The Lorentz Gas and Quasicrystals
The Lorentz gas model dates to the early 20th century, when it was proposed as a model for the free electron in a crystal. The study of the Lorentz gas has driven many of the major developments in ergodic theory, starting with the works of Sinai in the late 60's and early 70's, and by now the theory of Lorentz gases for solids with periodic structure is very sophisticated and advanced. In the early 80's Shechtman discovered quasicrystals, which are solids whose atomic structure is not modeled by any periodic structure such as a lattice, the discovery of which led to a Nobel prize in 2011. Very little is known about the Lorentz gas for solids with aperiodic structure such as quasicrystals. In this talk I will talk about recent developments in the theory of Lorentz gases for solids with aperiodic structure, including joint work with A. Zelerowicz.