Quantum mixing (Q1923692)

The purpose of this article is to define a quantum analogue of weak mixing for Hamiltonian dynamical systems, and to study its relation to classical weak mixing in the semiclassical limit. The Hamiltonian system is here the geodesic flow of a compact Riemannian manifold, and the quantum Hamiltonian is the square root of the Laplacian (semiclassics can occur despite the discreteness of its spectrum). The main results pertain to the behaviour of quantum weak mixing under products and develop some recent works on quantum (noncommutative) ergodicity.