Density Scaling of Avalanche Statistics in Amorphous Solids

Stress vs. strain fluctuations in athermal amorphous solids are an example of `crackling noise' of the type studied extensively in the context of elastic membranes moving through random potentials. Contrary to the latter, we do not have a stochastic equation whose statistics agree with the measured ones. On the other hand we show in this Letter that the statistics of the former exhibit 'density scaling' when the interparticle potential can be well approximated by a power law. The distributions of sizes of dissipative events for a wide range of densities and system sizes follow a single scaling function. We find that both the system-size scaling of energy drops and the entire strain interval statistics are invariant to changes in density. We use this to determine accurately the exponents in the scaling laws, establishing that the present crackling noise belongs to a different universality class.