Journal ArticleDOI
Existence and Bifurcation Theorems for the Ginzburg‐Landau Equations
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TLDR
In this article, the second-order transition of a superconducting material from normal to superconding state according to the Ginzburg-Landau theory is rigorously discussed and the existence of a mixed state for all values of flux below the critical value is also proved.Abstract:
The second‐order transition of a superconducting material from normal to superconducting state according to the Ginzburg‐Landau theory is rigorously discussed. The bifurcation of a superconducting state is proved for both the Abrikosov mixed state and the case of a film in a parallel magnetic field when the flux or external field is slightly less than critical. The existence of a mixed state for all values of flux below the critical value is also proved.read more
Citations
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Analysis and approximation of the Ginzburg-Landau model of superconductivity
TL;DR: First some well-known features of superconducting materials are reviewed and then various results concerning the model, the resultant differential equations, and their solution on bounded domains are derived.
Journal ArticleDOI
Macroscopic models for superconductivity
TL;DR: There are severe limitations on the range of validity of these analogies and outside this range many interesting open questions can be posed about the solutions to the macroscopic models.
Journal ArticleDOI
Global existence and uniqueness of solutions of the time-dependent ginzburg-landau model for superconductivity
TL;DR: In this paper, the initial-boundary value problems of the timc-dependmt nod near Ginzburg-Landau equations in superconductivity were considered, where the material sample occupies a bounded domain in two nd three dimensional spaces.
Journal ArticleDOI
Stable Nucleation for the Ginzburg-Landau System with an Applied Magnetic Field
TL;DR: In this paper, the Ginzburg-Landau system with an applied magnetic field was considered and the authors analyzed the behavior of solutions when the domain is a cylinder and the applied field is parallel to the axis.
References
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Journal ArticleDOI
Quasi-convexity and the lower semicontinuity of multiple integrals
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Onset of superconductivity in decreasing fields
D. Saint-James,P. G. Gennes +1 more
TL;DR: In this paper, the authors used the Landau-Ginzburg wave function to show that in ideal samples the nucleation of superconducting regions in decreasing fields should always occur near the surface of the sample.
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Bulk solution of ginzburg-landau equations for type ii superconductors: upper critical field region
TL;DR: In this article, a solution of the Ginzburg-Landau equations of the Abrikosov type for a homogeneous type II superconductor just below the upper critical field is described.
Journal ArticleDOI
Bloch Electrons in a Uniform Magnetic Field
TL;DR: In this paper, it was shown that a ray group of unitary operators, isomorphic to pure translations, commutes with the Hamiltonian in the case of uniform magnetic fields, and it was used to construct an effective Hamiltonian appropriate to finite magnetic fields in crystals.