Superdiffusion in a Honeycomb Billiard

We investigate particle transport in the honeycomb billiard that consists of connected channels placed on the edges of a honeycomb structure. The spreading of particles is superdiffusive due to the existence of ballistic trajectories which we term perfect paths. Simulations give a time exponent of 1.72 for the mean square displacement and a starlike, i.e., anisotropic particle distribution. We present an analytical treatment based on the formalism of continuous-time random walks and explain both the time exponent and the anisotropic distribution. In billiards with randomly distributed channels, conventional diffusion is always observed in the long-time limit, although for small disorder transient superdiffusional behavior exists. Our simulation results are again supported by an analytical analysis.