Abstract
The low energy quantal spectrum is considered as a function of the total angular momentum for a system of weakly interacting bosonic atoms held together by an external isotropic harmonic potential. It is found that besides the usual condensation into the lowest state of the oscillator the system exhibits two additional kinds of condensate and associated thermodynamic phase transitions. These new phenomena are derived from the degrees of freedom of ``partition space'' which describe the multitude of different ways in which the angular momentum can be distributed among the atoms while remaining all the time in the lowest state of the oscillator.
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