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.