Time Reparametrization Symmetry and Spatial-Temporal Fluctuations in Glasses

<p>In this dissertation we focus on the dynamics of glasses and other complex systems. Dynamical heterogeneity, initially proposed to explain non exponential relaxation, has been found in simulations and experiments of glassy systems. The origin of dynamical heterogeneity remains poorly understood, despite growing evidence that glass dynamics is heterogeneous. There is no consensus in the glass community on any one of the proposed theories that explains the phenomenon. Over the last decade a theoretical framework has been proposed, based on the presence of Goldstone modes associated with a broken time reparametrization symmetry in the long time dynamics of glasses. The symmetry has been shown to be present in the Edwards-Anderson model of spin glasses and in the mean field equations of p-spin models. We study time reparametrization symmetry in p-spin models of arbitrary interaction range. Starting from the Martin-Siggia-Rose generating functional, we analytically probe the long-time dynamics by performing a renormalization group analysis where we systematically integrate over short-time scale fluctuations. We find three families of stable fixed points. The fixed points in two of these families are not time reparametrization invariant, while one family, corresponding to the low temperature dynamics, is made up of time reparametrization invariant fixed points. We hint at the possibility of doing a similar analysis on structural glasses, given the connection between p-spin models and structural glasses.</p><p>We then investigate fluctuating local phases and fluctuating local relaxation times in structural glasses. The presence of fluctuating local relaxation times, <span>\tau_{r}(t)</span> has been used for some time as a conceptual tool to describe dynamical heterogeneities in glass-forming systems. However, until now no general method is known to extract the full space and time dependent <span>\tau_{r}(t)</span> from experimental or numerical data. Here we introduce a new method for determining the local phase field,</p><p><span>\phi_{r}(t)\equiv\int^{t}\frac{dt'}{\tau_{r}(t')}</span> from snapshots r(t_i)_i=1...M of the positions of the particles in a system, and we apply it to extract <span>\phi_{r}(t)</span> and <span>\tau_{r}(t)</span> from numerical simulations. By studying how the phase field depends on the number of snapshots, we find that it is a well defined quantity. By studying fluctuations of the phase field, we find that they describe heterogeneities well at long distance scales. We find non Gaussian distribution functions of the time derivatives of <span>\phi_{r}(t)</span>, with more deviation from the Gaussian form in an aging system, which is at a lower temperature, than in an equilibrium system. We find power spectra that are fitted by a Lorentzian form for an equilibrium system and are fitted by a power law in an aging system.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Physics and Astronomy (Arts and Sciences)

Grantor dc:publisher

Ohio University

Year dc:date

2012

Author dc:creator

• Mavimbela, Gcina A.

Contributors dc:contributor

• Castillo, Horacio E.

• Condensed Matter Physics
• Physics
• Dynamical Heterogeneity
• Time Reparametrization Symmetry
• Local Relaxation Times

Statement dc:rights

• unrestricted
• This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.

Language dc:language

English

Repository record dc:identifier

http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1354211400

OAI identifier oai:identifier

oai:etd.ohiolink.edu:ohiou1354211400