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}
}

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