Theoretical Investigations On The Thermodynamic Properties Of Fermi Gases

The achievements of degenerate Fermi gases and the successful observations of molecular BEC (Bose-Einstein condensation) in experimental researches have created a wave of renewed interest in the theoretical study of the low temperature properties of Fermi gases. The dissertation is contributed to the investigations on the thermodynamic characteristics of ultracold Fermi gases, which include the spatial and momentum distributions of a weakly interacting Fermi gas trapped in a spherical-symmetric external potential, the thermodynamic properties of a relativistic ideal Fermi gas with particle-antiparticle pair production and the properties of an ideal Fermi gas with q-deformed Fermi-Dirac distribution. The results obtained here may be helpful to the further understanding of the degenerate behaviors of Fermi gases at low temperatures and the underlying nature of various macroscopic quantum effects. The main contents are arranged as follows:In Chapter 2, the spatial and momentum distributions of a weakly interacting Fermi gas trapped in a spherical symmetric power-law potential are investigated, based on the mean field approximation. The effects of the external potential, interatomic interaction and temperature on the spatial and momentum distributions are discussed. It is shown that, when T = 0K, all the particles distribute inside the spherical region with a certain radius in both the coordinate and momentum spaces, and consequently, the concept of "Fermi spheres" in the two spaces is introduced. The problem of how the sizes of the "Fermi spheres" depend on the external potential and interatomic interaction is discussed. When T≠0K, some particles escape out of the "Fermi spheres" and the distribution curves become smoother. In addition, it is found that the effects of the interatomic interaction on the spatial and momentum distributions are different: the repulsive interaction results in the smoother spatial distribution curve but steeper momentum distribution curve.In Chapter 3, the thermodynamic properties of relativistic Fermi gas are studied, in which the effects of particle-antiparticle pair production are taken into account. It is shown that when the kinetic energy of a particle is comparable with its static energy, the relativistic effects can not be ignored even when T→0K . It is also observed that the effects of the pair production are negligible at low temperatures, but may results in some novel characteristics at high temperatures, which include the asymptotic behavior ofμ→0 and the rapid increase of the heat capacity in the hightemperature regions, etc..In Chapter 4, the thermostatistic properties of a q-deformed Fermi gas with a general energy spectrum are researched. It is revealed that the thermostatistic properties of q-deformed Fermi gases are different from those of ordinary ones. However, if q→1, all the properties of q-deformed Fermi gases will reduced to those of the ordinary Fermi systems. This indicates that q-deformed statistics may be considered as a more generalized statistical theory.