### 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 language | English (US) |
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Article number | 042908 |

Journal | Physical Review E |

Volume | 98 |

Issue number | 4 |

DOIs | |

State | Published - Oct 25 2018 |

### ASJC Scopus subject areas

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

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## Cite this

*Physical Review E*,

*98*(4), [042908]. https://doi.org/10.1103/PhysRevE.98.042908