Simple criterion for the occurrence of Bose-Einstein condensation

Details Simple criterion for the occurrence of Bose-Einstein condensation Simple criterion for the occurrence of Bose-Einstein condensation

1995-08-13

arxiv.org/abs/hep-th/9508055v1

Phys.Lett. B368 (1996) 119-123

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, latex, no figures

Scientific paper

10.1016/0370-2693(95)01505-1

We examine the occurrence of Bose-Einstein condensation in both nonrelativistic and relativistic systems with no self-interactions in a general setting. A simple condition for the occurrence of Bose-Einstein condensation can be given if we adopt generalized $\zeta$-functions to define the quantum theory. We show that the crucial feature governing Bose-Einstein condensation is the dimension $q$ associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of the Klein-Gordon operator for relativistic systems. In either case Bose-Einstein condensation can only occur if $q\ge3$.

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