Superdiffusion in a Honeycomb Billiard

Abstract

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.

12 figures, submitted to Phys. Rev. E

References in corpus (5)

• Finite thermal conductivity in 1D models having zero Lyapunov exponents
• Occurrence of normal and anomalous diffusion in polygonal billiard channels
• Anomalous Diffusion in Infinite Horizon Billiards
• Photon Channelling in Foams
• Fine structure of distributions and central limit theorem in diffusive billiards

Cited by in corpus (5)

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• Creating conditions of anomalous self-diffusion in a liquid with molecular dynamics