Nonequilibrium Stationary States of Harmonic Chains with Bulk Noises

TL;DR

This paper studies the macroscopic behavior and fluctuations of energy and displacement in harmonic chains with bulk noise, revealing new hydrodynamical equations and large deviation results.

Contribution

It introduces new hydrodynamical equations and fluctuation results for harmonic chains with bulk noises, advancing understanding of nonequilibrium stationary states.

Findings

Hydrodynamical equations for energy and displacement profiles

Analysis of fluctuations and large deviations

Validation of Fourier's law in these models

Abstract

We consider a chain composed of $N$ coupled harmonic oscillators in contact with heat baths at temperature $T_\ell$ and $T_r$ at sites 1 and $N$ respectively. The oscillators are also subjected to non-momentum conserving bulk stochastic noises. These make the heat conductivity satisfy Fourier's law. Here we describe some new results about the hydrodynamical equations for typical macroscopic energy and displacement profiles, as well as their fluctuations and large deviations, in two simple models of this type.