Pierfrancesco Buonsante - Università di Parma #
Transport and Scaling in Quenched 2D and 3D Lévy quasicrystals 
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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 <i> single-long jump </i>
approximation, we analytically determine the long-time 
asymptotic behaviour of the moments of the probability 
distribution, as a function of &alpha; and of the dynamic 
exponent <i>z</i> 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&eacute;vy-walk models. <br/><br/>
<a href="http://arxiv.org/abs/1104.1817">arxiv:1104.1817</a>