| The tremendous progress in the experimental techniques for Bose-Einstein condensates during the last decade lead to the realization of almost arbitrarily shaped confinement and waveguide geometries for interacting matter waves. This opens new experimental possibilities for probing the transport of Bose-Einstein condensates through various mesoscopic structures. We numerically investigate the quasi-stationary propagation of a condensate through two dimensional cavities within the mean-field approximation of the condensate. Our calculations rely on a nonlinear Green function method that is based on the Gross-Pitaevskii equation. We study, on the one hand, resonant transport through nearly closed cavities, where the presence of the nonlinearity results in strong nontrivial distortions of the resonance peaks. On the other hand, we are investigating the transmission of the condensate through wide open cavities with chaotic classical dynamics. Here we focus on the question how the scenario of weak localization is modified by the presence of the atom-atom interaction. |
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