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, and a contribution to the distribution of energy barriers ΔH that scales as ΔH^-1/3 at low barrier heights.
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Xu et al. (2017) studied this question.
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