Approach to equilibrium in systems with continuous symmetries
Mondello, Maurizio
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/18954
Description
Title
Approach to equilibrium in systems with continuous symmetries
Author(s)
Mondello, Maurizio
Issue Date
1991
Doctoral Committee Chair(s)
Goldenfeld, Nigel D.
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, General
Language
eng
Abstract
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.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
