L{é}vy walks on finite intervals: A step beyond asymptotics

Abstract

A L{é}vy walk of order $\beta$ is studied on an interval of length $L$, driven out of equilibrium by different-density boundary baths. The anomalous current generated under these settings is nonlocally related to the density profile through an integral equation. While the asymptotic solution to this equation is known, its finite-$L$ corrections remain unstudied despite their importance in the study of anomalous transport. Here a perturbative method for computing such corrections is presented and explicitly demonstrated for the leading correction to the asymptotic transport of a L{é}vy walk of order $\beta =5/3$, which represents a broad universal class of anomalous transport models. Surprisingly, many other physical problems are described by similar integral equations, to which the method introduced here can be directly applied.

7 pages, 2 figures

References in corpus (5)

• Lévy walks
• Fractional Laplacian in Bounded Domains
• Anomalous energy transport in the FPU-beta chain
• Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas
• Temperature profile and boundary conditions in an anomalous heat transport model

Cited by in corpus (5)

• Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
• Harmonically confined particles with long-range repulsive interactions
• Lévy walk dynamics in an external harmonic potential
• Universality in the Onset of Super-Diffusion in Lévy Walks
• Origin of universality in the onset of superdiffusion in Lévy walks