Levy Walks On Finite Intervals: A Step Beyond Asymptotics

Asaf Miron

Published 2019-02-24Version 1

The Levy walk of order \beta is studied on a finite interval of length L, driven out of equilibrium by boundary baths. In these settings the current, as well as various other quantities, satisfy integral equations with long-range kernels. For asymptotically large L, the equations are analytically soluble and several results have been derived. However, when finite-size corrections are also considered the equations remain unsolved. Here, a perturbative method is suggested for treating such equations and demonstrated by studying the model's anomalous transport for general \beta. The leading corrections to the asymptotic current and density profile are computed explicitly for \beta=\frac{5}{3}, which corresponds to a universal class of anomalous transport systems.