Nonlinear transport of Bose-Einstein condensates through waveguides with disorder

We study the coherent flow of a guided Bose-Einstein condensate incident over a disordered region of length $L$. We introduce a model of disordered potential that originates from magnetic fluctuations inherent to microfabricated guides. This model allows for analytical and numerical studies of realistic transport experiments. The repulsive interaction among the condensate atoms in the beam induces different transport regimes. Below some critical interaction (or for sufficiently small $L$) a stationary flow is observed. In this regime, the transmission decreases exponentially with increasing $L$. For strong interaction (or large $L$), the system displays a transition toward a time-dependent flow with an algebraic decay of the time-averaged transmission.