Statistic Properties Of Fermi Gas In Strong Magnetic Field

In the nineties of last century, people trapped weakly interacting alkali atomic gas inmagnetic-optical potential well, and Bose-Einstein condensation (BEC) was realized by usinglaser-cooled and evaporating technology.Over the last decade, people researched ultracold Fermi gas in many aspects, includingthe following:(1) Fermi gas model are: the ideal Fermi gas, a weakly interacting Fermi gas, stronglyinteracting Fermi gas.(2) Factors of thermodynamic quantities of Fermi gas: spatial dimension effect,relativistic effects, the dynamic characteristics of potential field outside the volume, Fermisystem temperature.(3) To study the thermodynamic properties of a Fermi gas: the total number ofparticles, total energy, chemical potential, heat capacity, magnetic, mechanical stability of theFermi system conditions.(4) Statistical law of Fermi gas are: the Fermi-Dirac statistics, Nonextensivestatistics.Because of the limited length, the present article just only involves thethermodynamic properties of Fermi gas, the calculation of the total number of particles,critical temperature, internal energy, heat capacity and other thermodynamic functions of theFermi gas have been studied.Based on a lot of the reference relating to the experiment and the theory of Fermi gas wehave done some theoretical work in the following respects.1. Reviewed the history of Fermi gas in the existing literature.2. The thermodynamic properties of an ideal Fermi gas in D-dimensional space in thepotential field was discussed, and the analytical expression of thermodynamic quantities wereobtained. The thermodynamic properties of an q-ideal Fermi gas in D-dimensional space inthe potential field was discussed, and the analytical expression of thermodynamic quantities were obtained.3. Discussed in the weak magnetic field of a weakly interacting Fermi gasthermodynamic properties, thermodynamic quantities have been derived.4. Discussed the thermodynamic properties of ideal Fermi gas in the strong magneticfield, thermodynamic quantities have been derived. Discussed the relativistic effect to thestatistical properties of the Fermi gas.