We propose a notion of quantum weak mixing for the wave group of a compact Riemannian manifold and study some of its properties. It is a semi-classical notion and can occur despite the descreteness of the spectrum of the Laplacian. The main results are the behaviour of quantum weak mixing under products, and the relation to weak mixing of the classical limit (geodesic flow). The article is a continuation of a previous paper and also develops some recent work of Sunada on quantum ergodicity.
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