On the Euclidean random matrix model of vibrations in glass
Abstract
Despite their important role in industrial applications and everyday life, and decades of research, disordered solids still lack a full theoretical understanding. In this perspective, we propose that the Euclidean random matrix model can serve as a paradigm for a low-temperature glass. It combines disorder, viz. random particle positions, with the harmonic approximation of the potential energy valid for any stable solid as temperature vanishes. It brings random-matrix concepts to bear on a fundamental understanding of the vibrational anomalies of glasses. We discuss recent studies that demonstrated non-affine displacements renormalizing the Born elastic constants, damping of sound waves via correlated scattering processes from the intrinsic disorder, excess low-frequency modes linked to the widely-observed boson peak, and elastic instabilities.
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BibTeX
@article{vogel2026euclidean,
title = {{On the Euclidean random matrix model of vibrations in glass}},
author = {Florian Vogel and Philipp Baumgärtel and Grzegorz Szamel and Matthias Fuchs},
journal = {Communications Physics},
year = {2026},
month = jul,
doi = {10.1038/s42005-026-02730-4},
url = {https://hal.science/hal-05754322v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - On the Euclidean random matrix model of vibrations in glass
AU - Florian Vogel
AU - Philipp Baumgärtel
AU - Grzegorz Szamel
AU - Matthias Fuchs
PY - 2026
DA - 2026/07/04
JO - Communications Physics
DO - 10.1038/s42005-026-02730-4
UR - https://hal.science/hal-05754322v1
AB - Despite their important role in industrial applications and everyday life, and decades of research, disordered solids still lack a full theoretical understanding. In this perspective, we propose that the Euclidean random matrix model can serve as a paradigm for a low-temperature glass. It combines disorder, viz. random particle positions, with the harmonic approximation of the potential energy valid for any stable solid as temperature vanishes. It brings random-matrix concepts to bear on a fundamental understanding of the vibrational anomalies of glasses. We discuss recent studies that demonstrated non-affine displacements renormalizing the Born elastic constants, damping of sound waves via correlated scattering processes from the intrinsic disorder, excess low-frequency modes linked to the widely-observed boson peak, and elastic instabilities.
SN - 2399-3650
SN - 2399-3650
ER -