Macroscopic Energy Diffusion in a Chain of An-harmonic Oscillators

In Collaboration with Makiko Sasada (Keio University, Japan).

We consider a chain of an-harmonic oscillators whose Hamiltonian dynamics is perturbed by a local energy conserving noise. Under a diffusive space-time rescaling, we prove that the fluctuations of the energy evolve following a linear SPDE, with diffusion coefficient given by the Green-Kubo formula.