Custom cover image
Spectral Methods in Surface Superconductivity / by Søren Fournais, Bernard Helffer
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Progress in Nonlinear Differential Equations and Their Applications ; 77 | SpringerLink BücherPublisher: Boston : Springer Science+Business Media, LLC, 2010Description: Online-Ressource (XX, 324p. 2 illus, online resource)ISBN:- 9780817647971
- Supraleitung
- Spektralanalyse
- Hamilton-Operator
- Ginzburg-Landau-Gleichung
- Magnetfeld
- Analysis (Mathematics)
- Mathematical analysis
- Electronics
- Microelectronics
- Superconductivity
- Superconductors
- Partial differential equations
- Special functions
- Differential equations, partial
- Functional analysis
- Functions, special
- Mathematics
- Superconductivity
- Spectral theory (Mathematics)
- Differential equations, Partial
- 515.7
- 515 23
- 537.623
- QA319-329.9
Contents:
Summary: 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.Summary: 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.PPN: PPN: 1649743440Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS | ZDB-2-SMA
""Spectral Methods in Surface Superconductivity""; ""Contents""; ""Preface""; ""Notation""; ""Part I Linear Analysis""; ""1 Spectral Analysis of SchrÂ?odinger Operators""; ""1.1 The Magnetic SchrÂ?odinger Operator""; ""1.2 Self-Adjointness""; ""1.3 Spectral Theory""; ""1.4 Preliminary Estimates for the Dirichlet Realization""; ""1.4.1 Lower bounds""; ""1.4.2 Two-dimensional case""; ""1.4.3 The case of three or more dimensions""; ""1.5 Perturbation Theory for Small B""; ""1.6 Notes""; ""2 Diamagnetism""; ""2.1 Preliminaries""; ""2.2 Diamagnetic Estimates""
""2.3 Monotonicity of the Ground State Energy for Large Field""""2.4 Katoâ€?s Inequality""; ""2.5 Notes""; ""3 Models in One Dimension""; ""3.1 The Harmonic Oscillator on R""; ""3.2 Harmonic Oscillator on a Half-Axis""; ""3.2.1 Elementary properties of hN,Î?""; ""3.2.2 Variation of Î? and Feynmanâ€?Hellmann formula.""; ""3.2.3 Formulas for the moments""; ""3.2.4 On the regularized resolvent""; ""3.3 Montgomeryâ€?s Model""; ""3.4 A Model Occurring in the Analysis of Infinite Sectors""; ""3.5 Notes""; ""4 Constant Field Models in Dimension 2: Noncompact Case""
""4.1 Preliminaries in Dimension 2""""4.2 The Case of R²""; ""4.3 The Case of R²,+""; ""4.4 The Case of an Infinite Sector""; ""4.5 Notes""; ""5 Constant Field Models in Dimension 2: Discs and Their Complements""; ""5.1 Introduction""; ""5.2 A Perturbed Model""; ""5.3 Asymptotics of the Ground State Energy for the Disc""; ""5.4 Application to the Monotonicity""; ""5.5 Notes""; ""6 Models in Dimension 3: R³ or R³,+""; ""6.1 The Case of R³""; ""6.2 The Case of R³,+""; ""6.2.1 An easy upper bound""; ""6.2.2 Preliminary reductions""; ""6.2.3 Spectral bounds""
""6.2.4 Analysis of the essential spectrum""""6.2.5 A refined upper bound: Ï?(Ï?) < 1""; ""6.2.6 Application""; ""6.3 Notes""; ""7 Introduction to Semiclassical Methods for the Schrödinger Operator with a Large Electric Potential""; ""7.1 Harmonic Approximation""; ""7.1.1 Upper bounds""; ""7.1.2 Harmonic approximation in general: Lower bounds""; ""7.1.3 The case with magnetic field""; ""7.2 Decay of Eigenfunctions and Applications""; ""7.2.1 Introduction""; ""7.2.2 Energy inequalities""; ""7.2.3 The Agmon distance""; ""7.2.4 Decay of eigenfunctions for the Schrodinger operator""
""7.2.5 Applications""""7.2.6 The case with magnetic fields but without electric potential""; ""7.3 Notes""; ""8 Large Field Asymptotics of the Magnetic Schrödinger Operator: The Case of Dimension 2""; ""8.1 Main Results""; ""8.2 Proof of Theorem 8.1.1""; ""8.2.1 Upper bounds""; ""8.2.2 Lower bounds""; ""8.2.3 Agmon�s estimates""; ""8.3 Constant Magnetic Field""; ""8.4 Refined Expansions and Spectral Gap""; ""8.5 Monotonicity""; ""8.6 Extensions""; ""8.6.1 Nonconstant magnetic fields with boundary localization""; ""8.6.2 Interior localization""; ""8.6.3 Montgomery�s model revisited""
""8.7 Notes""
No physical items for this record