Experimental investigation of L\'evy flights for step-length distributions with a length-dependent local power exponent

TL;DR

This paper experimentally studies how light propagates in dense atomic vapor, modeling it as a Le9vy flight with a length-dependent index, revealing how atomic collisions influence the step-length distribution.

Contribution

It introduces an experimental method to measure a variable Le9vy index in dense atomic vapor, linking system size and atomic density to the step-length distribution of light.

Findings

Le9vy index varies with system size and atomic density

Step-length distribution is modeled as a length-dependent power law

Atomic collisions cause walkers to alternate between distributions

Abstract

We experimentally investigate the transmission of light by dense atomic vapor. The light propagating in dense atomic vapor can be modeled as a L\'evy flight random walk. For such system, the step-length distribution can be modeled as $P(\ell)\sim \ell^{-1-\alpha(\ell)}$, with the L\'evy index $\alpha(\ell)$ varying smoothly with the step length. Moreover, the walkers alternate between two distinct distributions depending on the occurrence of collisions between atoms in the light scattering. We obtain the L\'evy index from transmission measurements for different system sizes and atomic densities. The measured L\'evy index is determined by the system size $\alpha=\alpha(\ell=L)$. Simulations are made for walkers alternating between two L\'evy like step-length