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Koopman wavefunctions and classical-quantum correlation dynamics

Bondar, Denys I., Gay-Balmaz, François and Tronci, Cesare (2019) Koopman wavefunctions and classical-quantum correlation dynamics Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman-von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical-quantum coupling. The proposed model not only describes the influence of a classical system onto a quantum one, but also the reverse effect -- the quantum backreaction. These interactions are described by a new Hamiltonian wave equation overcoming shortcomings of currently employed models. For example, the density matrix of the quantum subsystem is always positive-definite. While the Liouville density of the classical subsystem is generally allowed to be unsigned, its sign is shown to be preserved in time for a specific infinite family of hybrid classical-quantum systems. The proposed description is illustrated and compared with previous theories using the exactly solvable model of a degenerate two-level quantum system coupled to a classical harmonic oscillator.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Bondar, Denys I.
Gay-Balmaz, François
Date : 2019
Copyright Disclaimer : © 2019 The Authors.
Related URLs :
Depositing User : Clive Harris
Date Deposited : 08 Aug 2019 08:21
Last Modified : 09 Aug 2019 11:51

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