Ginzburg-Landau vortices
著者
書誌事項
Ginzburg-Landau vortices
（Modern Birkhäuser classics）
Birkhäuser , Springer, c2017
- : [pbk.]
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注記
"Reprint of the 1994 edition"
Includes bibliographical references (p. [154]-158) and index
内容説明・目次
内容説明
This book is concerned with the study in two dimensions of stationary solutions of ue of a complex valued Ginzburg-Landau equation involving a small parameter e. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter e has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as e tends to zero.
One of the main results asserts that the limit u-star of minimizers ue exists. Moreover, u-star is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree - or winding number - of the boundary condition. Each singularity has degree one - or as physicists would say, vortices are quantized.
The material presented in this book covers mostly original results by the authors. It assumes a moderate knowledge of nonlinear functional analysis, partial differential equations, and complex functions. This book is designed for researchers and graduate students alike, and can be used as a one-semester text. The present softcover reprint is designed to make this classic text available to a wider audience.
目次
Introduction.- Energy Estimates for S1-Valued Maps.- A Lower Bound for the Energy of S1-Valued Maps on Perforated Domains.- Some Basic Estimates for ue.- Toward Locating the Singularities: Bad Discs and Good Discs.- An Upper Bound for the Energy of ue away from the Singularities.- ue_n: u-star is Born! - u-star Coincides with THE Canonical Harmonic Map having Singularities (aj).- The Configuration (aj) Minimizes the Renormalization Energy W.- Some Additional Properties of ue.- Non-Minimizing Solutions of the Ginzburg-Landau Equation.- Open Problems.
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