Disorder-induced broadening of quantum momentum distribution

TL;DR

This paper investigates how a 2D quantum gas's momentum distribution becomes isotropic and broadens over time due to weak random potentials, providing theoretical expressions and simulation validation.

Contribution

It derives an analytical expression for the long-time average momentum distribution of a quantum gas in a correlated random potential and validates it with simulations.

Findings

Momentum distribution becomes isotropic over time.

Derived expression matches simulation results.

Discussed implications for spatial diffusion.

Abstract

We study the long-time behavior of a non-interacting two-dimensional quantum gas in a weak random potential with long-range correlations. Any peaked initial momentum distribution will eventually become isotropic and broaden due to scattering events with the random potential. We derive an expression for the long-time average of the momentum distribution and test it against computer simulations. We also discuss momentum isotropization and spatial diffusion.