On the third critical field in Ginzburg-Landau theory

Details On the third critical field in Ginzburg-Landau theory On the third critical field in Ginzburg-Landau theory

2005-07-25

arxiv.org/abs/math-ph/0507064v1

Physics

Mathematical Physics

Scientific paper

10.1007/s00220-006-0006-4

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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