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At the jamming transition, amorphous packings are known to display anomalousvibrational modes with a density of states (DOS) that remains constant at lowfrequency. The scaling of the DOS at higher densities remains, however,unclear. One might expect to find simple Debye scaling, but recent results fromeffective medium theory and the exact solution of mean-field models bothpredict an anomalous, non-Debye scaling. Being mean-field solutions, however,these solutions are only strictly applicable to the limit of infinite spatialdimension, and it is unclear what value they have for finite-dimensionalsystems. Here, we study packings of soft spheres in dimensions 3 through 7 andfind, far from jamming, a universal non-Debye scaling of the DOS that isconsistent with the mean-field predictions. We also consider how the soft modeparticipation ratio converges to the mean-field prediction as dimensionincreases.

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