 Bose-Einstein condensate

A Bose-Einstein condensate is a state with macroscopic occupation of a one-particle mode. A phase-selected mean-field description can use $⟨\psi ⟩\ne 0$, 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.

A Bose–Einstein condensate (BEC) is a state of matter that occurs at extremely low temperatures, close to absolute zero (0 K or -273.15 °C). It was predicted by the physicists Satyendra Nath Bose and Albert Einstein in the early 20th century.

Inward Bound by Abraham Pais (1988) page 282 shows how this can be generalized from the Maxwell-Boltzmann distribution