The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems

Details The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems

2007-06-29

arxiv.org/abs/0706.4395v2

Mathematics

Dynamical Systems

Corrected typos, added an index of notation

Scientific paper

The periodic Lorentz gas describes the dynamics of a point particle in a periodic array of spherical scatterers, and is one of the fundamental models for chaotic diffusion. In the present paper we investigate the Boltzmann-Grad limit, where the radius of each scatterer tends to zero, and prove the existence of a limiting distribution for the free path length of the periodic Lorentz gas. We also discuss related problems, such as the statistical distribution of directions of lattice points that are visible from a fixed position.

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