A simple random matrix model for the vibrational spectrum of jammed packings

Abstract

To better understand the surprising low-frequency vibrational modes in structural glasses, we study the spectra of a large ensemble of sparse random matrices where disorder is controlled by the distribution of bond weights and network coordination. We find $D(\omega )$ has three regimes: a very-low-frequency regime that can be predicted analytically using extremal statistics, an intermediate regime with quasi-localized modes, and a plateau with $D(\omega )\sim {\omega }^0$. In the special case of uniform bond weights, the intermediate regime displays $D(\omega )\sim {\omega }^4$, independent of network coordination and system size, just as recently discovered in simulations of structural glasses.

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Cited by in corpus (20)

• Low-frequency vibrational modes of stable glasses
• Pinching a glass reveals key properties of its soft spots
• Low-energy quasilocalized excitations in structural glasses
• Low-frequency vibrational spectrum of mean-field disordered systems
• Theory for the density of interacting quasi-localised modes in amorphous solids
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• Mean-field model of interacting quasilocalized excitations in glasses
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• Hydrodynamics of disordered marginally-stable matter
• Universal non-mean-field scaling in the density of state of amorphous solids
• Universal non-Debye low-frequency vibrations in sheared amorphous solids
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• Enhanced Vibrational Stability in Glass Droplets
• Evolution of Adaptive Force Chains in Reconfigurable Granular Metamaterials
• Singularities in Hessian element distributions of amorphous media
• Fluctuation Distributions of Energy Minima in Complex Landscapes