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

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(ω) obeys a characteristic power law, g(ω)∼ω^{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 characterize 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.