Distribution of the linear flow length in a honeycomb in the small-scatterer limit

Details Distribution of the linear flow length in a honeycomb in the small-scatterer limit Distribution of the linear flow length in a honeycomb in the small-scatterer limit

2009-07-15

arxiv.org/abs/0907.2496v3

Mathematics

Dynamical Systems

3rd draft. New title and improved presentation

Scientific paper

We study the statistics of the linear flow in a punctured honeycomb lattice, or equivalently the free motion of a particle on a regular hexagonal billiard table with holes of equal size at the corners and obeying the customary reflection rules. In the small-scatterer limit we prove the existence of the limiting distribution of the free path length with randomly chosen origin of the trajectory and explicitly compute it.

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