Is transport in time-dependent random potentials universal ?

TL;DR

This paper investigates the universal behavior of transport in time-dependent random potentials, revealing diverse universality classes in one dimension and linking diffusion properties to spectral characteristics and chaos theory.

Contribution

It introduces a classification of universality classes for transport in time-dependent random potentials, based on the velocity dependence of the diffusion coefficient, with a focus on one-dimensional systems.

Findings

One-dimensional systems exhibit multiple universality classes.

Diffusion coefficient scales with spectral density of the potential.

Numerical tests confirm theoretical predictions.

Abstract

The growth of the average kinetic energy of classical particles is studied for potentials that are random both in space and time. Such potentials are relevant for recent experiments in optics and in atom optics. It is found that for small velocities uniform acceleration takes place, and at a later stage fluctuations of the potential are encountered, resulting in a regime of anomalous diffusion. This regime was studied in the framework of the Fokker-Planck approximation. The diffusion coefficient in velocity was expressed in terms of the average power spectral density, which is the Fourier transform of the potential correlation function. This enabled to establish a scaling form for the Fokker-Planck equation and to compute the large and small velocity limits of the diffusion coefficient. A classification of the random potentials into universality classes, characterized by the form of the diffusion coefficient in the limit of large and small velocity, was performed. It was shown that one dimensional systems exhibit a large variety of novel universality classes, contrary to systems in higher dimensions, where only one universality class is possible. The relation to Chirikov resonances, that are central in the theory of Chaos, was demonstrated. The general theory was applied and numerically tested for specific physically relevant examples.