Statistics of coherent waves inside media with Lévy disorder

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