Dynamical dimension splitting on fractals: Structures with different diffusive 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 vibrational dynamics. However, in principle, two distinct parameters could be necessary to describe the two physical phenomena. In this paper we show the existence of fractal structures where two different spectral 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 of such dynamical dimension splitting. © World Scientific Publishing Company