A Davies model of an imperfect boson gas is considered. The model includes not only a convex, but also a concave type of an interaction function which depends on a dencity operator. A sufficient condition of the Bose–Einstein condensation is proved. An exact value of the critical temperature is obtained.
For a non-interacting many particle Bose system whose energy operator is diagonal in the number of occupation operators [Formula: see text] upper bounds on the thermal averages [Formula: see text] are obtained. These bounds lead to the proof of Bose–Einstein condensation for finite values of the inverse temperature β and for chemical potential μ=0. Finally for μ<0, in the case of a generalization of the studied model system, the property of Local Gaussian Domination for the grand canonical partition function is proved.
We study the Bose-Einstein condensation of a gas with SUq(2) symmetry. We show, in the thermodynamic limit, that the boson interactions introduced by the quantum group symmetries enhance Bose-Einstein condensation giving a discontinuity in the heat capacity Cv at the critical temperature Tc. The critical temperature and the gap in Cv increase with the value of the parameter q and become approximately constant for q>3.
This chapter focuses on integrating the distribution function over all the states of conserved Bosons to obtain a relation between particle density and the chemical potential. It describes the phenomenon of Bose-Einstein condensation in a perfect boson gas. The chapter discusses the experimental observation of Bose-Einstein condensation in perfect gases. There are two routes to obtaining Bose-Einstein condensation in a perfect gas. One is to reduce the mass of the particle, thus reducing critical density to a low value at a reasonable temperature. The other route is to lower the temperature to the point where the critical density is so low that the particles are too far apart to interact with each other.