Spectral Methods in Surface Superconductivity

In this book, two expert researchers present a comprehensive treatment of key results concerning the Ginzburg-Landau (GL) functional. Coverage examines in detail the two- and three-dimensional cases of the GL functional as they pertain to superconductivity.

During the past decade, the mathematics of superconductivity has been the subject of intense activity. This book examines in detail the nonlinear GinzburgLandau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large GinzburgLandau parameter kappa.

Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduate-level understanding of functional analysis, spectral theory, and the analysis of partial differential equations. The book also includes an overview of all nonstandard material as well as important semi-classical techniques in spectral theory that are involved in the nonlinear study of superconductivity.

Covers groundbreaking results in the fast growing field of superconductivity Provides a concrete introduction to PDEs and spectral methods Covers both two- and three-dimensional cases of GinzburgLandau function extensively Open problems included Includes supplementary material: sn.pub/extras

Inhalt
Linear Analysis.- Spectral Analysis of Schrödinger Operators.- Diamagnetism.- Models in One Dimension.- Constant Field Models in Dimension 2: Noncompact Case.- Constant Field Models in Dimension 2: Discs and Their Complements.- Models in Dimension 3: or