Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2000-12-04
Comptes Rendus de l'Academie des Sciences de Paris, tome 2, serie IV, p.419-443 (2001)
Physics
Condensed Matter
Soft Condensed Matter
24 pages, 2 figures, Lecture Notes of the Cargese School on Bose-Einstein condensates (July 2000); typos in Eqs.(72),(121) cor
Scientific paper
We consider two models of interacting Bose gases: a gas of spin one particles in the ground state of a cubic box and a one-dimension Bose gas with contact interactions. We show how to calculate exact eigenstates of the corresponding N-body Hamiltonians. Both models share the property of not leading to the formation of a Bose-Einstein condensate, even at zero temperature, in the strict sense of the existence of a single one-particle state with a macroscopic population. We show that a lot of physical insight can be gained on these two model systems by using the usual Hartree-Fock mean field approach: in this approximation, that we test against the exact result, everything happens as if a single realization of the system was a Bose-Einstein condensate in a state phi breaking the rotational or translational symmetry, and varying in a random way for any new experimental realization.
Castin Yvan
Herzog Christopher
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