Trapped Bose condensate in a gravitational field

The Bose condensation of atoms in finite 1D and 2D parabolic traps placed in a gravitational field is considered. The distortion of the trap potential in this field is modeled by a combination of two rectangular 1D and 2D traps. The change in the critical temperature Tc is found with regard to the cutoff and renormalization of the spectrum of these model potentials. The shift of the critical temperature Tc in the gravitational field is calculated. The shift sign and magnitude depend on the way of introducing the gravitational field. For a certain choice, three critical temperatures can be sequentially observed. These temperatures can be attributed to three Bose condensations that occur in the cyclic motion of the trap along the Earth (I)-space (II)-Earth (III) route.