Correlation and Branching Mechanisms in the Quantum-to-Classical Transition of Interacting Systems
Abstract
We analyze the quantum-to-classical transition of interacting systems from the viewpoint of reduced dynamical closure. Bohmian trajectories are used as a diagnostic of the probability flow generated by the full wavefunction, rather than as an alternative set of quantum predictions. A closed classical or semiclassical description of a retained coordinate can emerge either because interaction-induced correlations are suppressed or because the observable of interest is insensitive to the correlations that remain. Three models are used to isolate distinct mechanisms. In a hard-core collision, the leading tail of a broad relative-coordinate wave packet reaches the boundary before its center and generates spatial nonseparability through reflection and interference. In the Rabi model, the mixed quantum-classical Ehrenfest approximation fails when spin-position covariances prevent the spin dynamics from being determined solely by the mean oscillator coordinate. In an internal-state-dependent force model, the total mean position obeys an exact Ehrenfest equation, while the wavefunction separates into branch-resolved pointer components; mean classicality therefore does not imply branch-level classicality. These examples show that the quantum-to-classical transition of interacting systems is controlled not only by wave-packet localization but also by whether and how interaction-induced correlations enter the reduced equations of motion.
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BibTeX
@misc{cui2026correlation,
title = {{Correlation and Branching Mechanisms in the Quantum-to-Classical Transition of Interacting Systems}},
author = {Bingyu Cui},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14989},
eprint = {2609.14989},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14989},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Correlation and Branching Mechanisms in the Quantum-to-Classical Transition of Interacting Systems
AU - Bingyu Cui
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.14989
UR - https://arxiv.org/abs/2609.14989
AB - We analyze the quantum-to-classical transition of interacting systems from the viewpoint of reduced dynamical closure. Bohmian trajectories are used as a diagnostic of the probability flow generated by the full wavefunction, rather than as an alternative set of quantum predictions. A closed classical or semiclassical description of a retained coordinate can emerge either because interaction-induced correlations are suppressed or because the observable of interest is insensitive to the correlations that remain. Three models are used to isolate distinct mechanisms. In a hard-core collision, the leading tail of a broad relative-coordinate wave packet reaches the boundary before its center and generates spatial nonseparability through reflection and interference. In the Rabi model, the mixed quantum-classical Ehrenfest approximation fails when spin-position covariances prevent the spin dynamics from being determined solely by the mean oscillator coordinate. In an internal-state-dependent force model, the total mean position obeys an exact Ehrenfest equation, while the wavefunction separates into branch-resolved pointer components; mean classicality therefore does not imply branch-level classicality. These examples show that the quantum-to-classical transition of interacting systems is controlled not only by wave-packet localization but also by whether and how interaction-induced correlations enter the reduced equations of motion.
ER -