Thermodynamic properties of a rotating Bose gas in harmonic trap

In this paper, the thermodynamic properties of a rotating Bose gas in harmonic trap are investigated. In particularly, the condensate fraction, critical temperature and heat capacity are analytically calculated. A simple semiclassical approximation, which is the density of state approach, is suggested. This approach is able to include the effects, such as the finite size and the chemical potential when becomes equal to the energy of the lowest energy state, that altered the rotating ideal Bose gas simultaneously. The calculated results show that the thermodynamic properties depend strongly on the rotation rate. The rapid rotation leads to a highly anisotropic confinement potential. The possibility for dimensionality cross-over to lower dimensions for this system is discussed. We compare the outcome results with the experimental measured data of Coddington et al. [Phys. Rev. A 70 , 063607 (2004)].