Homogenization results for a linear dynamics in random Glauber type environment

TL;DR

This paper studies a linear energy-conserving system perturbed by a random Glauber dynamics, establishing hydrodynamic limits and showing the diffusion coefficient's dependence on the random environment's statistics.

Contribution

It provides the first proof of hydrodynamic limits for a non-reversible system in random media with a detailed analysis of the diffusion coefficient's homogenization.

Findings

Hydrodynamic limits are established for the system.

The diffusion coefficient depends only on the statistical properties of the random field.

Convergence of the Green-Kubo diffusion coefficient to a homogenized value is proved.

Abstract

We consider an energy conserving linear dynamics that we perturb by a Glauber dynamics with random site dependent intensity. We prove hydrodynamic limits for this non-reversible system in random media. The diffusion coefficient turns out to depend on the random field only by its statistics. The diffusion coefficient defined through the Green-Kubo formula is also studied and its convergence to some homogenized diffusion coefficient is proved.