Current and universal scaling in anomalous transport

TL;DR

This paper derives a universal scaling law for anomalous diffusion in tilted periodic potentials using fractional Fokker-Planck dynamics, supported by analytical solutions and extensive numerical validation across various potential shapes.

Contribution

It introduces a universal scaling law for anomalous transport in tilted periodic potentials, combining analytical derivation with comprehensive numerical verification.

Findings

Universal scaling law for anomalous diffusion derived

Analytical stationary current solution obtained

Numerical results confirm the scaling law across diverse potentials

Abstract

Anomalous transport in tilted periodic potentials is investigated within the framework of the fractional Fokker-Planck dynamics and the underlying continuous time random walk. The analytical solution for the stationary, anomalous current is obtained in closed form. We derive a universal scaling law for anomalous diffusion occurring in tilted periodic potentials. This scaling relation is corroborated with precise numerical studies covering wide parameter regimes and different shapes for the periodic potential, being either symmetric or ratchet-like ones.