Instabilities of Jammed Packings of Frictionless Spheres Under Load.

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 ω^{3} at low frequencies ω, and a contribution to the distribution of energy barriers ΔH that scales as ΔH^{-1/3} at low barrier heights.