Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation

TL;DR

This paper investigates transient anomalous diffusion in a periodically driven inertial Brownian particle, revealing mechanisms involving ergodicity, symmetry breaking, and velocity relaxation that cause extended superdiffusive, subdiffusive, and normal diffusive regimes.

Contribution

It uncovers the mechanisms behind diffusion anomalies in driven periodic systems, emphasizing the roles of ergodicity, symmetry breaking, and velocity relaxation in transient anomalous diffusion.

Findings

Multiple extended diffusive regimes can occur transiently.

Diffusion anomalies are highly sensitive to system parameters.

Similar diffusion behaviors are observed in various physical systems.

Abstract

We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected recently for a SQUID ratchet dynamics (Spiechowicz J. & Luczka J. Phys. Rev. E 91, 062104 (2015)), the mean square deviation of the particle position from its average may involve three distinct intermediate, although extended diffusive regimes: initially as superdiffusion, followed by subdiffusion and finally, normal diffusion in the asymptotic long time limit. Even though these anomalies are transient effects, their lifetime can be many, many orders of magnitude longer than the characteristic time scale of the setup and turns out to be extraordinarily sensitive to the system parameters like temperature or the potential asymmetry. In the paper we reveal mechanisms of diffusion anomalies related to ergodicity of the system, symmetry breaking of the periodic potential and ultraslow relaxation of the particle velocity towards its steady state. Similar sequences of the diffusive behaviours could be detected in various systems including, among others, colloidal particles in random potentials, glass forming liquids and granular gases.