Koopman wavefunctions and classical states in hybrid quantum–classical dynamics
Authors
François Gay-Balmaz, Cesare Tronci
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.
Citation
- Journal: Journal of Geometric Mechanics
- Year: 2022
- Volume: 14
- Issue: 4
- Pages: 559–596
- Publisher: American Institute of Mathematical Sciences (AIMS)
- DOI: 10.3934/jgm.2022019
BibTeX
@article{Gay_Balmaz_2022,
title={{Koopman wavefunctions and classical states in hybrid quantum–classical dynamics}},
volume={14},
ISSN={1941-4889},
DOI={10.3934/jgm.2022019},
number={4},
journal={Journal of Geometric Mechanics},
publisher={American Institute of Mathematical Sciences (AIMS)},
author={Gay-Balmaz, François and Tronci, Cesare},
year={2022},
pages={559--596}
}