Macroscopic energy diffusion for a chain of anharmonic oscillators (Q389276)

In this paper the authors discussed the energy diffusion in a chain of anharmonic oscillators where the Hamiltonian dynamics is perturbed by a local energy conserving noise. They proved 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. Moreover, they gave a variational expressions for the thermal diffusivity and some upper and lower bounds.