Ergodic properties of the quantum geodesic flow on tori

Abstract

We study ergodic averages for a class of pseudodifferential operators on the flat N-dimensional torus with respect to the Schrödinger evolution. The later can be consider a quantization of the geodesic flow on $\bT^N$. We prove that, up to semi-classically negligible corrections, such ergodic averages are translationally invariant operators.

16 pages, latex