Equivalence of Bose-Einstein condensation and symmetry breaking

Details Equivalence of Bose-Einstein condensation and symmetry breaking Equivalence of Bose-Einstein condensation and symmetry breaking

2004-12-16

arxiv.org/abs/math-ph/0412056v5

Phys.Rev.Lett. 94 (2005) 080402

Physics

Mathematical Physics

An error in my summary of previous results (the definition of F') is corrected. The correction is to be done also in the PRL

Scientific paper

10.1103/PhysRevLett.94.080402

Based on a classic paper by Ginibre [Commun. Math. Phys. {\bf 8} 26 (1968)] it is shown that whenever Bogoliubov's approximation, that is, the replacement of a_0 and a_0^* by complex numbers in the Hamiltonian, asymptotically yields the right pressure, it also implies the asymptotic equality of |< a_0>|^2/V and < a_0^*a_0>/V in symmetry breaking fields, irrespective of the existence or absence of Bose-Einstein condensation. Because the former was proved by Ginibre to hold for absolutely integrable superstable pair interactions, the latter is equally valid in this case. Apart from Ginibre's work, our proof uses only a simple convexity inequality due to Griffiths.

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