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

Erez Aghion, David A. Kessler, Eli Barkai

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14 Scopus citations

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 ~ τβ. 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.

Original languageEnglish
Article number17
JournalEuropean Physical Journal B
Volume91
Issue number1
DOIs
StatePublished - 1 Jan 2018

Bibliographical note

Publisher Copyright:
© 2018, EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature.

Funding

This work was supported by the Israel Science Foundation.

FundersFunder number
Israel Science Foundation

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