Ginzburg-landau phase transition theory and superconductivity

K.-H Hoffmann, Q Tang

384 pages, parution le 04/12/2001

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Résumé

The theory of complex Ginzburg-Landau type phase transition and its applications to superconductivity and superfluidity has been a topic of great interest to theoretical physicists and has been continously and persistently studied since the 1950s.

In this monograph, we collect, rearrange and refine recent research results in the complex G-L theory with or without immediate applications to the theory of superconductivity. The purpose is to present as many mathematically sound results as possible on various aspects of the PDE system, including rigorous mathematical analysis, formal asymptotics as well as numerical analysis. The book starts with some physical background material and discussions on the modelling and theoretical studies of physicists that invite further mathematical research. We then treat the mathematical scaling in a systematic way and analyze the implications on various limit problems. After addressing the mathematical foundation and formal asymptotic analysis of vortex motion we move on to rigorous results on existence, regularity and long-time behavior of solutions, as well as the vortex location and law of motion. Furthermore, we look at various ways of deriving lower-dimensional models from higher-dimensional ones and study rigorous results for the pinning of vortices. The book is meant to provide an authoritative reference for applied mathematicians, theoretical physicists and engineers interested in the quantitative description of superconductivity using Ginzburg-Landau theory.

Contents

Introduction
Mathematical Foundation
Asymptotics Involving Magnetic Potential
Steady State Solutions
Evolutionary Solutions
Complex G-L Phase Transition Theory
The Slow Motions of Vortices
Thin Plate/Film G-L Models
Pinning Theory
Numerical Analysis
References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	K.-H Hoffmann, Q Tang
Parution	04/12/2001
Nb. de pages	384
Format	16,5 x23,8
Couverture	Relié
Poids	853g
Intérieur	Noir et Blanc
EAN13	9783764364861