Modeling the transport of interacting matter-waves in disorder by a non-linear diffusion equation

TL;DR

This paper models the expansion of interacting Bose-Einstein condensates in disordered lattices using a nonlinear diffusion equation, successfully matching experimental results and linking density profiles to microscopic diffusion properties.

Contribution

It introduces a nonlinear diffusion model for matter-wave transport in disordered systems, bridging microscopic interactions and macroscopic expansion behavior.

Findings

The nonlinear diffusion equation accurately reproduces experimental expansion profiles.

A connection is established between density profile shapes and microscopic diffusion coefficients.

The model applies to both short-term and long-term expansion dynamics.

Abstract

We model the expansion of an interacting atomic Bose-Einstein condensate in a disordered lattice with a nonlinear diffusion equation normally used for a variety of classical systems. We find approximate solutions of the diffusion equation that well reproduce the experimental observations for both short and asymptotic expansion times. Our study establishes a connection between the peculiar shape of the expanding density profiles and the microscopic nonlinear diffusion coefficients.