Scattering lengths and universality in superdiffusive Lévy materials

Abstract

We study the effects of scattering lengths on Lévy 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

6 pages, 8 figures

References in corpus (4)

• Nonalgebraic length dependence of transmission through a chain of barriers with a Levy spacing distribution
• Conductance through quantum wires with Levy-type disorder: universal statistics in anomalous quantum transport
• Photonic heterostructures with Levy-type disorder: statistics of coherent transmission
• Local and average behavior in inhomogeneous superdiffusive media

Cited by in corpus (10)

• Light in correlated disordered media
• The Single Big Jump Principle in Physical Modelling
• Superdiffusion and Transport in 2d-systems with Lévy Like Quenched Disorder
• Random walks in a one-dimensional Lévy random environment
• Fast rare events in exit times distributions of jump processes
• Anomalous transmission and drifts in one-dimensional Levy structures
• A Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems
• Rare Events in Extreme Value Statistics of Jump Processes with Power Tails
• Rare Events and Single Big Jump Effects in Ornstein-Uhlenbeck Processes
• Limit theorems for Lévy flights on a 1D Lévy random medium