Thermodynamic Properties Of Bose-Einstein Condensation In An External Potential

Bose-Einstein condensation (BEC) is a kind of widespread physical phenomena in manyareas of physics. In the nineties of last century, people trapped weakly interacting alkaliatomic gas in magnetic-optical potential well. Bose-Einstein condensation was realized byusing laser-cooled and evaporating technology in 1995. In Bose-Einstein condensation, theatoms condensate at ground state of single particle and their phases are completely same.From then on, BEC has aroused great concern. so far, more than 40 countries and regions ofrelated research team around the world in the laboratory have done different discussions aboutBEC from various aspects such as system temperature T =0 and, condensation and excitationstates, scattering length and, the effect of external potential, the effect of spacesdimensionality, the dynamic features of particles, et al.Because of the limited length, the present article just only involves the thermodynamicproperties of the dilute Bose gases. In this paper, based on Bose-Einstein condensation atminimized momentum state, the thermodynamic properties of ideal bose gas in extralpotential are studied, and some generalized analytical results are derived by using the localdensity approximiation and the grand canonical system.Based on a lot of the reference relating to the experiment and the theory of BEC we havedone some theoretical work in the following respects. In the first chapter, we briefly introducethe history, realization, experiment technology of BEC. In the second chapter, we not onlyintroduce the concept of BEC, but also summary the Bose gas in the free space and extralpotential in order to get ready for my paper. In the third chapter, based on the Bose-Einsteincondensation at minimized momentum state, we give the quantum state density of Bose gas;some generalized analytical results such as the critical temperature and corresponding particlenumber are derived by using the local density approximiation in the grand canonicalensemble. Concerning the occurring of condensation and the continuity of heat capacity at thecritical temperature, simple criteria are obtained.