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The critical temperature for the BCS equation at weak coupling. (English) Zbl 1137.82025
In this paper it is studied the Bardeen-Cooper-Schrieffer (BCS) equation for a Fermi gas at real chemical potential μ and positive temperature T, with local two-body interaction λV(x), where λ denotes a coupling constant and vL 1 ( 3 )L 3/2 ( 3 ). The main result of the present paper establishes the asymptotic behaviour of the critical temperature as λ approaches 0. There are also obtained necessary and sufficient conditions on V(x) for the existence of a nontrivial solution for all values of λ>0. The approach developed in this paper is not restricted to the kinetic energy K T,μ appearing in the BCS model, but it can be adopted to any symbol vanishing on a manifold of codimension at least one.

MSC:
82D55Superconductors (statistical mechanics)
46N50Applications of functional analysis in quantum physics
82D50Superfluids (statistical mechanics)
81Q10Selfadjoint operator theory in quantum theory, including spectral analysis
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