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arXiv · 1104.1817

Transport and Scaling in Quenched 2D and 3D Lévy Quasicrystals

Pierfrancesco Buonsante·Raffaella Burioni·Alessandro Vezzani
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Abstract

We consider correlated Lévy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties. We introduce a geometric parameter $α$, playing a role analogous to the exponent characterizing the step-length distribution in random systems. By a {\it single-long jump} approximation, we analytically determine the long-time asymptotic behavior of the moments of the probability distribution, as a function of $α$ and of the dynamic exponent $z$ associated to the scaling length of the process. We show that our scaling analysis also applies to experimentally relevant quantities such as escape-time and transmission probabilities. Extensive numerical simulations corroborate our results which, in general, are different from those pertaining to uncorrelated Lévy-walks models.

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Pierfrancesco Buonsante, Raffaella Burioni, Alessandro Vezzani. 2011-07-02. Transport and Scaling in Quenched 2D and 3D Lévy Quasicrystals. https://doi.org/10.1103/physreve.84.021105

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