Master Degree Project Presentation: "The Low-Density Lorentz Gas with Non-Identical Scatterers"

Abstract: The Lorentz gas is a gas of non-interacting point particles in an array of identical spherical scatterers. It was originally introduced by Hendrik Lorentz in 1905 as a model of electron transport in metals. Lorentz was interested in the macroscopic dynamics of this gas, and conjectured that they obey the linear Boltzmann equation. This is now known to be true if the scatterers are randomly distributed, but periodic and quasicrystalline constellations turn out to yield a more complicated class of transport equations. Andreas Strömbergsson and Jens Marklof have recently developed a general framework that derives transport equations for a very large class of scatterer constellations. This talk presents an extended version of this framework that allows the scatterers to be non-identical. In particular, this extension applies to all periodic crystals with spherical nuclei.