Hybrid Quantum-Classical Ensembles
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The problem of defining hybrid systems comprising quantum and classical components is highly nontrivial, and the approaches that have been proposed to solve this problem run into various types of fundamental difficulties. The formalism of configuration-space ensembles is able to overcome many of these difficulties, allowing for a general and consistent description of interactions between quantum and classical ensembles. Such hybrid ensembles have a number of desirable features; e.g., quantum-classical interactions do not blur the fundamental distinction between the quantum and classical components; configuration separability is satisfied; and non-relativistic systems are Galilean invariant whenever the interaction potential itself is Galilean invariant. After demonstrating general properties of hybrid ensembles, we consider their application to the description of measurement of a quantum system by a classical apparatus, including examples of position and spin measurement; the scattering of a classical particle from a quantum superposition; and the definitions of Gaussian and coherent ensembles for quantum-classical oscillators. Finally, we generalise quantum Wigner functions to hybrid ensembles.
KeywordsConfiguration Space Wigner Function Quantum Particle Classical Particle Classical Ensemble
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