Following the evolution of glassy states under external perturbations: compression and shear-strain

TL;DR

This paper analyzes how glassy states respond to external perturbations like compression and shear-strain, revealing overshoot phenomena, yield stress, and Gardner transition behavior in infinite-dimensional hard sphere models.

Contribution

It provides an exact analysis of glassy state evolution under perturbations in infinite dimensions, including stability, yield stress, and Gardner transition insights.

Findings

Pressure and shear-stress overshoot before instability

Estimated yield stress of the glass

Gardner transition occurs near the dynamical transition

Abstract

We consider the adiabatic evolution of glassy states under external perturbations. Although the formalism we use is very general, we focus here on infinite-dimensional hard spheres where an exact analysis is possible. We consider perturbations of the boundary, i.e. compression or (volume preserving) shear-strain, and we compute the response of glassy states to such perturbations: pressure and shear-stress. We find that both quantities overshoot before the glass state becomes unstable at a spinodal point where it melts into a liquid (or yields). We also estimate the yield stress of the glass. Finally, we study the stability of the glass basins towards breaking into sub-basins, corresponding to a Gardner transition. We find that close to the dynamical transition, glasses undergo a Gardner transition after an infinitesimal perturbation.