Thermodynamic Properties Of Dilute Bose Gas

In the nineties of last century, people trapped weakly interacting alkali atomic gas in magnetic-optical potential well, and Bose-Einstein condensation (BEC) was realized by using laser-cooled and evaporating technology. In Bose-Einstein condensate, the atoms congregate at ground state of single particle and their phases are completely same, so Bose-Einstein condensate can be considered as macroscopic quantum interference gas. Since the achievement of Bose-Einstein Condensation (BEC) in ultracold magnetically trapped alkali atomic gas by laser-cooled and cooling by evaporating in 1995, people have done different discussions about BEC from various aspects such as system temperature T =0and , condensation and excitation states, scattering length and , the effect of external potential, the effect of spaces dimensionality, the dynamic features of particles, et al. The investigation indicates these are main influential factors when we study the thermodynamic properties of BEC(spin-0). T>0a >0a<0Because of the limited length, the present article just only involves the thermodynamic properties of the dilute Bose gases of low-temperature, spin-0, weakly repulsive interaction. The effects of spaces dimensionality, finite particle number and interaction are studied,and some generalized analytical results are derived by using the local density approximiation and the grand canonical ensemble.Based on a lot of the reference relating to the experiment and the theory of BEC we have done some theoretical work in the following respects.We analyze the results about the thermodynamic properties of BEC in literatures; We discuss the thermodynamic properties of perfect relativistic q-Bose gases and weakly interacting Bose gases in D-dimensional space, the thermodynamic function are derived; Concerning the occur of condensation and the continuity of heat capacity at the critical temperature, simple criteria are obtained.