Properties of stable ensembles of Euclidean random matrices

Author:

Philipp Baumgärtel, Florian Vogel, Matthias Fuchs

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn)

journal:

date:

2023-09-13 16:00:00

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. 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 expected for random matrix systems. We compare our results with predictions from two recent self-consistent field theories.

PDF: Properties of stable ensembles of Euclidean random matrices.pdf