| This thesis reports some theoretical studies of ultra-cold Fermi gases. This newly created system has attracted much attention in the last few years and also holds great promises in the future.;After a detailed introduction to the physics of BEC-BCS crossover, we consider two main problems in this thesis. In Chapter 4, we discuss the radio-frequency spectroscopy experiment, in which the first clear indication of new quantum state appeared. We gave an elementary derivation of the average shift and the width of the radio-frequency spectra using sum rule argument. We show that the result is in qualitative agreement with experiment.;In Chapter 5, we consider the BEC-BCS crossover problem in the dilute atomic gases frm a general point of view. We show that as a result of the specific properties of the ultra-cold Fermi gases, there exists a universal function which incorporates all the many-body information of the system. Although we do not yet know how to compute the function analytically, we show that many physical quantities can be expressed in terms of this function. It gives an intuitive way of understanding of how universality arises in the cold atomic gases. |
