Hybrid Koopman C∗ –formalism and the hybrid quantum–classical master equation

Based on Koopman formalism for classical statistical mechanics, we propose a formalism to define hybrid quantum–classical dynamical systems by defining (outer) automorphisms of the C ∗ algebra of hybrid operators and realizing them as linear transformations on the space of hybrid states. These hybri...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2023-09, Vol.56 (37), p.374001
Main Authors: Bouthelier-Madre, C, Clemente-Gallardo, J, González-Bravo, L, Martínez-Crespo, D
Format: Article
Language:English
Subjects:
algebras
hybrid quantum–classical systems
Koopman methods
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Summary:Based on Koopman formalism for classical statistical mechanics, we propose a formalism to define hybrid quantum–classical dynamical systems by defining (outer) automorphisms of the C ∗ algebra of hybrid operators and realizing them as linear transformations on the space of hybrid states. These hybrid states are represented as density matrices on the Hilbert space obtained from the hybrid C ∗ –algebra by the GNS construction. We also classify all possible dynamical systems which are unitary and obtain the possible hybrid Hamiltonian operators.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/aceed5