Loss of memory in the periodic Ehrenfest model with small polyhedral scatterers

RESUMO

We determine the Boltzmann--Grad limit of the Ehrenfest ``wind-tree'' model with a periodic configuration of polyhedral scatterers. The central result is a loss-of-memory effect in dimension $d\geq 3$ for a generic choice of polyhedron. This yields a Markovian limiting transport process on an extended state space and a generalised linear Boltzmann equation for the time evolution of the particle density.