The ubiquitous existence of low-energy excitations in disordered solids has proved a longstanding problem. These states have been empirically described, but never directly observed. More importantly the ‘why’ of their nearly uniform density and dynamical properties in disordered materials as diverse as floppy polymers and rigid silica has never been explained. Coming back to this field after a forty-year absence, I find theoretical and experimental advances that allow one to begin addressing this question. On the experimental side, disordered films can be prepared, by varying quench rates much more than previously, with correspondingly wider ranges of thermally induced disorder. This should allow mapping the density of such states with the density/disorder in the film. On the theoretical side, computer simulations of packed spheres show the existence of zero-energy states, the density of which vary with a power law of the density difference from a critical density. These are found to be localized states arising from the coordinate motion of O(10)s of spheres. It would be interesting to extend such simulations to structures with directed bonds.
