Vortices in the Magnetic Ginzburg-Landau Model

Vortices in the Magnetic Ginzburg-Landau Model by Etienne Sandier, Sylvia Serfaty.

With the discovery of type-II superconductivity by Abrikosov, the prediction of vortex lattices, and their experimental observation, quantized vortices have become a central object of study in superconductivity, superfluidity, and Bose--Einstein condensation. This book presents the mathematics of su...

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Bibliographic Details
Main Authors: Sandier, Etienne (Author), Serfaty, Sylvia (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2007.
Edition:1st ed. 2007.
Series:Progress in Nonlinear Differential Equations and Their Applications, 70
Springer eBook Collection.
Subjects:
Partial differential equations.
Mathematical physics.
Functions of complex variables.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Physical Presentation of the Model—Critical Fields
  • First Properties of Solutions to the Ginzburg-Landau Equations
  • The Vortex-Balls Construction
  • Coupling the Ball Construction to the Pohozaev Identity and Applications
  • Jacobian Estimate
  • The Obstacle Problem
  • Higher Values of the Applied Field
  • The Intermediate Regime
  • The Case of a Bounded Number of Vortices
  • Branches of Solutions
  • Back to Global Minimization
  • Asymptotics for Solutions
  • A Guide to the Literature
  • Open Problems.

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