Signatures of Lévy flights with annealed disorder

Abstract

We present theoretical and experimental results of Lévy flights of light originating from a random walk of photons in a hot atomic vapor. In contrast to systems with quenched disorder, this system does not present any correlations between the position and the step length of the random walk. In an analytical model based on microscopic first principles including Doppler broadening we find anomalous Lévy-type superdiffusion corresponding to a single-step size distribution P(x) proportional to x^(-1-alpha), with alpha=1. We show that this step size distribution leads to a violation of Ohm's law [T_(diff) proportional to L^(-alpha/2) different from 1/L], as expected for a Lévy walk of independent steps. Furthermore the spatial profile of the transmitted light develops power law tails [I(r) proportional to r^(-3-alpha)]. In an experiment using a slab geometry with hot rubidium vapor, we measured the total diffuse transmission T_(diff) and the spatial profile of the transmitted light T_{diff}(r). We obtained the microscopic Lévy parameter alpha under macroscopic multiple scattering conditions paving the way to investigation of Lévy flights in different atomic physics and astrophysics systems.

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• Topological constraints on the dynamics of vortex formation in a two-dimensional quantum fluid
• Leftward, Rightward and Complete Exit Time Distributions of Jump Processes
• Run-and-tumble particles in slit geometry as a splitting probability problem