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A pair Hamiltonian model of a non-ideal boson gas. (English) Zbl 0797.58078
Summary: The pressure in the thermodynamic limit of a non-ideal boson gas whose Hamiltonian includes only diagonal and pairing terms can be expressed as the infimum of a functional depending on two measures on momentum space: a positive measure describing the particle density and a complex measure describing the pair density. In this paper we examine this variational problem with the object of determining when the model exhibits Bose- Einstein condensation. In addition we show that if the pairing term in the Hamiltonian is positive then it has no effect.

MSC:
37N99 Applications of dynamical systems
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
82D05 Statistical mechanical studies of gases
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