Scaling for disordered viscoelastic matter at the onset of rigidity: Dynamical susceptibility,global behavior and spatio-temporal properties

The onset of rigidity in interacting liquids, as they undergo a transition to a disordered solid, is associated with a dramatic rearrangement of the low-frequency vibrational spectrum. In this talk, I will derive scaling forms for the singular dynamical response of disordered viscoelastic networks near both jamming and rigidity percolation. Using effective-medium theory, I will extract critical exponents, invariant scaling combinations and analytical formulas for universal scaling functions near these transitions. Our scaling forms describe the behavior in space and time near the various onsets of rigidity, for rigid and floppy phases and the crossover region, including diverging length and time scales at the transitions. We expect that these behaviors can be measured in systems ranging from colloidal suspensions to anomalous charge-density fluctuations of "strange" metals.