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/content/aip/journal/jmp/57/2/10.1063/1.4941723
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46. Here and the following, we shall use the notation C for generic constants, possibly having a different value in each appearance.
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50.
50. As already mentioned in Section II, complex conjugation in an abstract Hilbert space corresponds to the choice of an anti-linear involution. The reason for its necessity is the antilinearity of the annihilation operator. Alternatively, one could define the annihilation operator to accept as its argument an element of instead of (i.e., one replaces a by , where with being the conjugate linear map such that ()(ϕ) = 〈ψ|ϕ〉), in which case the antilinearity would be naturally absorbed in J. This is the approach followed in Ref. 40.
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/content/aip/journal/jmp/57/2/10.1063/1.4941723
2016-02-24
2016-09-29

Abstract

We review recent results concerning the mathematical properties of the Bardeen–Cooper–Schrieffer (BCS) functional of superconductivity, which were obtained in a series of papers, partly in collaboration with R. Frank, E. Hamza, S. Naboko, and J. P. Solovej. Our discussion includes, in particular, an investigation of the critical temperature for a general class of interaction potentials, as well as a study of its dependence on external fields. We shall explain how the Ginzburg–Landau model can be derived from the BCS theory in a suitable parameter regime.

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