Quantum ergodicity of C* dynamical systems

Details Quantum ergodicity of C* dynamical systems Quantum ergodicity of C* dynamical systems

2000-02-03

arxiv.org/abs/math-ph/0002008v1

Comm. Math. Phys. 177 (1996), no. 2, 507--528

Physics

Mathematical Physics

Only very minor differences with the published version

Scientific paper

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.

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