On the Dynamics of Glassy Systems

TL;DR

This paper explores the microscopic dynamics of glassy systems, introducing new models to understand structure-property relationships, and investigates threshold-driven erosion and spin glass self-organization, revealing insights into rigidity transitions and marginal stability.

Contribution

It introduces a new class of models linking structure, elasticity, and dynamics in supercooled liquids, and analyzes erosion and spin glass behavior at zero temperature, providing novel quantitative predictions.

Findings

New models elucidate the structure-elasticity-dynamics relationship.

Identifies the role of topology in rigidity transition in covalent networks.

Reveals the connection between pseudogap formation and anti-correlations in soft excitations.

Abstract

Glassy systems are disordered systems characterized by extremely slow dynamics. Examples are supercooled liquids, whose dynamics slow down under cooling. The specific pattern of slowing-down depends on the material considered. This dependence is poorly understood, in particular, it remains generally unclear which aspects of the microscopic structures control the dynamics and other macroscopic properties. Attacking this question is one of the two main aspects of this dissertation. We have introduced a new class of models of supercooled liquids, which captures the central aspects of the correspondence between structure and elasticity on the one hand, the correlation of structure and thermodynamic and dynamic properties on the other. Our results shed new light on the temperature-dependence of the topology of covalent networks, in particular, on the rigidity transition that occurs when the valence is increased. Other questions appear in glassy systems at zero temperature. In that situation, a glassy system can flow if an external driving force is imposed above some threshold. The first example we will consider is the erosion of a riverbed. Experiments support the existence of a threshold forcing, below which no erosion flux is observed. In this dissertation, we present a novel microscopic model to describe the erosion near threshold. This model makes new quantitative predictions for the spatial reparation of the flux. To study further the self-organization of driven glassy systems, we investigate the athermal dynamics of mean-field spin glasses. The spin glass self-organizes into the configurations that are stable, but barely so. Such marginal stability appears with the presence of a pseudogap in soft excitations. We show that the emergence of a pseudogap is deeply related to very strong anti-correlations emerging among soft excitations.