Ferromagnetic Phase Transition In A Fermi Gas Of Ultracold Atoms

The success for experiment of trapping untracold bosonic gases in 1995 opened up a new research field for us. It gived us a new state of matter:A macroscopicly degenerate quantum state. Since then, this kind of research was shifted on to fermionic atoms. In recent years, with the further study of the properties of an untracold atomic Fermi gas, more and more properties of degenerate atomic Fermi gas have been found. A gas of fermionic atoms become ferromagnetic because of interactions, which is one of important properties with its origin deeply rooted in the quantum nature of the gas of fermionic atoms.This paper is divided into three chapters. In Chapterâ… , The realization of an untracold Fermi gas of atoms and its phase transition are introduced. In this chapter we focus on the study of two-component fermionic gas of ultracold atoms. In Chapterâ…¡, the theories of ferromagnetism are discussed, with the emphasis on the Stoner model.In Chapter III which is the most important part of this dissertation, the properties of the ferromagnetic phase transition of a two-component fermionic gas of ultracold atoms are studied. This chapter contains the new results obtained in the present work performed for this dissertation. We first make use of the Stoner model and the mean-field approximation to derive the Hamiltonian of the fermionic gas of ultracold atoms. We then compute the pressure of the system. And then, through numerical computations, we study the dependencies of the magnetization, volume, and chemical potential on the temperature, pressure, total number of atoms and interaction in the phase transition of this system.