Superdiffusion in a Honeycomb Billiard

TL;DR

This paper studies superdiffusive particle transport in a honeycomb billiard, revealing anisotropic spreading and ballistic trajectories, with analytical and simulation results explaining the observed superdiffusion and its transition to normal diffusion with disorder.

Contribution

It provides an analytical framework for understanding superdiffusion in honeycomb billiards and demonstrates the transition to normal diffusion with channel disorder.

Findings

Mean square displacement exponent of 1.72

Anisotropic, starlike particle distribution

Superdiffusive behavior transitions to normal diffusion with disorder

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.