A semiclassical Egorov theorem and quantum ergodicity for matrix valued operators (Q1885632)

The paper is concerned with the establishment of quantum ergodicity in systems that can be represented in a Hilbert space \(L^{2} (\mathbb{R}^3)\otimes \mathbb{C}^{n}\). The semiclassical time evolution of observables given by matrix valued pseudodifferential operators is studied, leading to the proof of an Egorov theorem for a class of observables preserved by time evolution. A decomposition of the Hilbert space in almost invariant subspaces is constructed and quantum ergodicity is shown to hold for the projection of eigenvectors of the quantum Hamiltonian to these subspaces if the associated classical system is ergodic.