Dynamic structure factor of fractals

The dynamic structure factor S(q,ω) of the vibrational modes of a deterministic fractal is analyzed as a function of both frequency (ω) and momentum (q) 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. The results are obtained by a novel recursion method for the calculation of the vibration Green's function of a deterministic fractal. They confirm predictions based upon the fracton scaling model. © 1989.