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Journal of Anhui Normal University

Low-Temperature Properties of a Weakly Interacting Fermi Gas in Homogenous Gravitational Field

LV Lin

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The low-temperature properties of an idea and a weakly interacting Fermi gas in homogenous gravitational field are studied,based on the semiclassical(Thomas-Fermi) approximation and local-density approximation.The general analytical expressions of several thermodynamic quantities have been derived.The free system,idea system in homogenous gravitational field,and interacting system in homogenous gravitational field are compared.The effects of gravitational field and interparticle interactions on properties of Fermi gas are discussed.

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The low-temperature properties of an idea and a weakly interacting Fermi gas in homogenous gravitational field are studied,based on the semiclassical(Thomas-Fermi) approximation and local-density approximation.The general analytical expressions of several thermodynamic quantities have been derived.The free system,idea system in homogenous gravitational field,and interacting system in homogenous gravitational field are compared.The effects of gravitational field and interparticle interactions on properties of Fermi gas are discussed.
The properties of a weakly interactlng Fermi gas in homogenous gravitational field are studied when the temperature is higher than Fermi temperature,based on the local-density approximation(LDA).The general analytical expressions of several important thermodynamic quantities are derived and the rules of distribution of particle-number density and energy density of the system are analyzed.Both of systems in homogenous gravitational field with and without internal interactlons are compared.The effects of gravitational field and inter-particle interactions on properties of Fermi gas are discussed.
The properties of an ideal Fermi gas in finite 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 are 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 and Fermi gas in infinite gravitational field.The effects of finite gravitational field on properties of Fermi gas are discussed.
The study is on the thermodynamic properties of finite gravitational field weak degenerate ideal Fermi gas.Base on the Thomas-Fermi semiclassical approximation,after deriving the density of states of an ideal Fermi gas in finite gravitational field,the analytic formula of the chemical potential,internal energy and pressure under the condition of weak degeneration is obtained in this paper.The specific impact of the gravity field on the thermodynamic properties of weakly degenerate ideal Fermi gas is analyzed.The result showed that finite gravitational field has effect on the thermodynamic property of the system.
Based on the pseudopotential method and the local-density approximation, the thermodynamic properties of a weakly interacting Fermi gas in a strong magnetic filed are studied, the integrated analytical expressions of thermodynamic quantities of the system are derived, and the effects of magnetic field as well as interparticle interactions on the thermodynamic properties of the system are analyzed. It is shown that at both high and low temperatures, magnetic field may adjust the effects of interacting. At low temperatures, magnetic field can lower the chemical potential, total energy and heat capacity of the system compared with the situation of Fermi gas in the absence of the magnetic field. The repulsive interactions may increase the chemical potential, but reduce the total energy and heat capacity of the system compared with the situation of non-interacting Fermi gas. At high temperatures, magnetic field as well as repulsive interactions can reduce the total energy and increase heat capacity of the system, moreover, strong magnetic field may change the effects of interaction on the total energy and the heat capacity of the system.
The analytical expressions of internal energy, chemical potential and heat capacity of the little parameter r for a weakly interacting Fermi gas in weak magnetic field are derived by using “pseudopotential" method and ensemble theory. Based on the derived expressions, the thermodynamic properties of a weakly interacting Fermi gas in weak magnetic field at both high and low temperatures are given. The effects of magnetic field and interparticle interactions on the thermodynamic properties are discussed. The difference in the effects of magnetic trap and three-dimensional harmonic trap on the properties of the system and their reasons are analyzed.