Properties of stable ensembles of Euclidean random matrices
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917570389475328 |
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| author | Baumgärtel, Philipp Vogel, Florian Fuchs, Matthias |
| author_facet | Baumgärtel, Philipp Vogel, Florian Fuchs, Matthias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08028 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Properties of stable ensembles of Euclidean random matrices Baumgärtel, Philipp Vogel, Florian Fuchs, Matthias Disordered Systems and Neural Networks 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. |
| title | Properties of stable ensembles of Euclidean random matrices |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2309.08028 |