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- Title
Vibrational spectrum of Granular packings with random matrices.
- Authors
Narayan, Onuttom; Mathur, Harsh
- Abstract
The vibrational spectrum of granular packings can be used as a signature of the jamming transition, with the density of states at zero frequency becoming nonzero at the transition. It has been proposed previously that the vibrational spectrum of granular packings can be approximately obtained from random matrix theory. Here, we show that the autocorrelation function of the density of states shows good agreement between dynamical numerical simulations of frictionless bead packs near the jamming point and the analytic predictions of the Laguerre orthogonal ensemble of random matrices; there is clear disagreement with the Gaussian orthogonal ensemble, establishing that the Laguerre ensemble correctly reproduces the universal statistical properties of jammed granular matter and excluding the Gaussian orthogonal ensemble. We also present a random lattice model which is a physically motivated variant of the random matrix ensemble. Numerical calculations reveal that this model reproduces the known features of the vibrational density of states of frictionless granular matter, while also retaining the correlation structure seen in the Laguerre random matrix theory.
- Subjects
RANDOM matrices; VIBRATIONAL spectra; DENSITY of states; NUMERICAL calculations
- Publication
European Physical Journal E -- Soft Matter, 2024, Vol 47, Issue 3, p1
- ISSN
1292-8941
- Publication type
Article
- DOI
10.1140/epje/s10189-024-00414-x