Spectral Methods in Surface Superconductivity [electronic resource] / by Søren Fournais, Bernard Helffer.

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.

During the past decade, the mathematics of superconductivity has been the subject of intense activity. This book examines in detail the nonlinear Ginzburg-Landau 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 Ginzburg-Landau parameter kappa. Key topics and features of the work: * Provides a concrete introduction to techniques in spectral theory and partial differential equations * Offers a complete analysis of the two-dimensional Ginzburg-Landau functional with large kappa in the presence of a magnetic field * Treats the three-dimensional case thoroughly * Includes open problems 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.