Ebook: Spectral methods in surface superconductivity
- Genre: Physics // Mechanics: Nonlinear dynamics and chaos
- Tags: Functional Analysis, Strongly Correlated Systems Superconductivity, Partial Differential Equations, Special Functions
- Series: Progress in Nonlinear Differential Equations and Their Applications 77
- Year: 2009
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
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 problems
Spectral 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.