Diffusion coefficient for the disordered harmonic chain perturbed by an energy conserving noise

Abstract

We investigate the macroscopic behavior of the disordered harmonic chain of oscillators, through energy diffusion. The hamiltonian dynamics of the disordered system is perturbed by a degenerate conservative noise. After rescaling space and time diffusively, energy fluctuations in equilibrium evolve according to a linear heat equation (Simon, Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noise, 2013). Here we concentrate on the diffusion coefficient, given by the non-gradient Varadhan’s approach, and equivalently defined through the Green-Kubo formula. We compare the two approaches and investigate the convergence of the diffusion coefficient in a vanishing noise limit.