Macroscopic energy diffusion for a chain of anharmonic oscillators

Abstract

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.

Accepted for the publication in Probability Theory and Related Fields

References in corpus (1)

• A momentum conserving model with anomalous thermal conductivity in low dimension

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