  We investigate the coherent propagation of dilute atomic Bose-Einstein
condensates through irregularly shaped billiard geometries that are attached to
uniform incoming and outgoing waveguides. Using the mean-field description
based on the nonlinear Gross-Pitaevskii equation, we develop a diagrammatic
theory for the self-consistent stationary scattering state of the interacting
condensate, which is combined with the semiclassical representation of the
single-particle Green function in terms of chaotic classical trajectories
within the billiard. This analytical approach predicts a universal dephasing of
weak localization in the presence of a small interaction strength between the
atoms, which is found to be in good agreement with the numerically computed
reflection and transmission probabilities of the propagating condensate. The
numerical simulation of this quasi-stationary scattering process indicates that
this interaction-induced dephasing mechanism may give rise to a signature of
weak antilocalization, which we attribute to the influence of non-universal
short-path contributions.
