Statistics of coherent waves inside media with Lévy disorder

Abstract

Structures with heavy-tailed distributions of disorder occur widely in nature. The evolution of such systems, as in foraging for food or the occurrence of earthquakes is generally analyzed in terms of an incoherent series of events. But the study of wave propagation or lasing in such systems requires the consideration of coherent scattering. We consider the distribution of wave energy inside 1D random media in which the spacing between scatterers follow a Lévy $\alpha$-stable distribution characterized by a power-law decay with exponent $\alpha$. We show that the averages of the intensity and logarithmic intensity are given in terms of the average of the logarithm of transmission and the depth into the sample raised to the power $\alpha$. Mapping the depth into the sample to the number of scattering elements yields intensity statistics that are identical to those found for Anderson localization in standard random media. This allows for the separation for the impacts of disorder distribution and wave coherence in random media.

6 pages, 5 figures, minor changes

References in corpus (9)

• Lévy walks
• Leapover lengths and first passage time statistics for Lévy flights
• Nonalgebraic length dependence of transmission through a chain of barriers with a Levy spacing distribution
• Beyond Anderson Localization in 1D: Anomalous Localization of Microwaves in Random Waveguides
• Conductance through quantum wires with Levy-type disorder: universal statistics in anomalous quantum transport
• Controlling conductance statistics of quantum wires by driving ac fields
• Dirac wave transmission in Lévy disordered systems
• Invariance principle for wave propagation inside inhomogeneously disordered materials
• Statistics of quantum transmission in one dimension with broad disorder

Cited by in corpus (1)

• A Lévy flight for electrons in graphene: superdiffusive-to-diffusive transport transition