Cross-over from phonons to fractons

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Abstract
Recent theoretical results concerning the cross-over from phonon-like to fracton-like behaviour of excitations obeying linear equations of motion (for example, vibrational modes or spin waves in antiferromagnets, in systems which are fractal on short length-scales and homogeneous on long scales) are reviewed. Particularly, we discuss the scaling theory for the density of states, the lifetime of excitations due to elastic scattering by structural inhomogeneities, and the structure factor for scattering from these excitations.