Anomalous transport and current fluctuations in a model of diffusing Levy walkers

TL;DR

This paper investigates the steady state behavior and current fluctuations of Levy walkers in open systems and ring geometries, revealing anomalous transport properties due to heavy-tailed flight times.

Contribution

It introduces a detailed analysis of Levy walk transport in open and ring systems, including effects of boundary conditions and size-dependent flight time cut-offs.

Findings

Density profiles and current fluctuations exhibit anomalous behavior.

Finite system size influences current fluctuation characteristics.

Boundary injection/removal rates significantly affect steady state properties.

Abstract

A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a long-tailed distribution with a finite mean but an infinite variance. Here we consider an open system with boundary injection and removal of particles, at prescribed rates, and study the steady state properties of the system. In particular, we compute density profiles, current and current fluctuations in this system. We also consider the case of a finite density of Levy walkers on the ring geometry. Here we introduce a size dependent cut-off in the time of flight distribution and consider properties of current fluctuations.