We consider the contribution to the density of vibrational states and the distribution of energy barrier heights of incipient instabilities in a glass modeled by a jammed packing of spheres. On approaching an instability, the frequency of a normal mode and the height of the energy barrier to cross into a new ground state both vanish. These instabilities produce a contribution to the density of vibrational states that scales as ω3 at low frequencies ω, but which vanishes in the thermodynamic limit. In addition, they affect an anharmonic property, the distribution of energy barriers ΔH, giving a contribution that scales as ΔH−1/3 at low barrier heights, which should be universal for jammed and glassy systems.
@article{arxiv.1704.00900,
title = {Instabilities of jammed packings of frictionless spheres under compression},
author = {Ning Xu and Andrea J. Liu and Sidney R. Nagel},
journal= {arXiv preprint arXiv:1704.00900},
year = {2017}
}