Simple criterion for the occurrence of Bose-Einstein condensation and the Meissner-Ochsenfeld effect

Details Simple criterion for the occurrence of Bose-Einstein condensation and the Meissner-Ochsenfeld effect Simple criterion for the occurrence of Bose-Einstein condensation and the Meissner-Ochsenfeld effect

1997-03-17

arxiv.org/abs/cond-mat/9703161v1

Physics

Condensed Matter

Statistical Mechanics

12 pages, RevTeX, uses amssymb

Scientific paper

10.1103/PhysRevD.55.7797

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 is given. We show that condensation can occur only if $q\geq 3$, where $q$ is the dimension 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. Furthermore we show that the criterion for the appearance of the Meissner-Ochsenfeld effect is closely connected with that for the appearance of Bose-Einstein condensation.

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