L\'{e}vy walk dynamics in mixed potentials from the perspective of random walk theory

TL;DR

This paper analyzes Levy walk dynamics under constant and harmonic potentials using random walk theory, revealing non-Gaussian stationary states and anomalous diffusion behaviors.

Contribution

It introduces Hermite polynomial approximation to study Levy walks in complex potentials, uncovering new features of their stationary distributions and diffusion properties.

Findings

Non-Gaussian stationary distribution observed

Faster diffusion compared to classical models

Persistence of anomalous diffusion phenomena

Abstract

L\'evy walk process is one of the most effective models to describe superdiffusion, which underlies some important movement patterns and has been widely observed in the micro and macro dynamics. From the perspective of random walk theory, here we investigate the dynamics of L\'evy walks under the influences of the constant force field and the one combined with harmonic potential. Utilizing Hermite polynomial approximation to deal with the spatiotemporally coupled analysis challenges, some striking features are detected, including non Gaussian stationary distribution, faster diffusion, and still strongly anomalous diffusion, etc.