Weakly harmonic oscillators perturbed by a conservative noise

TL;DR

This paper investigates how energy diffuses in a chain of weakly harmonic oscillators with conservative noise, showing it can behave as Brownian motion, a superdiffusive Lévy process, or an interpolating process depending on the coupling strength.

Contribution

It introduces a detailed analysis of energy diffusion regimes in weakly harmonic oscillator chains with conservative noise, revealing a transition between Brownian and Lévy stable processes.

Findings

Energy diffusion can be Brownian or superdiffusive Lévy process.

A critical coupling value leads to an interpolating Lévy process.

Energy behavior depends on tuning the coupling constant.

Abstract

We consider a chain of weakly harmonic coupled oscillators perturbed by a conservative noise. We show that by tuning accordingly the coupling constant energy can diffuse like a Brownian motion or superdiffuse like a maximally 3/2-stable asymmetric L{\'e}vy process. For a critical value of the coupling, the energy diffusion is described by a family of L{\'e}vy processes which interpolates between these two processes.