Abstract
Using recent results by the authors on the spectral asymptotics of the Neumann Laplacian with magnetic field, we give precise estimates on the critical field, \(H_{C_3}\), describing the appearance of superconductivity in superconductors of type II. Furthermore, we prove that the local and global definitions of this field coincide. Near \(H_{C_3}\) only a small part, near the boundary points where the curvature is maximal, of the sample carries superconductivity. We give precise estimates on the size of this zone and decay estimates in both the normal (to the boundary) and parallel variables.
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Communicated by B. Simon
The two authors are supported by the European Research Network ‘Postdoctoral Training Program in Mathematical Analysis of Large Quantum Systems’ with contract number HPRN-CT-2002-00277, and the ESF Scientific Programme in Spectral Theory and Partial Differential Equations (SPECT). Part of this work was carried out while S.F. visited CIMAT, Mexico.
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Fournais, S., Helffer, B. On the Third Critical Field in Ginzburg-Landau Theory. Commun. Math. Phys. 266, 153–196 (2006). https://doi.org/10.1007/s00220-006-0006-4
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DOI: https://doi.org/10.1007/s00220-006-0006-4