Properties of stable ensembles of Euclidean random matrices

Abstract

We study the spectrum of a system of coupled disordered harmonic oscillators in the thermodynamic limit. This Euclidean random matrix ensemble has been suggested as model for the low-temperature vibrational properties of glass. Exact numerical diagonalization is performed in three and two spatial dimensions, which is accompanied by a detailed finite size analysis. It reveals a low-frequency regime of sound waves that are damped by Rayleigh scattering. At large frequencies localized modes exist. In between, the central peak in the vibrational density of states is well described by Wigner's semicircle law for not too large disorder, as is expected for simple random matrix systems. We compare our results with predictions from two recent self-consistent field theories.

revised version as published

References in corpus (12)

• The Ioffe-Regel criterion and diffusion of vibrations in random lattices
• Plasticity in amorphous solids is mediated by topological defects in the displacement field
• Acoustic excitations and elastic heterogeneities in disordered solids
• Topology of vibrational modes predict plastic events in glasses
• Elastic moduli fluctuations predict wave attenuation rates in glasses
• Low-frequency excess vibrational modes in two-dimensional glasses
• Microscopic analysis of sound attenuation in low-temperature amorphous solids reveals quantitative importance of non-affine effects
• Sparse random matrices and vibrational spectra of amorphous solids
• Density of States below the First Sound Mode in 3D Glasses
• Scaling of the Non-Phononic Spectrum of Two-Dimensional Glasses
• Vibrational phenomena in glasses at low temperatures captured by field theory of disordered harmonic oscillators
• Sound damping in frictionless granular materials: The interplay between configurational disorder and inelasticity

Cited by in corpus (5)

• The Origin of Sound Damping in Amorphous Solids: Defects and Beyond
• A self-consistent current response theory of jamming and vibrational modes in low-temperature amorphous solids
• Effective medium theory for viscoelasticity of soft jammed solids
• Sound Attenuation in Glasses
• Unified study of viscoelasticity and sound damping in hard and soft amorphous solids