Simple random matrix model for the vibrational spectrum of structural glasses

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Abstract

To better understand the surprising low-frequency vibrational modes in structural glasses, where the density of states D(ω) deviates from mean field predictions, 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 quasilocalized modes, and a plateau in D(ω). When there is a finite probability of bond weights approaching zero strength, the intermediate regime displays a scaling consistent with D(ω)∼ω4, independent of network coordination and system size, just as in simulated structural glasses.

Original languageEnglish (US)
Article number042908
JournalPhysical Review E
Volume98
Issue number4
DOIs
StatePublished - Oct 25 2018

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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