Random walks on bundled structures.

Abstract

Bundled structures (BS) are discrete structures obtained joining to each point of a ``base'' graph a copy of a ``fiber'' graph. In condensed matter physics BS are used as realistic models for the geometry and dynamics of nontranslationally invariant systems (polymers, inhomogeneous systems, etc.). We present an analytical solution for the random walk problem on these structures, which is possible when we know the solution for base and fiber separately. We obtain an expression for the spectral dimension of the BS as a function of the spectral dimensions of its components. Moreover, we discuss some applications of these results concerning anomalous diffusion laws, proving the existence of nondisordered structures with logarithmic and sublogarithmic diffusion laws due only to geometric features.