Disordered systems respond to external perturbations via a random,
discontinuous response. We present a way to derive the distribution of such
discontinuous jumps in mean-field systems with replica symmetry breaking, and
compare the results with quasi-static simulations of soft spheres in 3D,
either at jamming or in the denser (UNSAT) phase. In both cases a power law
behavior is found when the perturbation is sufficiently small, and the
predicted exponent, related to other critical exponents of soft spheres at
jamming, is shown to be in agreement with the one extracted from the
simulations.