PHASE-TRANSITION OF A BOSE-GAS IN A HARMONIC POTENTIAL

We consider a Bose gas confined by a harmonic potential. We define an appropriate thermodynamic limit and analyze the properties of the phas es and phase transition in this limit. Critical properties in the pres ence of the potential are found to be different from, though simply re lated to, those in the usual translationally invariant case. We argue that the properties of magnetically trapped rubidium and sodium gases (in which Bose-Einstein condensation has recently been observed) are w ell approximated by our thermodynamic limit except in a narrow window of temperature around the critical temperature. We also consider the e ffect of the confining potential on the non-equilibrium dynamics follo wing a rapid quench to the ordered side and give a scaling description of the late-time universal dynamics.