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Scattering lengths and universality in superdiffusive Lévy materials.

Authors
Type
Published Article
Journal
Physical Review E
1539-3755
Publisher
American Physical Society
Publication Date
Volume
86
Issue
3 Pt 1
Pages
31125–31125
Identifiers
PMID: 23030884
Source
Medline

Abstract

We study the effects of scattering lengths on Lévy walks in quenched, one-dimensional random and fractal quasilattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk probability distribution, we show that the effect of the varying scattering length can be reabsorbed in the multiplicative coefficient of the scaling length. This leads to a superscaling behavior, where the dy-namical exponents and also the scaling functions do not depend on the value of the scattering length. Within the scaling framework, we obtain an exact expression for the multiplicative coefficient as a function of the scattering length both in the annealed and in the quenched random and fractal cases. Our analytic results are compared with numerical simulations, with excellent agreement, and are supposed to hold also in higher dimensions.

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