Ginzburg-Landau phase transition theory and superconductivity
The book aims to collect results obtained in the studies of phase transitions in two- and three-dimensional space based on the Ginzburg-Landau equations (stationary and nonstationary ones), with emphasis on the Ginzburg-Landau (phenomenological) theory of the transition between superconducting and normal states in metals. A physical introduction to the subject is followed by the presentation of mathematical results, collected at three different levels: formal asymptotic findings, obtained at the ``physical'' level of the analysis, rigorously proved mathematical results, and results of large-scale numerical simulations. Special attention is paid to dynamics of vortices in superconductors, including analysis of slow motion and pinning of the vortices in external fields. Also considered in detail is the transition from the full multidimensional models to low-dimensional cases.
scientific article; zbMATH DE number 1549022