Abstract
Consequences of Bose-Einstein condensation on the long-range behavior of the two-body density matrix are investigated. An exact relationship between the chemical potential and the functionF 1 (r) characterizing the long-range order of the half-diagonal density matrix is derived. The hydrodynamic(q → 0) limit of the Fourier transformF 1 (q) is discussed and shown to be determined by the pressure dependence of the density of particles in the condensate. Consequences on the residue of the particle-particle Green's function in the phonon branch are pointed out.
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