From normal diffusion to superdiffusion of energy in the evanescent flip noise limit

TL;DR

This paper investigates how energy transport in a harmonic chain transitions from normal diffusion to superdiffusion as a parameter varies, revealing a crossover between two distinct diffusive regimes.

Contribution

It establishes the existence of a crossover between diffusive and superdiffusive energy transport regimes depending on the parameter $\gamma$ in a perturbed harmonic chain.

Findings

Energy diffuses as a heat equation for $\gamma$ of order one.

Energy superdiffuses as a fractional heat equation when $\gamma=0$.

The study demonstrates a transition between these regimes as $\gamma$ varies.

Abstract

We consider a harmonic chain perturbed by an energy conserving noise depending on a parameter $\gamma$. When $\gamma$ is of order one, the energy diffuses according to the standard heat equation after a space-time diffusive scaling. On the other hand, when $\gamma=0$, the energy superdiffuses according to a 3/4 fractional heat equation after a subdiffusive space-time scaling. In this paper, we study the existence of a crossover between these two regimes as a function of $\gamma$.