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

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

2011-04-10

arxiv.org/abs/1104.1817v4

Phys. Rev. E 84, 021105 (2011)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 11 figures; some concepts rephrased to improve on clarity; a few references added; symbols and line styles in some f

Scientific paper

10.1103/PhysRevE.84.021105

We consider correlated L\'evy 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 $\alpha$, 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 $\alpha$ 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 L\'evy-walks models.

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