6533b7d6fe1ef96bd1266fd5

RESEARCH PRODUCT

Scattering lengths and universality in superdiffusive L\'evy materials

Stefano LepriSerena Di SantoRaffaella BurioniAlessandro Vezzani

subject

DISORDERScatteringStochastic processMultiplicative functionMathematical analysisFLIGHTSACCELERATED DIFFUSIONScattering lengthCHAOTIC SYSTEMSUniversality (dynamical systems)FractalProbability distributionScalingANOMALOUS DIFFUSIONCondensed Matter - Statistical MechanicsMathematics

description

We study the effects of scattering lengths on L\'evy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk probability distribution, we show that the effect of the varying scattering length can be reabsorbed in the multiplicative coefficient of the scaling length. This leads to a superscaling behavior, where the dynamical exponents and also the scaling functions do not depend on the value of the scattering length. Within the scaling framework, we obtain an exact expression for the multiplicative coefficient as a function of the scattering length both in the annealed and in the quenched random and fractal cases. Our analytic results are compared with numerical simulations, with excellent agreement, and are supposed to hold also in higher dimensions

yearjournalcountryeditionlanguage
2012-09-20
10.1103/physreve.86.031125http://arxiv.org/abs/1206.0856