Thermodynamic Properties Of A Relativistic Fermi System Trapped In A General External Potential

The relativity can be said to have infiltrated into the various areas of research and some physical scientists have paid to the relativistic quantum gas, since Einstein proposed the theory of relativity. Although Fermi gas is not like that the Bose gas occur Bose-Einstein condensate phenomenon at low temperature, but in the appropriate external conditions, the degenerate Fermi systems can be observed in Bardeen-Cooper-Schrieffer phase transition, and attracting effect each other can promote the formation of Cooper pairs that the behave like bosons in the vicinity of Fermi level. But now none of the Fermi systematic studies considers the theory of relativity. This paper mainly studies the relativistic effects effect on the thermodynamic properties of Fermi systems.Firstly, we have been grand partition function of the relativistic Fermi system trapped in general external potential, by the quantum statistical approach. Thus the general analytical expressions of the average particle number, internal energy and heat capacity have been derived, and the Fermi energy of a relativistic Fermi gas trapped in a general external potential is given. Secondly, we have studied the thermodynamic properties of the relativistic Fermi system trapped in hard-sphere potential. By quantum statistics and numerical simulation, we obtain the energy and heat capacity curves of the Fermi system trapped in three-dimensional hard-sphere potential. And the energy and heat capacity in the high- and low-temperature approximations are given. Then we studied the thermodynamic properties of the relativistic of Fermi systems trapped in harmonic potential. The results showed that: both the hard-sphere potential and the resonance potential, the internal energy and heat capacity of relativistic Fermi gas are higher compared with non-relativistic. As the temperature rises, the greater the relativistic Eigen value the larger the internal energy; the larger relativistic Eigen value the lower the transition temperature of the heat capacity; the changes of internal energy and heat capacity is different in low-temperature and high-temperature cases; the internal energy and heat capacity relativistic Fermi system trapped in harmonic potential is higher than that trapped in the hard-sphere potential. Finally, the whole paper is summarized and the prospect of future study in the region is put.