Koopman wavefunctions and classical states in hybrid quantum-classical dynamics

• URL: http://arxiv.org/abs/2108.01482v2
• Date: Tue, 24 May 2022 16:36:40 GMT
• Title: Koopman wavefunctions and classical states in hybrid quantum-classical dynamics
• Authors: Fran\c{c}ois Gay-Balmaz, Cesare Tronci
• Abstract summary: We deal with the reversible dynamics of coupled quantum and classical systems. We exploit the theory of hybrid quantum-classical wavefunctions to devise a closure model for the coupled dynamics.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We deal with the reversible dynamics of coupled quantum and classical systems. Based on a recent proposal by the authors, we exploit the theory of hybrid quantum-classical wavefunctions to devise a closure model for the coupled dynamics in which both the quantum density matrix and the classical Liouville distribution retain their initial positive sign. In this way, the evolution allows identifying a classical and a quantum state in interaction at all times, thereby addressing a series of stringent consistency requirements. After combining Koopman's Hilbert-space method in classical mechanics with van Hove's unitary representations in prequantum theory, the closure model is made available by the variational structure underlying a suitable wavefunction factorization. Also, we use Poisson reduction by symmetry to show that the hybrid model possesses a noncanonical Poisson structure that does not seem to have appeared before. As an example, this structure is specialized to the case of quantum two-level systems.

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