We plan to investigate nonlinear bosonic transport processes with electromagnetic and matter waves in complex scattering geometries. A central aim is to study the effect of nonlinearities on interference phenomena, in particular weak (anti-)localization for Bose-Einstein condensates in chaotic mesoscopic cavities, and to provide a semiclassical understanding of this effect. Moreover, we intend to investigate, both on the mean-field and on the many-body level, Aharonov-Bohm-type oscillations of interacting Bose-Einstein condensates propagating through two-arm interferometers. In the electromagnetic context, we plan to study echo and time-reversal focusing phenomena in cavities, nonlinear coherent backscattering of photons in random networks of optical fibers, as well as dynamical tunneling of laser light through microcavities. Finally, our long-term aim is to develop a nonperturbative many-body approach to scattering of ultracold bosonic atoms through quantum dots and disorder geometries.
