Effect of interactions on the diffusive expansion of a Bose-Einstein condensate in a 3D random potential

TL;DR

This paper develops a perturbative theoretical framework to analyze how weak interactions affect the diffusive expansion of a Bose-Einstein condensate in a 3D random potential, revealing interaction-induced renormalization of diffusion.

Contribution

The study introduces an analytical first-order nonlinear correction to the density evolution, linking interaction and disorder effects through a single dimensionless parameter.

Findings

Interactions renormalize the diffusion coefficient.

Nonlinear correction depends on a combined interaction-disorder parameter.

Analytical approach provides insight into disorder-interaction interplay.

Abstract

We theoretically study the influence of weak interactions on the diffusive expansion of a Bose-Einstein condensate in a three-dimensional random potential. For this purpose we develop a perturbative approach and calculate analytically the first-order nonlinear correction to the ensemble-averaged atomic density as a function of position and time. We find that interactions renormalize the typical diffusion coefficient of the condensate. The magnitude of the nonlinear correction is controlled by a single dimensionless parameter that includes both interaction and disorder strengths.