On the stability of normal states for a generalized Ginzburg-Landau model

Details On the stability of normal states for a generalized Ginzburg-Landau model On the stability of normal states for a generalized Ginzburg-Landau model

2006-09-08

arxiv.org/abs/math-ph/0609026v5

Physics

Mathematical Physics

52 pages (revised version)

Scientific paper

We formulate a spectral problem related to the onset of superconductivity for a generalized Ginzburg-Landau model, where the order parameter and the magnetic potential are defined in the whole space. This model is devoted to the `proximity effect' for a superconducting sample surrounded by a normal material. In the regime when the Ginzburg-Landau parameter (of the superconducting material) is large, we estimate the critical applied magnetic field for which the normal state will lose its stability, a result that has some roots in the physical literature. In some asymptotic situations, we recover results related to the `standard' Ginzburg-Landau model, where we mention in particular the two-term expansion for the upper critical field obtained by Helffer-Pan.

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