Transport in time-dependent random potentials

TL;DR

This paper investigates classical particle dynamics in time-dependent random potentials, deriving a diffusion coefficient and classifying anomalous diffusion, with applications demonstrated in optics and atom optics.

Contribution

It provides a simple expression for the diffusion coefficient in such potentials and classifies the universality classes of anomalous diffusion.

Findings

Derived a simple formula for the diffusion coefficient.

Classified anomalous diffusion into universality classes.

Validated theory with numerical examples in optics and atom optics.

Abstract

The classical dynamics in stationary potentials that are random both in space and time is studied. It can be intuitively understood with the help of Chirikov resonances that are central in the theory of Chaos, and explored quantitatively in the framework of the Fokker-Planck equation. In particular, a simple expression for the diffusion coefficient was obtained in terms of the average power density of the potential. The resulting anomalous diffusion in velocity is classified into universality classes. The general theory was applied and numerically tested for specific examples relevant for optics and atom optics.