6533b826fe1ef96bd1284950

RESEARCH PRODUCT

Lévy walks and scaling in quenched disordered media.

Luca CaniparoliRaffaella BurioniAlessandro Vezzani

subject

Quantum PhysicsDistribution (mathematics)Stochastic processScatteringElectrical resistivity and conductivityMathematical analysisExponentFunction (mathematics)ScalingCondensed Matter - Statistical MechanicsDisplacement (vector)Mathematics

description

We study L\'evy walks in quenched disordered one-dimensional media, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling relations for the random-walk probability and for the resistivity in the equivalent electric problem, we obtain the asymptotic behavior of the mean square displacement as a function of the exponent characterizing the scatterers distribution. We demonstrate that in quenched media different average procedures can display different asymptotic behavior. In particular, we estimate the moments of the displacement averaged over processes starting from scattering sites, in analogy with recent experiments. Our results are compared with numerical simulations, with excellent agreement.

10.1103/physreve.81.060101https://pubmed.ncbi.nlm.nih.gov/20866363