# Instabilities of jammed packings of frictionless spheres under compression

## TL;DR

This paper investigates the nature of instabilities in jammed sphere packings, revealing how they influence vibrational states and energy barriers, with implications for understanding glassy systems.

## Contribution

It introduces a universal scaling law for the distribution of energy barriers and analyzes the impact of instabilities on vibrational density of states in jammed packings.

## Key findings

- Vibrational density of states scales as ω^3 near instabilities.
- Energy barrier distribution scales as ΔH^(-1/3) at low barriers.
- Instabilities vanish in the thermodynamic limit, affecting glassy system properties.

## Abstract

We consider the contribution to the density of vibrational states and the distribution of energy barrier heights of incipient instabilities in a glass modeled by a jammed packing of spheres. On approaching an instability, the frequency of a normal mode and the height of the energy barrier to cross into a new ground state both vanish. These instabilities produce a contribution to the density of vibrational states that scales as $\omega^3$ at low frequencies $\omega$, but which vanishes in the thermodynamic limit. In addition, they affect an anharmonic property, the distribution of energy barriers $\Delta H$, giving a contribution that scales as $\Delta H^{-1/3}$ at low barrier heights, which should be universal for jammed and glassy systems.