On the weak coupling limit of the periodic quantum Lorentz gas

Abstract

We report partial progress on the weak coupling limit behavior of observables for the periodic quantum Lorentz gas. Our results indicate that for certain observables, the limit behavior is trivial and can be described via a transport equation, while for other observables, the existence of the limit hinges on the regularity properties at resonant momenta of a certain Bloch-Wigner transform. We are currently unable to prove or disprove this regularity property, and so the weak coupling limit for these observables remains an open question. A novelty of this work is the use of the sewing lemma in the derivation of the kinetic scaling limit for almost every mometum.