Rare events and scaling properties in field-induced anomalous dynamics

TL;DR

This paper demonstrates that a small external field can induce anomalous diffusion and power-law tails in displacement distributions in various CTRW models, revealing new effects of rare events in disordered systems.

Contribution

It shows how external fields cause anomalous behavior and non-Gaussian distributions in CTRW models, highlighting the role of rare events in anomalous dynamics.

Findings

External fields induce power-law tails in displacement distributions.

Rare events lead to strong anomalous superdiffusion.

Subdiffusive CTRW exhibits non-Gaussian, long-tailed distributions under bias.

Abstract

We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and glassy materials, and in the L\'evy walk process, which describes superdiffusion within inhomogeneous media. For both models, in the presence of an external field, rare events induce a singular behavior in the originally Gaussian displacements distribution, giving rise to power-law tails. Remarkably, in the subdiffusive CTRW, the combined effect of highly fluctuating waiting times and of a drift yields a non-Gaussian distribution characterized by long spatial tails and strong anomalous superdiffusion.