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

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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.

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Authors and Affiliations

  1. Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel

    Erez Aghion, David A. Kessler & Eli Barkai

  2. Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel

    Erez Aghion & Eli Barkai

Authors
  1. Erez Aghion
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  2. David A. Kessler
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  3. Eli Barkai
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Correspondence to Erez Aghion.

Additional information

Contribution to the Topical Issue “Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook”, edited by Ryszard Kutner and Jaume Masoliver.

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Aghion, E., Kessler, D.A. & Barkai, E. Asymptotic densities from the modified Montroll-Weiss equation for coupled CTRWs. Eur. Phys. J. B 91, 17 (2018). https://doi.org/10.1140/epjb/e2017-80401-4

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