Novel ground state properties of rotating Bose gases have been intensively
studied in the context of neutral cold atoms. We investigate the rotating Bose
gas in a trap from a thermodynamic perspective, taking the charged ideal Bose
gas in magnetic field (which is equivalent to a neutral gas in a synthetic
magnetic field) as an example. It is indicated that the Bose-Einstein
condensation temperature is irrelevant to the magnetic field, conflicting with
established intuition that the critical temperature decreases with the field
increasing. The specific heat and Landau diamagnetization also exhibit
intriguing behaviors. In contrast, we demonstrate that the condensation
temperature for neutral Bose gases in a rotating frame drops to zero in the
fast rotation limit, signaling a non-condensed quantum phase in the ground
state.Comment: 4 pages, 1 figur