Spectral Methods in Surface Superconductivity

 
9780817672478: Spectral Methods in Surface Superconductivity

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. 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.

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Review:

From the reviews:

“The book is concerned with the analysis of mathematical problems connected with the theory of superconductivity. The authors consider a standard basic model of superconductivity described by the Ginzburg-Landau functional. ... The authors attempt to make the book self-contained, having graduate students and researchers in mind. For this purpose, at the end of the book they add various appendices containing somewhat standard material. ... The book concludes with a fairly complete bibliography on the subject.” (Yuri A. Kordyukov, Mathematical Reviews, Issue 2011 j)

From the Back Cover:

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.

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