= Bose-Einstein condensate
{c}
{title2=$N_0=O(N)$}
A Bose-Einstein condensate is a state with macroscopic occupation of a one-particle mode. A phase-selected mean-field description can use $\langle\psi\rangle\ne0$, while a fixed-number finite-volume state need not have a nonzero field expectation. <Bose-Einstein condensation> and <superfluidity> are related but distinct notions; long-wavelength phase fluctuations can invalidate a uniform condensate saddle in low dimensions.
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