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Acta Physica Sinica

Relativistic effect of ultracold Fermi gas in a strong magnetic field

Men Fu-Dian, He Xiao-Gang, Yong Zhou, Song Xin-Xiang

Published Jan 1, 2011• 1 citation
Publisher

Abstract

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.

DOI
10.7498/aps.60.100502

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Acta Physica Sinica•Jan 1, 2011•2 citations
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.
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 methods of quantum statistics, by considering relativistic correction of single particle and introducing the nonrelativistic free energy of the system of spinless and free fermions,the free energy for Fermi gas in a weak magnetic field is derived, thereout the analytical expressions of thermodynamic quantities of the system under various temperature condtions are given, the effects of relativistic correction on the properties of the nonrelativistic system are exhibited particular and concrete, and the mechanism of the effects is analysed. Compared with those of nonrelativistic situation, it is shown that the effects of relativistic correction always reduce chemical potential. The effects of relativistic correction decrease the total energy and heat capacity at low temperatures, while increase them at high temperatures. The changes of the total energy and heat capacity (not include the low-temperature heat capacity ) are proportional to the square of magnetic field.
Based on the thermodynamic potential function of Fermi gas in a strong magnetic field, using the thermodynamics method, the integrated analytical expressions of thermodynamic quantities of the system at low temperatures are derived, and the effects of the magnetic field on the statistic properties of the system are analysed. It is shown that, as long as the temperature is not zero, the effects of the magnetic field on the thermodynamic quantities of the system contain both oscillatory and non-oscillatory parts. For the non-oscillatory part, compared with the situation of Fermi gas in a weak magnetic field, the influence of the magnetic field on the thermodynamic quantities is not exactly the same. For the oscillatory part, the period and amplitude of the oscillation are all related to the magnetic field. Due to the oscillation, the chemical potential may be greater than Ferim energy of the system, but the oscillation does not affect the thermodynamic stability of the system.
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.
This paper derives the analytical expression of free energy for a weakly interacting Fermi gas in a weak magnetic field, by using the methods of quantum statistics as well as considering the relativistic effect. Based on the derived expression, the thermodynamic properties of the system at both high and low temperatures are given and the relativistic effect on the properties of the system is discussed. It shows that, in comparison with a nonrelativistic situation, the relativistic effect changes the influence of temperature on the thermodynamic properties of the system at high temperatures, and changes the influence of particle-number density on them at extremely low temperature. But the relativistic effect does not change the influence of the magnetic field and inter-particle interactions on the thermodynamic properties of the system at both high and extremely low temperatures.
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.