Anomalous diffusion and Tsallis statistics in an optical lattice

TL;DR

This paper links anomalous quantum transport in optical lattices to Tsallis' generalized thermostatistics, showing that the stationary solutions of the momentum equation are Tsallis distributions, thus enabling experimental study of Tsallis statistics.

Contribution

It demonstrates that optical lattices can serve as experimental systems to observe Tsallis statistics through their anomalous transport properties.

Findings

Stationary solutions are Tsallis distributions.

Optical lattices exhibit anomalous diffusion.

Tsallis statistics can be experimentally tested in optical systems.

Abstract

We point out a connection between anomalous quantum transport in an optical lattice and Tsallis' generalized thermostatistics. Specifically, we show that the momentum equation for the semiclassical Wigner function that describes atomic motion in the optical potential, belongs to a class of transport equations recently studied by Borland [PLA 245, 67 (1998)]. The important property of these ordinary linear Fokker--Planck equations is that their stationary solutions are exactly given by Tsallis distributions. Dissipative optical lattices are therefore new systems in which Tsallis statistics can be experimentally studied.