Oleksandr Fialko
Ultracold fermions in optical potentials
Supervisor: Prof. Dr. Klaus Ziegler [Theoretical physics II]
Date of oral examination: 06/11/2010
130 pages, english
In this thesis, many-particle problems of strongly interacting fermions in optical potentials are investigated by means of functional mean-field methods. The integration over microscopic quantum fields (Grassmann fields) has been traded for an integration over degrees of freedom adjusted to the low-energy characteristic of the system (complex fields). This allowed to explore the ground state properties of the system as well as low-energy fluctuations on top of that, which are accessible in experiments. In particular, the superfluid-Mott insulator and the Anderson localization transitions are studied for interacting fermions in optical potentials.