Approach to equilibrium in systems with continuous symmetries

Mondello, Maurizio

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https://hdl.handle.net/2142/18899 Copy

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 Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• quenched systems
• continuous symmetry
• relaxational dynamics
• topological defects

Language

en

Abstract

In this thesis, I 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 and relevant theoretical, numerical and experimental results from the literature are discussed in chapter 1. In chapters 2 and 3, I 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, indicating that the vortex annihilation dynamics significantly affects the initial ordering process in the system. 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. An experiment is suggested, which could reproduce the conditions of the simulation in bulk samples of quenched nematic liquid crystals. Possible relevance to superfluids systems is also discussed. In chapter 4, I consider a system with conserved order parameter, which is proposed as a model of crystal surface relaxation. The observed value for the growth of order in the system is in agreement with arecent theoretical prediction. 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, while the conservation constraint does not influence the structure of the vortex defects, it significantly affects their dynamics. In chapter 5, I discuss a model of the superconducting transition. A linear stability analysis of the normal-superconductor interface for type I superconductors is presented. The presence of an instability analogous to that responsible for dendritic patterns in solidification is pointed out. Numerical simulations of the phase propagation in type I superconductors confirm the indications of the linear stability analysis. 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. These two regimes can be understood in terms of the spatial dependence of the vortex-string interaction. Numerical simulations of type II superconductors in the spinodal regime bear out this prediction, confirming that the quenched dynamics of this system is well described by the effective interaction among the defects.

Type of Resource

text

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Copyright and License Information

1991 Maurizio Mondello

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