistique [cond-mat.stat-mech]

Stefano Olla, Makiko Sasada. Macroscopic energy diffusion for a chain of anharmonic oscillators. 2011. ⟨hal-00626266v1⟩