Lorentz gas

The Lorentz gas is a model of particle transport in a periodic array of convex scatterers, introduced by Hendrik Lorentz in 1905 to describe electron motion in crystals. A point particle moves in straight lines between collisions with fixed spherical obstacles, and the chaotic nature of the resulting trajectories makes the Lorentz gas a canonical model for studying non-uniform hyperbolicity and statistical properties of deterministic chaos.

The Lorentz gas was proved to be ergodic and mixing using Pesin theory, and it exhibits decay of correlations that connects chaotic dynamics to statistical mechanics. The model is closely related to the Sinai billiard, in which the scatterers are confined to a bounded domain rather than periodically extended. The connection between microscopic chaos and macroscopic transport — whether the Lorentz gas satisfies the Boltzmann equation in the appropriate limit — remains one of the deepest open problems in non-equilibrium statistical mechanics.