Spectral Methods in Surface Superconductivity
(Sprache: Englisch)
In this book, two expert researchers present a comprehensive treatment of key results concerning the Ginzburg-Landau (GL) functional. Coverage examines in detail the two- and three-dimensional cases of the GL functional as they pertain to superconductivity.
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In this book, two expert researchers present a comprehensive treatment of key results concerning the Ginzburg-Landau (GL) functional. Coverage examines in detail the two- and three-dimensional cases of the GL functional as they pertain to superconductivity.
Klappentext zu „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.
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.
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.
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.
Inhaltsverzeichnis zu „Spectral Methods in Surface Superconductivity “
Preface.- Notation.- Part I Linear Analysis.- 1 Spectral Analysis of Schr¨odinger Operators.- 2 Diamagnetism.- 3 Models in One Dimension.- 4 Constant Field Models in Dimension 2: Noncompact Case.- 5 Constant Field Models in Dimension 2: Discs and Their Complements.- 6 Models in Dimension 3: R3 or R3,+.- 7 Introduction to Semiclassical Methods for the Schr¨odinger Operator with a Large Electric Potential.- 8 Large Field Asymptotics of the Magnetic Schr¨odinger Operator: The Case of Dimension 2.- 9 Main Results for Large Magnetic Fields in Dimension 3.- Part II Nonlinear Analysis.-10 The Ginzburg-Landau Functional.- 11 Optimal Elliptic Estimates.- 12 Decay Estimates.- 13 On the Third Critical Field HC3.- 14 Between HC2 and HC3 in Two Dimensions.- 15 On the Problems with Corners.- 16 On Other Models in Superconductivity and Open Problems.- A Min-Max Principle.- B Essential Spectrum and Persson's Theorem.- C Analytic Perturbation Theory.- D About the Curl-Div System.- E Regularity Theorems and Precise Estimates in Elliptic PDE.- F Boundary Coordinates.- References.- Index.
Bibliographische Angaben
- Autoren: Søren Fournais , Bernard Helffer
- 2010, 324 Seiten, Maße: 15,6 x 23,4 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 0817647961
- ISBN-13: 9780817647964
Sprache:
Englisch
Rezension zu „Spectral Methods in Surface Superconductivity “
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)
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