System Representation of the Lorentz Gas

Abstract

We introduce a random environment system modeling a Lorentz Gas with semi-randomly positioned, periodic scatterers. Each system is determined through a probabilistic method producing a deterministic walk. We prove that the path within the generalized system must be periodic and calculate the expected number of loops within the path of a 1-door system. For n-door systems, where $n>1$, we describe an algorithm to calculate the expected number of loops of its path by making use of its bijection to the Lorentz Gas.