TY - JOUR

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

AU - Stanifer, E.

AU - Morse, P. K.

AU - Middleton, A. A.

AU - Manning, M. L.

N1 - Funding Information:
We thank Fernanda Benetti, Gabriele Sicuro, and Giorgio Parisi for discussions. This work was partially supported by the Simons Foundation Grant No. 454947 (E.S., P.M., M.L.M.) and by NSF-DMR-1352184 (E.S., M.L.M.). Computational resources were provided by support from Syracuse University and NSF ACI-1541396.
Publisher Copyright:
© 2018 American Physical Society.

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 -