Acoustic excitations and elastic heterogeneities in disordered solids

In the recent years, much attention has been devoted to the inhomogeneous nature of the mechanical response at the nanoscale in disordered solids. Clearly, the elastic heterogeneities that have been characterized in this context are expected to strongly affect the nature of the sound waves which, in contrast to the case of perfect crystals, cannot be completely rationalized in terms of phonons. Building on previous work on a toy model showing an amorphization transition, we investigate the relationship between sound waves and elastic heterogeneities in a unified framework by continuously interpolating from the perfect crystal, through increasingly defective phases, to fully developed glasses. We provide strong evidence of a direct correlation between sound wave features and the extent of the heterogeneous mechanical response at the nanoscale.