DYNAMICAL DIMENSION SPLITTING ON FRACTALS - STRUCTURES WITH DIFFERENTDIFFUSIVE AND VIBRATIONAL SPECTRAL DIMENSIONS

On fractals and inhomogeneous structures that have been studied up to now, a single parameter, the spectral dimension, rules diffusion and v ibrational dynamics. However, in principle, two distinct parameters co uld be necessary to describe the two physical phenomena. In this paper we show the existence of fractal structures where two different spect ral dimensions are required. Random walks and vibrational spectrum are studied by renormalization group as well as alternative techniques to obtain the exact values of the dimensions and to clarify the origin o f such dynamical dimension splitting.