Dynamics of swollen fractal networks

The dynamics of swollen fractal networks (Rouse model) has been studied through computer simulations. The fluctuation-relaxation theorem was used instead of the usual Langevin approach to Brownian dynamics. We measured the equivalent of the mean square displacement $\langle {\bf r}\,^2\rangle$ and the coefficient of self-diffusion D of two- and three-dimensional Sierpinski networks and of the two-dimensional percolation network. The results showed an anomalous diffusion, i.e. , a power law for D, decreasing with time with an exponent proportional to the spectral dimension of the network