The condensation of ideal Bose gas in a gravitational field

Bose–Einstein condensation of two- and three-dimensional boson gases confined in the one-dimensional gravitational field is investigated. Using the semiclassical approximation method, the expressions for the BEC transition temperature, condensate fraction, heat capacity and the entropy of the system are obtained. The heat capacities of the systems with D  =1, 2, 3 (DD is the dimension) at the critical temperature are discussed. We find that for the 1-D and 2-D boson systems, the heat capacities are continuous, but for the 3-D case there is a gap at the critical temperature TcTc. The entropies of the systems with D=1, 2, 3 are also studied in detail. It is found that the entropies increase with the increasing of the temperature T.