2021/07/13 by Remy Messadene, Messadene, Remy
Physics and Astronomy · #47B93 #FOS: Physical sciences #Mathematical Physics (math-ph) #Model Reduction and Neural Networks #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2107.06004
openalex publication_date 2021/07/13 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
A recent formalism capturing the classical-quantum coupling in a Hamiltonian\ntheory for probabilistic classical mechanics has been proposed: the Koopman-van\nHove formulation. The aims of this report are twofolds. First, we rigourously\nexpose this new framework for a non-expert audience and present a construction\nfor the operatorial analogues to the classical angular and linear momentum\noperators. We then investigate the group actions generating their average as\nmomentum maps as well as their associated dynamics. Finally, we illustrate the\ntheory by deriving the Koopman-van Hove formulation to the Kepler problem,\nharmonic and anharmonic oscillators.\n