Diffusion and harmonic oscillations on bundled structures: Analytical techniques and dynamical dimension splitting

We present in details the general analytical techniques allowing to obtain the exact solution for random walks and harmonic oscillations problems on bundled graphs. These are networks obtained joining a copy of a fiber graph to each point of a base graph and are used as geometrical models for a wide class of real noncrystalline structures. The results show the remarkable phenomenon of dynamical dimension splitting: namely the noncoincidence of diffusive and vibrational spectral dimensions, usually supposed to be the same.