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

E M Stanifer; P K Morse; A A Middleton; M L Manning

doi:10.1103/physreve.98.042908

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arXiv · 1804.04074

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

E M Stanifer·P K Morse·A A Middleton·M L Manning

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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 $D(ω)$ 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 $D(ω) \sim ω^0$. In the special case of uniform bond weights, the intermediate regime displays $D(ω) \sim ω^4$, independent of network coordination and system size, just as recently discovered in simulations of structural glasses.

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E M Stanifer, P K Morse, A A Middleton, M L Manning. 2018-04-27. A simple random matrix model for the vibrational spectrum of jammed packings. https://doi.org/10.1103/physreve.98.042908

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