title: Transport and scaling in quenched two- and three-dimensional Lévy quasicrystals.
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 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 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 Lévy-walk models.
authors.affiliation: Dipartimento di Fisica, Università degli Studi di Parma, Viale Usberti 7/a, I-43124 Parma, Italy.
authors.forename: P
authors.initials: P
authors.lastname: Buonsante
authors.forename: R
authors.initials: R
authors.lastname: Burioni
authors.forename: A
authors.initials: A
authors.lastname: Vezzani