Vibrational properties of hard and soft spheres are unified at jamming

TL;DR

This paper demonstrates that the vibrational properties of hard and soft sphere systems are unified at the jamming transition, revealing universal vibrational spectra across different models and conditions.

Contribution

It introduces a method to analyze the vibrational spectrum of hard spheres using an effective free energy approach, unifying their vibrational properties with soft spheres at jamming.

Findings

Vibrational spectra of hard spheres near jamming match those of soft spheres.

Universal vibrational behavior extends below and above jamming.

Hard sphere systems exhibit low frequency modes similar to soft sphere systems.

Abstract

The unconventional thermal properties of jammed amorphous solids are directly related to their density of vibrational states. While the vibrational spectrum of jammed soft sphere solids has been fully described, the vibrational spectrum of hard spheres, a model for colloidal glasses, is still unknown due to the difficulty of treating the non-analytic interaction potential. We bypass this difficulty using the recently described effective interaction potential for the free energy of thermal hard spheres. By minimizing this effective free energy we mimic a quench and produce typical configurations of low temperature colloidal glasses. We measure the resulting vibrational spectrum and characterize its evolution towards the jamming point where configurations of hard and soft spheres are trivially unified. For densities approaching jamming from below, we observe low frequency modes which agree with those found in numerical simulations of jammed soft spheres. Our measurements of the vibrational structure demonstrate that the jamming universality extends away from jamming: hard sphere thermal systems below jamming exhibit the same vibrational spectra as thermal and athermal soft sphere systems above the transition.