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The BCS functional for general pair interactions. (English) Zbl 1161.82027
This paper deals with the study of the Bardeen-Cooper-Schrieffer regime, in the case where the interaction potentials are local for atomic Fermi gases. The mathematical framework is described by a functional, initially derived by Leggett. The main purpose of the present paper is to obtain necessary and sufficient conditions on pair interaction potentials such that the system behaves a superfluid behavior. The authors deduce the existence of a critical temperature below which the Bardeen-Cooper-Schrieffer pairing wave function does not vanish identically. The arguments developed in this paper combine variational techniques with related ${L}^{p}$ estimates.

##### MSC:
 82D55 Superconductors (statistical mechanics) 82B10 Quantum equilibrium statistical mechanics (general)
##### References:
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