Consistency of Hybrid Quantum-Classical Ensembles
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The formalism of ensembles on configuration space allows for a general description of interactions between quantum and classical ensembles. In this chapter, we consider such hybrid ensembles and focus on consistency requirements for models of quantum-classical interactions. We show how the configuration ensemble approach is able to satisfy desirable properties such as a Lie algebra of observables and Ehrenfest relations, while evading no-go theorems based in part on such properties. We then discuss issues concerning locality. It is found that, in principle, noninteracting ensembles of quantum and classical particles can be associated with nonlocal energy flows and nonlocal signaling. However, it is shown that such effects can be suppressed by a requirement of ‘classicality’, that localised classical systems have a very large number of degrees of freedom. Measurement aspects are also discussed and again ‘classicality’ plays an important role, this time ensuring an effective and irreversible decoherence. Finally, comparisons are briefly made with elements of the mean-field approach to quantum-classical interactions.
KeywordsPoisson Bracket Classical Particle Strong Separability Quantum Observable Quantum Ensemble
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