Dualidade na teoria de Landau-Ginzburg da supercondutividade

Abstract

In this work we introduced the Ginzburg-Landau theory of superconductivity (GL theory). We have shown your foundations, features and more important results. The fundamental idea of this theory is to describe the phase transition that some metals undergoes from a normal to a superconductor phase. During a phase transition in superconductors of type II is common the appearance of magnetic flux lines in given regions of finite size called of vortices. The knowledge of the dynamics of these vortices is of great importance in the current cientific community and drives many research centers to study the superconductivity. In view of this we study how these vortices changes a phase transition in a bidimensional model known as XY model.In XY model one can show that the main responsible for the phase transition are the vortices (or still, vortice-antivortice pairs). Villain, noting this fact, realized that could to turn explicit the contribution of theses topological defects in the partition function of XY model making a duality transformation. This model inspired us to study the subject of this master thesis. We presented here a model based in physical considerations about systems of condensed matter. At the same time we used a formalism developed in reference [29] that permits to turn explicit the contribution of these vortices in the original action proposed in our theory. Finally we analysed some classical limits and we looked for the quantum fluctuations to obtain the complete expression of the correlation function of vortices, whose utility is in the study of interacting vortices is wide (vortex dynamics).