Ergodic properties of the quantum geodesic flow on tori

Physics – Mathematical Physics

Scientific paper

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16 pages, latex

Scientific paper

We study ergodic averages for a class of pseudodifferential operators on the
flat N-dimensional torus with respect to the Schr\"odinger 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.

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