Ultracold gases provide a means to study basic problems in many-body physics, which are difficult to access in a different context. Within the present project, we want to investigate mixtures of fermions and bosons to investigate.

A) strong pairing in Fermi superfluids due to Feshbach resonances or the exchange of bosons
B) the effects of weak disorder in ultracold Bose or Fermi gases.

Our aim is to provide quantitative results for the conditions to reach and verify experimentally paring and superfluidity of fermions in a strong coupling regime. In the context of cold gases in the presence of quenched disorder, we will investigate the statistical properties of correlation functions for weak interactions and disorder. In this regime mesoscopic fluctuations are expected e.g. in noise-correlations or in the interference pattern of overlapping condensates, which have analogies to effects like universal conductance fluctuations in weakly disordered electronic systems.