DYNAMICS OF MIXED CLASSICAL-QUANTUM SYSTEMS, GEOMETRIC QUANTIZATION AND COHERENT STATES
Hans Rudolf Jauslin, Dominique Sugny
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between classical and quantum systems. We give a summary of the main tools of Berezin-Toeplitz and geometric quantization, that provide a relation between the classical and the quantum models, based essentially on the selection of a subspace of the classical Hilbert space. Coherent states provide a systematic tool for the inverse process, called dequantization, that associates a classical Hamiltonian system to a given quantum dynamics through the choice of a complete set of coherent states.
arXiv:1111.5774•Lecture notes series, Institute For Mathematical Sciences•Jun 1, 2010•13 citations