Energy transport in stochastically perturbed lattice dynamics

TL;DR

This paper studies how energy propagates in a lattice with small random disturbances, showing that on large scales, the energy distribution follows a transport equation and the energy current correlation decays slowly over time.

Contribution

It proves that stochastic perturbations lead to a linear transport equation for the spectral density and predicts a slow decay of energy current correlations in energy-momentum conserving chains.

Findings

Spectral density evolves according to a linear transport equation.

Energy current correlations decay as 1/√t in equilibrium.

Results agree with previous studies using different methods.

Abstract

We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order \varepsilon\^-1 the local spectral density (Wigner function) evolves according to a linear transport equation describing inelastic collisions. For an energy and momentum conserving chain the transport equation predicts a slow decay, as 1/\sqrt{t}, for the energy current correlation in equilibrium. This is in agreement with previous studies using a different method.