Universal non-Debye scaling in the density of states of amorphous solids

TL;DR

This paper investigates the vibrational density of states in amorphous solids across multiple dimensions, revealing a universal non-Debye scaling consistent with mean-field theory predictions, extending understanding beyond the jamming transition.

Contribution

It demonstrates that non-Debye scaling of the density of states is universal in finite dimensions from 3 to 7, aligning with mean-field predictions.

Findings

Universal non-Debye scaling observed in dimensions 3-7

Soft mode participation ratio converges to mean-field predictions with increasing dimension

Results extend the applicability of mean-field theories to finite-dimensional amorphous solids

Abstract

At the jamming transition, amorphous packings are known to display anomalous vibrational modes with a density of states (DOS) that remains constant at low frequency. The scaling of the DOS at higher densities remains, however, unclear. One might expect to find simple Debye scaling, but recent results from effective medium theory and the exact solution of mean-field models both predict an anomalous, non-Debye scaling. Being mean-field solutions, however, these solutions are only strictly applicable to the limit of infinite spatial dimension, and it is unclear what value they have for finite-dimensional systems. Here, we study packings of soft spheres in dimensions 3 through 7 and find, far from jamming, a universal non-Debye scaling of the DOS that is consistent with the mean-field predictions. We also consider how the soft mode participation ratio converges to the mean-field prediction as dimension increases.