### 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 |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review E*,

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

**Simple random matrix model for the vibrational spectrum of structural glasses.** / Stanifer, E.; Morse, P. K.; Middleton, Arthur Alan; Manning, Mary Elizabeth.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 98, no. 4, 042908. https://doi.org/10.1103/PhysRevE.98.042908

}

TY - JOUR

T1 - Simple random matrix model for the vibrational spectrum of structural glasses

AU - Stanifer, E.

AU - Morse, P. K.

AU - Middleton, Arthur Alan

AU - Manning, Mary Elizabeth

PY - 2018/10/25

Y1 - 2018/10/25

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85055802018&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055802018&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.98.042908

DO - 10.1103/PhysRevE.98.042908

M3 - Article

AN - SCOPUS:85055802018

VL - 98

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 4

M1 - 042908

ER -