Recurrence for quenched random Lorentz tubes

TL;DR

This paper proves that in a class of randomly configured billiard systems called quenched random Lorentz tubes, almost all such systems exhibit recurrent behavior under broad conditions.

Contribution

It establishes recurrence for almost every system in the ensemble of quenched random Lorentz tubes, extending understanding of dynamical behavior in random billiard models.

Findings

Almost every quenched random Lorentz tube is recurrent.

Recurrence holds under general conditions for the scatterer configurations.

The result applies to a broad class of tessellated billiard systems.

Abstract

We consider the billiard dynamics in a strip-like set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called `quenched random Lorentz tube'. We prove that, under general conditions, almost every system in the ensemble is recurrent.