Transport and scaling in quenched two- and three-dimensional Lévy quasicrystals

Year: 2011

Authors: Buonsante P., Burioni R., Vezzani A.

Autors Affiliation: Dipartimento di Fisica, Università degli Studi di Parma, Viale Usberti 7/a, I-43124 Parma, Italy; INFN, Gruppo Collegato di Parma, viale G. P. Usberti 7/A, 43100 Parma, Italy; Centro S3, CNR–Istituto di Nanoscienze, via Campi 213A, 41125 Modena, Italy

Abstract: We consider correlated Levy 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 a, playing a role analogous to the exponent characterizing the step-length distribution in random systems. By a single-long-jump approximation, we analytically determine the long-time asymptotic behavior of the moments of the probability distribution as a function of a and of the dynamic exponent z associated with 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 Levy-walk models.

Journal/Review: PHYSICAL REVIEW E

Volume: 84 (2)      Pages from: 021105  to: 021105

More Information: This work has been partially supported by the MIUR Project PRIN 2008 \”Nonlinearity and disorder in classical and quantum processes.\” Some of our simulations were performed on the Turing PC cluster of the Milano-Bicocca INFN Section. The authors acknowledge useful discussions with S. Lepri, R. Livi, F. Ginelli, and K. Vynck.
KeyWords: Levy walk; anomalous diffusion; Levy glass; anomalous diffusion; chaotic systems
DOI: 10.1103/PhysRevE.84.021105

Citations: 26
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