Quantum ergodicity of C* dynamical systems

Abstract

This paper contains a very simple and general proof that eigenfunctions of quantizations of classically ergodic systems become uniformly distributed in phase space. This ergodicity property of eigenfunctions f is shown to follow from a convexity inequality for the invariant states (Af,f). This proof of ergodicity of eigenfunctions simplifies previous proofs (due to A.I. Shnirelman, Colin de Verdiere and the author) and extends the result to the much more general framework of C* dynamical systems.