Evidence for Phonon-Fracton Crossover in Silica Aerogels by Brillouin-Scattering Measurements
Systems crossing over from homogeneity to self-similarity at a correlation length ξ are expected to exhibit rather peculiar elastic properties.1 Phonons of well-defined frequency ω and wavevector q can propagate in such media if their wavelength λ = 2π/q is larger than ξ. In contrast, a crossover to fractons, the vibrational excitations characteristic of fractal structures,2,3 should occur as qξ increases towards 1.
KeywordsElastic Scattering Fractal Structure Silica Aerogel Vibrational Excitation Scalar Elasticity
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