Instabilities of Time-averaged Configurations in Thermal Glasses

TL;DR

This paper extends Hessian matrix analysis to thermal glasses to understand and predict plastic instabilities in their time-averaged configurations, revealing that low-lying eigenmodes accurately forecast non-affine responses.

Contribution

It introduces a method to apply Hessian-based analysis to thermal glasses, enhancing understanding of their plastic instabilities compared to athermal systems.

Findings

Eigenfunctions of low-lying eigenvalues predict non-affine changes during instabilities.

Hessian methods can be adapted to thermal glasses to analyze plastic responses.

The approach helps identify potential instabilities in time-averaged configurations.

Abstract

In amorphous solids at finite temperatures the particles follow chaotic trajectories which, at temperatures sufficiently lower than the glass transition, are trapped in "cages". Averaging their positions for times shorter than the diffusion time, one can define a time-averaged configuration. Under strain or stress, these {\em average} configurations undergo sharp plastic instabilities. In athermal glasses the understanding of plastic instabilities is furnished by the Hessian matrix, its eigenvalues and eigenfunctions. Here we propose an uplifting of Hessian methods to thermal glasses, with the aim of understanding the plastic responses in the time-averaged configuration. We discuss a number of potential definitions of Hessians and identify which of these can provide eigenvalues and eigenfunctions which can explain and predict the instabilities of the time-averaged configurations. The conclusion is that the non-affine changes in the average configurations during an instability is accurately predicted by the eigenfunctions of the low-lying eigenvalues of the chosen Hessian.