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Journal of Atomic and Molecular Physics

Study of the stability and paramagnetism of Fermi gas based on the semiclassical approximation

Tian Qing

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

Based on the semiclassical approximation,the energy spectrum of single fermion trapped in both gravitational field and strong magnetic field is given. By using Poisson's formula,the thermodynamic potential function of Fermi gas is derived. Furthermore,by using the thermodynamic relationships,the analytical expressions of the stability and magnetic susptibility of the system at low temperature are obtained. The influence mechanism of gravitational field on the thermodynamic properties of the system in the background of strong magnetic field is analysed by numerical simulation.

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Based on the semiclassical approximation,the energy spectrum of single fermion trapped in both gravitational field and strong magnetic field is given. By using Poisson's formula,the thermodynamic potential function of Fermi gas is derived. Furthermore,by using the thermodynamic relationships,the analytical expressions of the stability and magnetic susptibility of the system at low temperature are obtained. The influence mechanism of gravitational field on the thermodynamic properties of the system in the background of strong magnetic field is analysed by numerical simulation.
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.
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.
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.
With semi-classical approximation,thermodynamic properties of Fermi gas trapped in both gravity field and magnetic field are studied. By using theoretical analysis and numerical simulation,influence of gravity field on thermodynamic properties of the system in strong magnetic field is analyzed. It shows that,compared with the case of strong magnetic field only,gravity field makes the energy,chemical potential reduced. With rising temperature,influence of gravity field on chemical potential is gradually enlarged.There is a maximal influence of gravity field on heat capacity. Gravity field makes oscillation of heat capacity almost unchangeable while oscillation center of chemical potential shift down.
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 theoretical analysis and numerical simulation, the stability and the paramagnetism of Fermi gas in a strong magnetic field at low temperatures are studied, and the influences of temperature and magnetic field on the stability and susceptibility of the system are analyzed. The results show that the strong magnetic field causes variation of a system stability, and such a change relates to temperature. While the effects of temperature on stability and susceptibility are relevant to the chemical potential (i.e. the particle number density) of free gas. When the chemical potential is even, the magnetic field weakens the stability of the system, and the increasing of temperature leads to the reduction in the susceptibility of the system. When the chemical potential is odd, the magnetic field strengthens the stability of the system, while the increasing of temperature can increase the susceptibility of the system. With temperature increasing, the effect of the magnetic field on the stability is weakened. With magnetic field increasing, the change of the stability of the system becomes oscillatory, and the oscillation center of the susceptibility shifts down.