Quantum approach to coupling classical and quantum dynamics - art. no. 022108

We present a consistent framework of coupled classical and quantum dynamics . Our result allows us to overcome severe limitations of previous phenomeno logical approaches, such as evolutions that do not preserve the positivity of quantum states or that allow one to activate quantum nonlocality for sup erluminal signaling. A "hybrid" quantum-classical density is introduced, an d its evolution equation derived. The implications and applications of our result are numerous: it incorporates the back-reaction of quantum on classi cal variables, and it resolves fundamental problems encountered in standard mean-field theories, and remarkably, also in the quantum measurement proce ss; i.e., the most controversial example of quantum-classical interaction i s consistently described within our approach, leading to a theory of dynami cal collapse.