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An application of semi-classical analysis to the asymptotic study of the supercooling field of a superconducting material. (English) Zbl 0779.35104
The authors study the Ginzburg-Landau equations associated to a superconducting film submitted to an external magnetic field parallel to its surface. More precisely, they investigate the values \(h\) of the intensity of the field for which all the normal solutions are metastable. They show that for sufficiently large values of the thickness \(d\) of the film, the lower bound of such values of \(h\) is given by a function of \(d\) whose behaviour is in accordance with previous numerical computations. Their proof involves semiclassical analysis of a related Neumann problem, as \(d\) tends to infinity.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
82D55 Statistical mechanical studies of superconductors
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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References:
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