Approach to equilibrium in systems with continuous symmetries

In this thesis, we consider the approach to equilibrium of quenched systems with continuous symmetry, whose relaxational dynamics is dominated by topological defects. The general aspects of the problem are discussed in chapter 1. In chapters 2 and 3, we report the results of two and three dimensional simulations of a simple model with non-conserved order parameter and the symmetry of a planar ferromagnet. A transient behavior is observed at early times in two dimensions. Finite-size scaling of the scattering function is demonstrated and it is shown that dynamical scaling is satisfied not only by the correlation functions of the order parameter but also by the correlation functions of the defects (point-vortices in two dimensions and vortex-strings in three dimensions). In the three dimensional case, the effect of a bias in the initial conditions is considered. The introduction of a bias (or external field) leads to exponential relaxation and the break-down of dynamical scaling. In chapter 4, we consider a system with conserved order parameter, which is proposed as a model of crystal surface relaxation. Multiscaling behavior for the scattering function is investigated, with negative results. A comparison of the correlation functions in the conserved and non-conserved case indicates that the conservation constraint significantly affects the vortex dynamics. In chapter 5, we discuss a model of the superconducting transition. A linear stability analysis of the normal-superconductor interface for type I superconductors indicates the presence of an instability, analogous to that responsible for dendritic patterns in solidification. A simple mean-field picture of the transition kinetics of type II superconductors suggests the existence of two dynamical regimes, characterized by a power-law and a logarithmic growth of ordered (superconducting) domains in the system. Numerical simulations of type II superconductors in the spinodal regime bear out this prediction. Selected computer programs are given in the appendices.U of I OnlyETDs are only available to UIUC Users without author permissio