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 large N thermodynamic behaviour through two dimensionless scaling parameters. These are the reduced temperature t=T/T^0_c 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 non-interacting model. The scaling functions relative to the condensate fraction, energy, chemical potential and moment of inertia are calculated within the Popov approximation.