Geometric interpretation of pre-vitrification in hard sphere liquids

TL;DR

This paper presents a geometric criterion for the stability of hard sphere configurations, linking it to the glass transition and soft modes, supported by empirical evidence and theoretical analysis.

Contribution

It introduces a microscopic stability criterion for hard sphere glasses and connects soft modes to pre-vitrification phenomena.

Findings

The stability criterion is marginally satisfied in glasses.

Soft modes characterize the glass structure.

Dynamics and activation occur mainly along soft modes.

Abstract

We derive a microscopic criterion for the stability of hard sphere configurations, and we show empirically that this criterion is marginally satisfied in the glass. This observation supports a geometric interpretation for the initial rapid rise of viscosity with packing fraction, or pre-vitrification. It also implies that barely stable soft modes characterize the glass structure, whose spatial extension is estimated. We show that both the short-term dynamics and activation processes occur mostly along those soft modes, and we study some implications of these observations. This article synthesizes new and previous results [C. Brito and M. Wyart, Euro. Phys. Letters, {\bf 76}, 149-155, (2006) and C. Brito and M. Wyart, J. Stat. Mech., L08003 (2007) ] in a unified view.