Nonequilibrium static diverging length scales on approaching a prototypical model glassy state

TL;DR

This study investigates the emergence of diverging static length scales in overcompressed hard sphere packings approaching the jammed glassy state, revealing precursors and nonequilibrium characteristics before jamming.

Contribution

It introduces a novel analysis of static length scales and nonequilibrium indices in hard sphere packings nearing jamming, highlighting precursors to the glass transition.

Findings

Identification of a growing length scale diverging at jamming

Detection of a precursor to the glassy jammed state

Demonstration of intrinsic nonequilibrium behavior before jamming

Abstract

Maximally random jammed states of hard spheres are prototypical glasses. We study the small wavenumber $k$ behavior of the structure factor $S(k)$ of overcompressed million-sphere packings as a function of density up to the jammed state. We find both a precursor to the glassy jammed state evident long before the jamming density is reached and an associated growing length scale, extracted from the volume integral of the direct correlation function $c(r)$, which diverges at the "critical" jammed state. We also define a nonequilibrium index $X$ and use it to demonstrate that the packings studied are intrinsically nonequilibrium in nature well before the critical point is reached.