Thermodynamics of a gas of bosons in a harmonic trap in the Gross-Pitaevskii approximation

With the extension of the Gross-Pitaevskii approximation to non-ground states for weakly interacting dilute atomic gases in magnetic traps, as introduced by Yukalov, Yukalova, and Bagnato, we study the thermodynamic properties of such a system. We analyze the number of particles in the condensate and the heat capacity. Strong dependences on the scattering length and the number of particles are found. For systems with positive scattering lengths, the shifts on critical temperature and the increase of the discontinuity in the heat capacity are predicted to be observable. We study systems with the parameter values of the JILA, MIT, and RQI traps.