2006/09/08 by Ayman Kachmar, Kachmar, Ayman · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #35P15 35Q55 82D55 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:35P15 #msc:35Q55 #msc:82D55
paper · pdf · doi:10.48550/arxiv.math-ph/0609026
52 pages (revised version)
openalex publication_date 2006/09/08 · arxiv created 2007/06/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.