Energy diffusion in a pinned harmonic chain with free boundary condition and interactions of increasing range

Abstract

We consider a finite two-dimensional pinned harmonic chain with an interaction range that diverges with the system size and with conservative rotational noise. Under a joint scaling in which the interaction range diverges microscopically but vanishes macroscopically, we prove that the expected em- pirical energy measures converge to the unique measure-valued weak solution of the heat equation.