Macroscopic energy diffusion for a chain of anharmonic oscillators

TL;DR

This paper demonstrates that energy fluctuations in a chain of anharmonic oscillators with noise follow a diffusive behavior described by a linear stochastic differential equation, providing bounds for thermal diffusivity.

Contribution

It proves energy diffusion in anharmonic oscillator chains with noise and derives variational formulas and bounds for thermal diffusivity.

Findings

Energy fluctuations diffuse under diffusive scaling.

Energy evolution follows a linear stochastic differential equation.

Provides bounds for thermal diffusivity.

Abstract

We study the energy diffusion in a chain of anharmonic oscillators where the Hamiltonian dynamics is perturbed by a local energy conserving noise. We prove that under diffusive rescaling of space-time, energy fluctuations diffuse and evolve following an infinite dimensional linear stochastic differential equation driven by the linearized heat equation. We also give variational expressions for the thermal diffusivity and some upper and lower bounds.