The Study Of Thermodynamic Properties Of A Fermi System Trapped In Gravitational Field

Recently, the simultaneous study of the effects of external potential and interparticle interactions on thermodynamic system has become a popular subject. Especially, the quantum systems trapped in harmonic potential have been deeply investigated and a series of fruits have been obtained. However, gravitational field is a kind of familiar and important field, and the study of thermodynamic properties of systems in gravitational field have important theoretical and practical significance. In this thesis, the stability conditions of a weakly interacting Fermi gas in homogenous gravitational field, as well as the thermodynamic properties of both an ideal and interacting Fermi gas in homogenous gravitational field are studied, by using some methods of quantum statistics. The effects of external field and interparticle interactions on properties of systems are mainly analyzed.Firstly, the properties of an ideal Fermi gas in finite homogenous gravitational field are studied, based on the semiclassical (Thomas-Fermi) approximation. The general analytical expressions of the total energy, Fermi energy, chemical potential and heat capacity have been derived. Moreover, the analytical expressions of the chemical potential and heat capacity in the high- and low-temperature approximations are given, and then, the example of electron gas is used to calculate exactly. All these results are compared with those of free Fermi gas. The effects of finite gravitational field on properties of Fermi gas are discussed.Secondly, the low-temperature(the temperature which is lower than Fermi temperature) properties of an ideal and a weakly interacting Fermi gas in infinite homogenous gravitational field are studied, based on the semiclassical approximation and local-density approximation(LDA). The general analytical expressions of several thermodynamic quantities have been derived. The free system, both ideal system and interacting system in homogenous gravitational field are analyzed and compared. The effects of gravitational field and interparticle interactions on properties of Fermi gas are discussed. Based on the derived expressions, the properties of a weakly interacting Fermi system in gravitational field at temperatures which are higher than Fermi temperature are further studied, and some results which are different from those of low temperatures are obtained.Then, the total energy of a weakly interacting Fermi gas in homogenous gravitational is derived within local-density approximation framework. By using the energy-minimum theory of stability, the stability conditions of the system at different temperatures are studied, and the analytical expressions of stability conditions are given.Finally, the whole paper is summarized and the prospect of future study in the region is put.