https://doi.org/10.1140/epjp/s13360-023-04266-w
Regular Article
Effective nonlinear Ehrenfest hybrid quantum-classical dynamics
1
Department of Theoretical Physics, Facultad de Ciencias, University of Zaragoza, Campus San Francisco, 50009, Zaragoza, Spain
2
Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, Edificio I+D-Campus Río Ebro, 50018, Zaragoza, Spain
3
Center for Astroparticles and High Energy Physics CAPA, University of Zaragoza, Facultad de Ciencias, Campus San Francisco, 50009, Zaragoza, Spain
Received:
17
February
2023
Accepted:
6
July
2023
Published online:
25
July
2023
The definition of a consistent evolution equation for statistical hybrid quantum-classical systems is still an open problem. In this paper, we analyze the case of Ehrenfest dynamics on systems defined by a probability density and identify the relations of the nonlinearity of the dynamics with the obstructions to define a consistent dynamics for the first quantum moment of the distribution. This first quantum moment represents the physical states as a family of classically-parametrized density matrices 
, for 
a classical point; and it is the most common representation of hybrid systems in the literature. Due to this obstruction, we consider higher order quantum moments, and argue that only a finite number of them are physically measurable. Because of this, we propose an effective solution for the hybrid dynamics problem based on approximating the distribution by those moments and representing the states by them.
The original online version of this article was revised to replace [XXXX] with [30] on page 10.
Contribution to the Focus Point on “Mathematics and Physics at the Quantum-Classical Interface” edited by D.I. Bondar, I. Joseph, G. Marmo, C. Tronci.
A correction to this article is available online at https://doi.org/10.1140/epjp/s13360-023-04321-6.
Copyright comment corrected publication 2023
© The Author(s) 2023. corrected publication 2023
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