# Low-frequency vibrations of jammed packings in large spatial dimensions

Abstract : Amorphous packings prepared in the vicinity of the jamming transition play a central role in theoretical studies of the vibrational spectrum of glasses. Two mean-field theories predict that the vibrational density of states $g(\omega)$ obeys a characteristic power law, $g(\omega)\sim\omega^2$, called the non-Debye scaling in the low-frequency region. Numerical studies have however reported that this scaling breaks down at low frequencies, due to finite dimensional effects. In this study, we prepare amorphous packings of up to $128000$ particles in spatial dimensions from $d=3$ to $d=9$ to characterise the range of validity of the non-Debye scaling. Our numerical results suggest that the non-Debye scaling is obeyed down to a frequency that gradually decreases as $d$ increases, and possibly vanishes for large $d$, in agreement with mean-field predictions. We also show that the prestress is an efficient control parameter to quantitatively compare packings across different spatial dimensions.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-02880594
Contributor : L2c Aigle <>
Submitted on : Thursday, June 25, 2020 - 10:09:26 AM
Last modification on : Friday, June 26, 2020 - 3:30:16 AM

### Citation

Masanari Shimada, Hideyuki Mizuno, Ludovic Berthier, Atsushi Ikeda. Low-frequency vibrations of jammed packings in large spatial dimensions. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2020, pp.052906. ⟨10.1103/PhysRevE.101.052906⟩. ⟨hal-02880594⟩

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