The motto of connectivity and superconductivity is that the solutions of the Ginzburg-Landau
equations are qualitatively in?uenced by the topology of the boundaries. Special attention is
given to the zero set the set of the positions (usually known as quantum vortices) where the
order parameter vanishes. The paradigm of connectivity and superconductivity is the Little-
Parks e?ect discussed in most textbooks on superconductivity. This volume is intended to serve
as a reference book for graduate students and researchers in physics or mathematics interested
in superconductivity or in the Schr¿ odinger equation as a limiting case of the
Ginzburg-Landau equations. The e?ects considered here usually become important in the regime
where the coherence length is of the order of the dimensions of the sample. While in the
Little-Parks days a lot of ingenuity was required to achieve this regime present
microelectronic techniques have transformed it into a routine. Mo- over measurement and
visualization techniques are developing at a pace which makes it reasonable to expect
veri?cation of distributions and not only of global properties. Activity in the ?eld has grown
and diversi?ed substantially in recent years. We have therefore invited experts ranging from
experimental and theoretical physicists to pure and applied mathematicians to contribute
articles for this book. While the skeleton of the book deals with superconductivity micron-
works and generalizations of the Little-Parks situation there are also articles which deal with
applications of the Ginzburg-Landau formalism to several fundamental topics such as quantum
coherence cosmology and questions in materials science.
