Time-Dependent Ginzburg-Landau Theory and Duality
Abstract
Description
In the first part of this review paper, the time-dependent Ginzburg-Landau theory is derived starting from the microscopic BCS model with the help of a derivative expansion. Special attention is paid to two space dimensions, where the entire crossover from the weak-coupling BCS limit to the strong-coupling BEC limit of tightly bound fermion pairs is accessible analytically. The second part deals with the dual approach to the time-independent Ginzburg-Landau theory in three space dimensions. In this approach, the magnetic vortices of a superconductor play the central role, and the superconductor-to-normal phase transition is understood as a proliferation of these vortices.
16 pages, 1 figure. Lectures presented at the NATO Winter School and European Science Foundation (ESF) Workshop Topological Defects and the Non-Equilibrium Dynamics of Symmetry Breaking Phase Transitions, Les Houches, February 16-26, 1999, in Topological Defects in Cosmology and Condensed Matter Physics, edited by Yu. Bunkov and H. Godfrin (Kluwer, Dordrecht, 2000)
16 pages, 1 figure. Lectures presented at the NATO Winter School and European Science Foundation (ESF) Workshop Topological Defects and the Non-Equilibrium Dynamics of Symmetry Breaking Phase Transitions, Les Houches, February 16-26, 1999, in Topological Defects in Cosmology and Condensed Matter Physics, edited by Yu. Bunkov and H. Godfrin (Kluwer, Dordrecht, 2000)