Scaling and thermodynamics of a trapped Bose-condensed gas

We investigate the thermodynamics of a Bose gas interacting with repulsive forces and confined in a harmonic trap. We show that the relevant parameters of the system (temperature, number N of atoms, harmonic oscillator length, deformation of the trap, s-wave scattering length) fix its thermodynamic behavior in the large N limit through two dimensionless scaling parameters. These are the reduced temperature t = T/T-c(0) and the ratio eta between the T = 0 value of the chemical potential, evaluated in the Thomas-Fermi limit, and the critical temperature T-c(0) of the noninteracting model. The scaling functions relative to the condensate fraction, energy, chemical potential, and moment of inertia are calculated within the Popov approximation.