In the wake of successful experiments in Fermi condensates, experimen- tal attention is broadening to include resonant interactions in degenerate Bose- Fermi mixtures. In this thesis we wish to study the equilibrium properties of the fermionic molecules that can be created in such a mixture.

To this end, we first discuss the two body properties of the system, and introduce the model Hamiltonian we use to describe the resonant physics, high- lighting its virtues, as well as its limitations. We then proceed by analyzing the mean field solution of this model, by studying both the equilibrium problem, and the non-equilibrium equations of motion, thus developing a powerful language to discuss the system. We then highlight the limitations of the mean-field approach, and develop a numerically tractable generalized version of this theory, which is able to correctly describe the two-body properties of the system in the low-density limit.

Finally, we study the properties of the system using this generalized mean- field theory, by first analyzing the two-body scattering matrix in the many-body environment, assessing its complex poles in order to understand the stability prop- erties of the Feshbach molecules in the gas. Secondly we solve the equilibrium equations self-consistently, to study the molecular populations and density distri- butions at equilibrium, as a function of external bias magnetic field.

}, year = {2007}, publisher = {University of Colorado Boulder}, address = {Boulder}, }