Approach to equilibrium in systems with continuous symmetries

quenched systems;continuous symmetry;relaxational dynamics;topological defects

Mondello, Maurizio

关键词: quenched systems;    continuous symmetry;    relaxational dynamics;    topological defects;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/18899/1991_mondello.pdf?sequence=2&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

In this thesis, I consider the approach to equilibrium of quenched systemswith continuous symmetry, whose relaxational dynamics is dominated by topologicaldefects. The general aspects of the problem and relevant theoretical,numerical and experimental results from the literature are discussed in chapter1. In chapters 2 and 3, I report the results of two and three dimensional simulationsof a simple model with non-conserved order parameter and the symmetryof a planar ferromagnet. A transient behavior is observed at early times in twodimensions, indicating that the vortex annihilation dynamics significantly affectsthe initial ordering process in the system. Finite-size scaling of the scatteringfunction is demonstrated and it is shown that dynamical scaling is satisfied notonly by the correlation functions of the order parameter but also by the correlationfunctions of the defects (point-vortices in two dimensions and vortex-stringsin three dimensions). In the three dimensional case, the effect of a bias in theinitial conditions is considered. The introduction of a bias (or external field)leads to exponential relaxation and the break-down of dynamical scaling. Anexperiment is suggested, which could reproduce the conditions of the simulationin bulk samples of quenched nematic liquid crystals. Possible relevance to superfluidssystems is also discussed. In chapter 4, I consider a system with conservedorder parameter, which is proposed as a model of crystal surface relaxation. Theobserved value for the growth of order in the system is in agreement with arecenttheoretical prediction. Multiscaling behavior for the scattering function isinvestigated, with negative results. A comparison of the correlation functionsin the conserved and non-conserved case indicates that, while the conservationconstraint does not influence the structure of the vortex defects, it significantlyaffects their dynamics. In chapter 5, I discuss a model of the superconductingtransition. A linear stability analysis of the normal-superconductor interface fortype I superconductors is presented. The presence of an instability analogousto that responsible for dendritic patterns in solidification is pointed out. Numericalsimulations of the phase propagation in type I superconductors confirmthe indications of the linear stability analysis. A simple mean-field picture ofthe transition kinetics of type II superconductors suggests the existence of twodynamical regimes, characterized by a power-law and a logarithmic growth ofordered (superconducting) domains in the. system. These two regimes can beunderstood in terms of the spatial dependence of the vortex-string interaction.Numerical simulations of type II superconductors in the spinodal regime bearout this prediction, confirming that the quenched dynamics of this system is welldescribed by the effective interaction among the defects.