Vibrational properties of hard and soft spheres are unified at jamming

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.

7 pages (supplement in the last page), 7 figures (5 in the main text, 2 in the supplement)

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• Hyperuniform Jammed Sphere Packings Have Anomalous Material Properties
• Mean-Field Predictions of Scaling Prefactors Match Low-Dimensional Jammed Packings
• Contact network changes in ordered and disordered disk packings
• Scaling theory of wave confinement in classical and quantum periodic systems
• Hard-Sphere Jamming through the Lens of Linear Optimization
• Inferring the particle-wise dynamics of amorphous solids from the local structure at the jamming point
• Comment on "Explicit Analytical Solution for Random Close Packing in $d=2$ and $d=3$"