Subdiffusion via dynamical localization induced by thermal equilibrium fluctuations

TL;DR

This paper uncovers a new mechanism for subdiffusion in classical nonequilibrium systems, showing that thermal noise can induce dynamical localization in velocity space, leading to long-lived transient subdiffusive behavior.

Contribution

It introduces the concept of thermal noise induced dynamical localization in velocity space as a novel cause of subdiffusion, distinct from traditional explanations.

Findings

Subdiffusion can be a long-lived transient in a classical Brownian ratchet.

Thermal noise induces dynamical localization in velocity space.

This localization explains the subdiffusive behavior observed.

Abstract

We reveal the mechanism of subdiffusion which emerges in a straightforward, one dimensional classical nonequilibrium dynamics of a Brownian ratchet driven by both a time-periodic force and Gaussian white noise. In a tailored parameter set for which the deterministic counterpart is in a non-chaotic regime, subdiffusion is a long-living transient whose lifetime can be many, many orders of magnitude larger than characteristic time scales of the setup thus being amenable to experimental observations. As a reason for this subdiffusive behaviour in the coordinate space we identify thermal noise induced dynamical localization in the velocity (momentum) space. This novel idea is distinct from existing knowledge and has never been reported for any classical or quantum systems. It suggests reconsideration of generally accepted opinion that subdiffusion is due to road distributions or strong correlations which reflect disorder, trapping, viscoelasticity of the medium or geometrical constraints.