Fractons

The fracton description of vibrational excitations in the strong scattering regime, above the Ioffe-Regel limit is reviewed. The reasons why this is a plausible model for vibrations in amorphous materials are explained and some predictions discussed. It is shown how such a model arises in the context of scattering theory when the Ioffe-Regel length is large and a new self-consistency argument suggesting that the relevant fraction dimension for such vibrations has a universal value of 43 is described.