R. Burioni, S. di Santo, S. Lepri, A. Vezzani
We study the effects of scattering lengths on L\'evy walks in quenched disordered and quasi-crystalline one-dimensional materials, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk probability distribution, we show that the exponents describing the asymptotic behavior of its moments as a function of the step lengths distribution does not depend on the value of the scattering length, and feature an universal behavior. The effect of the varying scattering length can be reabsorbed in the multiplicative coefficient of the scaling length of the process, leading to a superscaling behavior. Our analytic results are compared with numerical simulations, with excellent agreement, and are supposed to hold also in higher dimensions.
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http://arxiv.org/abs/1206.0856
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