Perturbative analysis of anharmonic chains of oscillators out of equilibrium

TL;DR

This paper develops a perturbative method to analyze how small anharmonicities affect the stationary correlations and heat transport in a non-equilibrium harmonic chain, revealing size-independent heat current corrections and unusual temperature profiles.

Contribution

It introduces a first-order perturbative approach to compute corrections in anharmonic chains out of equilibrium, including a formula for the covariance matrix of the invariant state.

Findings

First-order correction to heat current is system-size independent.

Temperature profile remains linear when on-site harmonic potential is absent.

The temperature gradient's sign opposes the temperature difference of heat baths.

Abstract

We compute the first-order correction to the correlation functions of the stationary state of a stochastically forced harmonic chain out of equilibrium when a small on-site anharmonic potential is added. This is achieved by deriving a suitable formula for the covariance matrix of the invariant state. We find that the first-order correction of the heat current does not depend on the size of the system. Second, the temperature profile is linear when the harmonic part of the on-site potential is zero. The sign of the gradient of the profile, however, is opposite to the sign of the temperature difference of the two heat baths.