Phonon-fracton crossover and scaling of the sound velocity

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Abstract
The thermal properties of amorphous materials above 1–5 K are explained within the framework of phonon and fracton excitations provided that there is a frequency window where both of these excitations coexist. A generalized scaling approach shows that the width of this region in the dispersion curves is related to the scaling of the sound velocity as a function of the characteristic length scale that determines the crossover from self-similarity to translational invariance. Comparisons with other theories and with the effective-medium-approximation results for a percolating network are made.