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A Free Particle System at Low Density and High Temperature

Zhiwen Li

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The thermodynamics properties of the Fermi system and the Boson system at high temperature and low density without arrliel field is discussed and the valuable result is also educed.

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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.
The effect of spin polarization in the slave boson mean field theory in the strongly correlated Heavy electron systems is discussed concerning the thermodynamical properties of the Hubbard model. The free energy is evaluated by taking into account the effective reduction of the quantum states due to the exclusion of double occupation in a site through the introduction of the spin-dependent slave boson. The magnetic susceptibility, calculated as a function of temperature, shows the Fermi liquid property at low temperature and the local moment behaviour with the proper Curie constant at high temperature. The present results, including the temperature dependence of the specific heat, are compared with the previous results without the reduction of quantum states.
The low-temperature properties of an idea and a weakly interacting Fermi gas in homogenous gravitational field are studied,based on the semiclassical(Thomas-Fermi) approximation and local-density approximation.The general analytical expressions of several thermodynamic quantities have been derived.The free system,idea system in homogenous gravitational field,and interacting system in homogenous gravitational field are compared.The effects of gravitational field and interparticle interactions on properties of Fermi gas are discussed.