Scaling properties of field-induced superdiffusion in Continous Time Random Walks

TL;DR

This paper analyzes the scaling behavior of superdiffusion in continuous time random walks, focusing on how external fields influence the probability distributions and moments, with implications for disordered and inhomogeneous materials.

Contribution

It derives the scaling form and asymptotic properties of probability distributions and moments for a broad class of CTRWs under external fields, using novel analytical techniques.

Findings

Derived the scaling form of probability distributions under fields

Established asymptotic properties of moments in superdiffusive CTRWs

Analyzed effects of rare events on power-law tails

Abstract

We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process, often used to model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.