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The Journal of Atomic and Molecular Sciences

Relativistic Thermodynamic Properties of Interacting Fermi Gas in a Strong Magnetic Field

Hai-Tang Wang, Men Fu-Dian, Xin-Long Chen

Published Nov 17, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.4208/jams.052313.080313a

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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.
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.
By using the methods of theoretical analysis and numerical simulation, the relativistic effects of the thermodynamic properties of Fermi gas in a strong magnetic field are studied, and the influential mechanisms of temperatures and the magnetic field on the relativistic effects of the system are analyzed.It is shown that, at low temperatures, the effects of temperatures on the relativistic effect relate to the chemical potential of the free system.The magnetic field's effects on the relativistic effects of heat capacity and chemical potential display oscillating characteristics.At high temperatures, the relativistic effects of the thermodynamic quantities trigger oscillations with increasing of temperatures and magnetic field, and its amplitude decreases obviously to disappearing with the increasing of temperatures.However, its amplitude increases evidently due to the amplified magnetic field.
Based on the single particle energy spectrum of weak relativity and Poissons formula,the thermodynamic potential function of Fermi gas in a strong magnetic field is derived. Furthermore, by using the thermodynamic relationships, the analytical expressions of statistic characteristic quantities of the system at low temperatures are obtained, and the influence mechanism of relativistic effect on the statistic properties of the system is analysed. It is shown that the relativistic effect becomes more significant with the magnetic field increasing. Compared with the corresponding oscillating amplitude, the monotonic term, which is caused by the relativistic effect, is much larger than the amplitude for the total energy, however, for the chemical potential and magnetic moment, they are almost of the same order.
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.
By means of the single particle energy spectrum of weak interaction between fermions and Poisson formula,the thermodynamic potential function of relativistic Fermi gas in a strong magnetic field is derived.Based on this,we obtained the criterion of stability for the system.The results show that the mechanics stability of a Fermi gas with weak interacting is influenced by the interacting.While the magnetic field is able to regulate the influence and the relativistic effect has almost no effect on it.
Taking the anomalous magnetic moment into consideration, the analytical expression of the free energy for a weakly interacting Fermi gas in a weak magnetic field is derived by using the pseudopotential method and thermodynamic theory, therefore the thermodynamic properties can be studied. Based on the derived expression, the thermodynamic properties of this system at both high and low temperatures are given, and the effect of anomalous magnetic moment on thermodynamic properties can be analyzed. The effect of anomalous magnetic moment on the thermodynamic properties is related to temperature, and with the rise of temperature this effect increases in the low temperature zone, but decreases in the high temperature zone. For the chemical potential and internal energy of the system, the anomalous magnetic moment strengthens the influence of the magnetic field, but weakens the influence of the interaction. Under the influence of anomalous magnetic moment, the heat capacity of the system decreases in the low temperature zone, but increases in the high temperature zone.