Soren Fournais, Bernard Helffer Spectral Methods in Surface Superconductivity

Annotation

In the past decade, the mathematics of superconductivity has been the subject of intense study. This book examines in detail the nonlinear Ginzburg-Landau (GL) functional, the model most commonly used. Specifically, cases in the presence of a strong magnetic field and with a sufficiently large GL parameter kappa are covered.Key topics and features:*Provides a concrete introduction to techniques in spectral theory and PDEs*Offers a complete analysis of the two-dimensional GL-functional with large kappa in the presence of a magnetic field*Treats the three-dimensional case thoroughly*Includes exercises and open problemsSpectral Methods in Surface Superconductivity is intended for students and researchers with a graduate level understanding of functional analysis, spectral theory, and PDE analysis. Anything which is not standard is recalled as well as important semiclassical techniques in spectral theory that are involved in the nonlinear study of superconductivity.