Normal modes analysis of the microscopic dynamics in hard discs

TL;DR

This paper investigates the microscopic vibrational modes in hard disc glasses, revealing a characteristic density of states near the glass transition that relates to marginal stability and influences short-time dynamics.

Contribution

It provides a numerical analysis of normal modes in hard disc glasses, linking the density of states to marginal stability and predicting anomalously large mean square displacements.

Findings

Density of states shows a frequency scale $\omega^* \\sim p^{1/2}$ near the glass transition.

The density of states reflects the short-time dynamics of the system.

Mean square displacement scales as $p^{-3/2}$ in the glass phase.

Abstract

We estimate numerically the normal modes of the free energy in a glass of hard discs. We observe that, near the glass transition or after a rapid quench deep in the glass phase, the density of states (i) is characteristic of a marginally stable structure, in particular it di splays a frequency scale $\omega^*\sim p^{1/2}$, where $p$ is the pressure and (ii) gives a faithful representation of the short-time dyn amics. This brings further evidences that the boson peak near the glass transition corresponds to the relaxation of marginal modes of a we akly-coordinated structure, and implies that the mean square displacement in the glass phase is anomalously large and goes as $< \delta R^2 > \sim p^{-3/2}$, a prediction that we check numerically.