Formulation of the thermodynamic properties of an interacting Bose gas trapped in a power-law potential

An analytical description on the thermodynamic properties of a weakly interacting Bose gas trapped in a power-law potential is presented, based on the local-density approximation (LDA) and the principle of the constancy of chemical potentials in equilibrium. The analytical expressions for some important parameters, such as the critical temperature of Bose–Einstein condensation (BEC), ground-state fraction, chemical potential, total energy and entropy, are derived, and some new characteristics of trapped interacting Bose gases are revealed. It is important that the expressions provide a unified description for the thermodynamic properties of a class of Bose gases so that many results in literature can be included in the present paper. It is more important that the analytical results obtained here are in excellent agreement with the experimental data and the theoretical predictions based on the numerical calculation.