Dynamic structure factor of a deterministic fractal

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 fraction scaling model