Towards a definition of the quantum ergodic hierarchy: Ergodicity and mixing

In a previous paper we have given a general framework for addressing the definition of quantum chaos by identifying the conditions that a quantum system must satisfy to lead to non-integrability in its classical limit. In this paper we will generalize those results, with the purpose of defining the two lower levels of the quantum ergodic hierarchy: ergodicity and mixing. We will also argue for the physical relevance of this approach by considering a particular example where our formalism has been successfully applied.