Levy Flights in Inhomogeneous Media

TL;DR

This paper studies how external periodic potentials influence Levy flights, revealing that superdiffusive transport is highly sensitive to potential shape but not to the Levy index, with implications for complex systems.

Contribution

It introduces a novel generalized Fokker-Planck equation to analyze Levy flights in inhomogeneous media, highlighting their sensitivity to potential shape.

Findings

Superdiffusive Levy flights are affected by external potentials.

Asymptotic behavior of Levy flights is independent of the Levy index.

Results apply to systems with topological complexity like polymers and networks.

Abstract

We investigate the impact of external periodic potentials on superdiffusive random walks known as Levy flights and show that even strongly superdiffusive transport is substantially affected by the external field. Unlike ordinary random walks, Levy flights are surprisingly sensitive to the shape of the potential while their asymptotic behavior ceases to depend on the Levy index $\mu $. Our analysis is based on a novel generalization of the Fokker-Planck equation suitable for systems in thermal equilibrium. Thus, the results presented are applicable to the large class of situations in which superdiffusion is caused by topological complexity, such as diffusion on folded polymers and scale-free networks.