Superdiffusion in a honeycomb billiard

Michael Schmiedeberg and Holger Stark
Phys. Rev. E 73, 031113 – Published 24 March 2006

Abstract

We investigate particle transport in the honeycomb billiard which 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 the anisotropic distribution under the assumption that the perfect paths follow the directions of the six lattice axes. Furthermore, we derive a relation between the time exponent and the exponent of the distribution function for trajectories close to a perfect path. 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.

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  • Received 19 December 2005

DOI:https://doi.org/10.1103/PhysRevE.73.031113

©2006 American Physical Society

Authors & Affiliations

Michael Schmiedeberg and Holger Stark

  • Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany and Max-Planck-Institute for Dynamics and Self-Organization, D-37073 Göttingen, Germany

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Issue

Vol. 73, Iss. 3 — March 2006

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