For a homogeneous bosonic condensate, the one-body density matrix retains a nonzero long-distance component. More generally, macroscopic occupation is identified by an eigenvalue of that density matrix proportional to particle number. This gives a number-conserving description even when the one-point annihilation-field expectation vanishes. In a paired fermionic system the corresponding macroscopic order belongs to the two-particle density matrix, rather than an electron single-particle condensate.
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