A novel recursion method is devised for the calculation of the vibration Green’s function of a deterministic fractal. It is applied to obtain the dynamic structure factor S(q, ω), measured in scattering experiments. The structure factor is analysed as a function of both frequency and momentum transfer. It is found that S(q, ω) is peaked at qmax∝ω2/2+ϑ, where ϑ is the anomalous diffusion exponent, and is a scaling function of q(2+ϑ)/2/ω. Our results confirm predictions based upon the fracton scaling model.
ASJC Scopus subject areas
- Physics and Astronomy (all)