Koopman wavefunctions and classical states in hybrid quantum–classical dynamics
Aug 3, 202138 pages
Published in:
- J.Geom.Mech. 14 (2022) 4, 559-596
- Published: Nov 30, 2022
e-Print:
- 2108.01482 [math-ph]
DOI:
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Abstract: (AIMS Press)
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.Note:
- Second version. Largely revised. Comments welcome!
- Koopman wavefunction
- quantum dynamics
- prequantization
- mixed quantum–classical dynamics
- momentum map
- model: hybrid
- mechanics: classical
- quantum mechanics
- density matrix
- Liouville
References(61)
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