Abstract
It is known that elementary bosons condense in a unique state, not so much because this state has the lowest free-particle energy but because it costs a macroscopic amount of energy to put the particles into different states which can then interact through quantum particle exchanges. Since individual exchanges between the two fermions of a composite boson are ignored when composite particles are replaced by elementary bosons, it is of importance to reconsider the exchange-energy argument for the stability of the Bose-Einstein condensate in the case of composite bosons. We do this here in the light of the new many-body theory which allows us to take exactly into account all possible exchanges between the fermionic components of the composite bosons. We confirm that the condensate of composite bosons occupies a single state, this state being moreover pure: a coherent superposition of states close in energy is shown to be less favorable for both elementary and composite bosons.
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