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.