Transport aspects in anomalous diffusion: Lévy walks

A. Blumen, G. Zumofen, and J. Klafter
Phys. Rev. A 40, 3964 – Published 1 October 1989
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Abstract

In this paper we present a combined analytical and numerical study of transport properties of Lévy walks. Here, within the framework of continuous-time random walks (CTRW’s) with coupled memories, we focus on the probability P0(t) of being at the initial site at time t and on S(t), the mean number of distinct sites visited in time t. We use the connection between P0(t) and S(t), which are related via their Laplace transform, and we reanalyze our previous findings for 〈r2(t)〉, the mean-squared displacement. Furthermore, S(t) shows, as a function of the memory parameters, a very interesting, nonuniversal, nonmonotonic behavior, which we corroborate by numerical simulations in one dimension. We compare the findings with those for decoupled CTRW’s on regular lattices and on fractals.

  • Received 7 March 1989

DOI:https://doi.org/10.1103/PhysRevA.40.3964

©1989 American Physical Society

Authors & Affiliations

A. Blumen

  • Physics Institute and Bayreuther Institut für Makromolekülforschung, University of Bayreuth, D-8580 Bayreuth, West Germany

G. Zumofen

  • Laboratorium für Physikalische Chemie, Eidgenössische Technische Hochschule–Zentrum, CH-8092 Zürich, Switzerland

J. Klafter

  • School of Chemistry, Tel-Aviv University, Tel-Aviv, 69978 Israel

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Vol. 40, Iss. 7 — October 1989

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