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

Abstract

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.

3rd draft. New title and improved presentation

References in corpus (5)

• The Lyapunov exponent in the Sinai billiard in the small scatterer limit
• The statistics of the trajectory in a certain billiard in a flat two-torus
• The Boltzmann-Grad limit of the periodic Lorentz gas in two space dimensions
• Recent Results on the Periodic Lorentz Gas
• The average length of a trajectory in a certain billiard in a flat two-torus

Cited by in corpus (2)

• The low-density limit of the Lorentz gas: periodic, aperiodic and random
• Kinetic Theory for the Low-Density Lorentz Gas