Ginzburg-Landau theory is an important tool in condensed matter physics research, describing the ordered phases of condensed matter, including the dynamics, elasticity, and thermodynamics of the condensed configurations. In this systematic introduction to Ginzberg-Landau theory, both common and topological excitations are considered on the same footing (including their thermodynamics and dynamical phenomena). The role of the topological versus energetic considerations is made clear. Required mathematics (symmetry, including lattice translation, topology, and perturbative techniques) are introduced as needed. The results are illustrated using arguably the most fascinating class of such systems, high Tc superconductors subject to magnetic field. This book is an important reference for both researchers and graduate students working in condensed matter physics or can act as a textbook for those taking advanced courses on these topics.
The original motivation of this study comes from the following questions that were mentioned to one ofus by H. Matano. Let 2 2 G= B = {x=(X1lX2) E 2 ; x~ + x~ = Ixl < 1}. 1 Consider the...
This monograph compiles, rearranges, and refines recent research results in the complex G-L theory with or without immediate applications to the theory of superconductivity. An authoritative...
This book presents the mathematical study of vortices of the two-dimensional Ginzburg-Landau model, an important phenomenological model used to describe superconductivity. The vortices, identified as...