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Jisuan wuli

Thermodynamic Properties of Fermi Gas Trapped in Both Gravity Field and Magnetic Field

Tian Qingson

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

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.

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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.
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With quasi-classical approximations,statistic properties of Fermi gas in a strong magnetic field at high temperatures are studied.Analytical statistic characteristic quantities are given,and effects of magnetic field as well as temperature on statistic properties of the system are analyzed.Compared with a system in low temperatures,statistic characteristic quantities of Fermi gas in a strong magnetic field at high temperatures do not oscillate.The magnetic field decreases total energy of the system,and increases the chemical potential,heat capacity,entropy,pressure and stability of the system.The higher the temperature is,the weaker effects of magnetic field on total energy and heat capacity and the stronger effects on chemical potential are.
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 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.
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.
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.