Ginzburg-Landau Vortices (1st ed. 2017)

This book is concerned with the study in two dimensions of stationary solutions of u? of a complex valued Ginzburg-Landau equation involving a small parameter ?.

Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids.

The parameter ? has a dimension of a length which is usually small.  Thus, it is of great interest to study the asymptotics as ? tends to zero. One of the main results asserts that the limit u-star of minimizers u? 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.