Asymptotic densities from the modified Montroll-Weiss equation for coupled CTRWs

Erez Aghion (), David A. Kessler and Eli Barkai
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Erez Aghion: Bar-Ilan University
David A. Kessler: Bar-Ilan University
Eli Barkai: Bar-Ilan University

The European Physical Journal B: Condensed Matter and Complex Systems, 2018, vol. 91, issue 1, 1-17

Abstract: Abstract We examine the bi-scaling behavior of Lévy walks with nonlinear coupling, where χ, the particle displacement during each step, is coupled to the duration of the step, τ, by χ ~ τ β . An example of such a process is regular Lévy walks, where β = 1. In recent years such processes were shown to be highly useful for analysis of a class of Langevin dynamics, in particular a system of Sisyphus laser-cooled atoms in an optical lattice, where β = 3/2. We discuss the well-known decoupling approximation used to describe the central part of the particles’ position distribution, and use the recently introduced infinite-covariant density approach to study the large fluctuations. Since the density of the step displacements is fat-tailed, the last travel event must be treated with care for the latter. This effect requires a modification of the Montroll-Weiss equation, an equation which has proved important for the analysis of many microscopic models.

Date: 2018
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DOI: 10.1140/epjb/e2017-80401-4

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