Properties of stable ensembles of Euclidean random matrices

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2024
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Physical Review E. American Physical Society (APS). 2024, 109(1), 014120. ISSN 2470-0045. eISSN 2470-0053. Available under: doi: 10.1103/physreve.109.014120
Zusammenfassung

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 a 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.

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ISO 690BAUMGÄRTEL, Philipp, Florian VOGEL, Matthias FUCHS, 2024. Properties of stable ensembles of Euclidean random matrices. In: Physical Review E. American Physical Society (APS). 2024, 109(1), 014120. ISSN 2470-0045. eISSN 2470-0053. Available under: doi: 10.1103/physreve.109.014120
BibTex
@article{Baumgartel2024-01-17Prope-69170,
  year={2024},
  doi={10.1103/physreve.109.014120},
  title={Properties of stable ensembles of Euclidean random matrices},
  number={1},
  volume={109},
  issn={2470-0045},
  journal={Physical Review E},
  author={Baumgärtel, Philipp and Vogel, Florian and Fuchs, Matthias},
  note={Article Number: 014120}
}
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