The Distribution of Distances to Instabilities of Jammed Packings of Frictionless Spheres Under Load*

We study an athermal, jammed packing of frictionless soft spheres to revisit the contribution of local (fold) instabilities to the vibrational density of states D(ω). For low frequencies, they result in a power-law behaviour D(ω)~ω^α. We show that we can infer this exponent α from a careful inspection of incipient instabilities under shear and pressure load exploiting the fact that the underlying statistics has to take the form of an extreme value distribution. Taking into account shear- and compression-stable packings, we gather some physical insight into the meaning of α and its dependence on finite-size effects and preparation protocol.