Dynamic Structure Factor of Vibrating Fractals

Motivated by novel experimental work and the lack of an adequate theory, we study the dynamic structure factor S(k, t) of large vibrating fractal networks at large wave numbers k. We show that the decay of S(k, t) is dominated by the spatially averaged mean square displacement of a network node, which evolves subdiffusively in time, <((u) over right arrow (i)(t) - (u) over right arrow (i)(0))(2)> similar to t(v), where v depends on the spectral dimension d(s) and fractal dimension d(f). As a result, S(k, t) decays as a stretched exponential S(k, t) approximate to S(k)e(-(Gamma kt)v) with Gamma(k) similar to k(2/v). Applications to a variety of fractal-like systems are elucidated.