Isaac C. Nunes | Searcharxiv

arXiv2026

Experimental investigation of Lévy flights for step-length distributions with a length-dependent local power exponent

We experimentally investigate the transmission of light by dense atomic vapor. The light propagating in dense atomic vapor can be modeled as a Lévy flight random walk. For such system, the step-length distribution can be modeled as $P(\ell)\sim \ell^{-1-α(\ell)}$, with the Lévy index $α(\ell)$ 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 Lévy index from transmission measurements for different system sizes and atomic densities. The measured Lévy index is determined by the system size $α=α(\ell=L)$. Simulations are made for walkers alternating between two Lévy like step-length

physics.optics↗

arXiv2024

Frequency redistribution and step-size distribution of light scattered by atomic vapor: applications to Lévy flight random walk

The propagation of light that undergoes multiple-scattering by resonant atomic vapor can be described as a Lévy flight. Lévy flight is a random walk with heavy tailed step-size (r) distribution, decaying asymptotically as $P(r)\sim r^{-1-α}$, with $α<2$. The large steps, typical of Lévy flights, have its origins in frequency redistribution of the light scattered by the vapor. We calculate the frequency redistribution function and the step-size distribution for light diffusion in atomic vapor. From the step-size distribution we extract a Lévy parameter $α$ that depends on the step's size. We investigate how the frequency redistribution function and step-size distribution are influenced by the finite size of the vapor and the many-level structure typical for alkali vapors. Finite size of the vapor introduces cutoff on the light scattered spectrum and thus in the size of steps. Multi-level structure introduces oscillations in $P(r)$ slope. Both effects might have an impact on measurables related to the Lévy flight random walk.

physics.optics↗