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Journal of Beijing Normal University

THERMODYNAMIC PROPERTIES OF THREE-DIMENSIONAL FERMI GASES WITH FERROMAGNETIC COUPLINGS

Wang Baoba

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

Thermodynamic properties of Fermi gas with ferromagnetic coupling were studied under external magnetic field within mean-field theory.The strength of paramagnetic effect was measured by the Landefactor.Specific heat and entropy with reduced magnetic field strength,reduced ferromagnetic couplings intensity,Lande-factor and reduced temperature were calculated.Data showed that the specific heat was proportional to the square of reduced temperature.

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Thermodynamic properties of Fermi gas with ferromagnetic coupling were studied under external magnetic field within mean-field theory.The strength of paramagnetic effect was measured by the Landefactor.Specific heat and entropy with reduced magnetic field strength,reduced ferromagnetic couplings intensity,Lande-factor and reduced temperature were calculated.Data showed that the specific heat was proportional to the square of reduced temperature.
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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.
Based on the Mean Field Theory, the relativistic thermodynamic potential function (RTPF) of interacting Fermi gases in a strong magnetic field is derived. On this basis, by taking the interacting term from the RTPF and using the thermodynamic relations, analytical expressions of the energy, the heat capacity and the chemical potential are calculated at low temperatures. And combined with numerical simulation analysis, the effect of interaction on the thermodynamic properties of the system is analyzed and the regulation mechanisms on the interaction impacts of both the magnetic field and the relativistic effect 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.
The magnetic properties of a charged spin-1 Bose gas with ferromagnetic interactions are investigated within mean-field theory. It is shown that a competition between paramagnetism, diamagnetism and ferromagnetism exists in this system. It is shown that diamagnetism, being concerned with spontaneous magnetization, cannot exceed ferromagnetism in a very weak magnetic field. The critical value of reduced ferromagnetic coupling of the paramagnetic phase to ferromagnetic phase transition I[combining overline](c) increases with increasing temperature. The Landé-factor g is introduced to describe the strength of the paramagnetic effect which comes from the spin degree of freedom. The magnetization density M[combining overline] increases monotonically with g for fixed reduced ferromagnetic coupling I[combining overline] as I[combining overline] > I[combining overline](c). In a weak magnetic field, ferromagnetism makes an immense contribution to the magnetization density. On the other hand, at a high magnetic field, the diamagnetism tends to saturate. Evidence for condensation can be seen in the magnetization density at a weak magnetic field.
Magnetic properties of two-dimensional (2D) spin-polarized Fermi gas with dipole-dipole interaction are studied in the presence of external magnetic field at zero temperature. Within perturbation theory and the second quantization formalism, the total energy is explicitly obtained as a function of three dimensionless parameters: the spin polarization, dipolar coupling, and Zeeman parameters. We examine the effects of these agents on the magnetic properties of 2D Fermi gas. The results show that an induced ferromagnetic phase transition is observed only for adequately large values of magnetic field. This paper offers two controllable factors to change the spin polarization of the system.