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. 
Michael Schmiedeberg and Holger Stark (Universitaet Konstanz,   Fachbereich Physik, Konstanz, Germany)