Finite-Size Effects in Strongly-Interacting Fermionic Systems

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Experiments with ultracold fermionic atoms provide a clean and controllable environment to test our understanding of a dynamical formation of condensates and the generation of bound states in strongly interacting systems. These experiments are relevant for a broad collection of phenomena, ranging from superconductivity in metals to the generation of hadronic masses and the state of hadronic matter during the early stages of the evolution of the universe. Providing a consistent theoretical description of the available experimental data is, however, challenging since the phase structure of trapped Fermi gases may strongly depend on the experimental setup, such as the trap geometry and the total particle number. Density Functional Theory combined with functional Renormalization Group techniques offers a great potential for theoretical advances in many-body physics. This project exploits the advantages of both approaches in order to gain a better understanding of confined systems of strongly-interacting fermions and to provide an ab-initio description of condensation and bound-state formation in strongly-interacting theories with an emphasis on the phase structure of trapped strongly-interacting Fermi gases.