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

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.