Schmiedeberg M, Stark H (2006)
Publication Status: Published
Publication Type: Journal article
Publication year: 2006
Publisher: AMER PHYSICAL SOC
Book Volume: 73
Journal Issue: 3
DOI: 10.1103/PhysRevE.73.031113
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.
APA:
Schmiedeberg, M., & Stark, H. (2006). Superdiffusion in a honeycomb billiard. Physical Review E, 73(3). https://dx.doi.org/10.1103/PhysRevE.73.031113
MLA:
Schmiedeberg, Michael, and Holger Stark. "Superdiffusion in a honeycomb billiard." Physical Review E 73.3 (2006).
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