Dynamics of mixed classical-quantum systems, geometric quantization and coherent states

TL;DR

This paper develops a framework for mixed quantum-classical dynamics using geometric quantization and coherent states, illustrating entanglement possibilities and the classical-quantum relationship.

Contribution

It introduces a unified Hilbert space approach for mixed systems and employs geometric quantization and coherent states for classical-quantum correspondence.

Findings

Demonstrates entanglement between classical and quantum systems.

Shows how geometric quantization relates classical and quantum models.

Uses coherent states for dequantization and classical Hamiltonian reconstruction.

Abstract

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.