Søren Fournais, Bernard Helffer

Spectral Methods in Surface Superconductivity (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 324
• Erscheinungstermin: 19. Mai 2010
• Englisch
• ISBN-13: 9780817647971
• Artikelnr.: 43731470

Inhaltsangabe

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

Rezensionen

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)