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Acta Physica Sinica

Thermodynamic properties of a weakly interacting Fermi gas

Guozhen Su, Lixuan Chen, 厦门大学物理系，厦门 361005

Published Jan 1, 2004• 13 citations
Publisher

Abstract

The analytical expressions of chemical potential, total energy and heat capacity at a constant volume for a weakly interacting Fermi gas in the absence of external potential are derived by using “pseudopotential” method. Based on the derived expressions, the thermodynamic properties of a weakly interacting Fermi gas trapped in a harmonic potential are studied under the local-density approximation. The effects of interparticle interactions on the properties of the systems are discussed.

DOI
10.7498/aps.53.984

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The analytical expressions of chemical potential, total energy and heat capacity at a constant volume for a weakly interacting Fermi gas in the absence of external potential are derived by using “pseudopotential” method. Based on the derived expressions, the thermodynamic properties of a weakly interacting Fermi gas trapped in a harmonic potential are studied under the local-density approximation. The effects of interparticle interactions on the properties of the systems are discussed.
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.
Based on the theoretical results derived from pseudopotential method and local approximation, this paper studies the thermodynamic stability of a weakly interacting Fermi gas trapped in a harmonic potential by using analytical method of thermodynamics. The effects of the interparticle interactions as well as external potential on the thermodynamic stability of the system are discussed. It is shown that the system is stable as for the complete average, but as for local parts, the system is unstable anywhere. This instability shows that the stability conditions of mechanics cannot be satisfied anywhere, and the stability conditions of thermostatics cannot be satisfied somewhere. In addition, the interactions and external potential have direct effects on the local stability 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.