Instabilities of jammed packings of frictionless spheres under compression

Abstract

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 $\omega^3$ at low frequencies $\omega$, but which vanishes in the thermodynamic limit. In addition, they affect an anharmonic property, the distribution of energy barriers $\Delta H$, giving a contribution that scales as $\Delta H^{-1/3}$ at low barrier heights, which should be universal for jammed and glassy systems.