Classical and Bohmian trajectories in semiclassical systems: Mismatch in dynamics, mismatch in reality?

The de Broglie–Bohm (BB) interpretation of quantum mechanics aims to give a realist description of quantum phenomena in terms of the motion of point-like particles following well-defined trajectories. This work is concerned with the BB account of the properties of semiclassical systems. Semiclassical systems are quantum systems that display classical trajectories: the wavefunction and the observable properties of such systems depend on the trajectories of the classical counterpart of the quantum system. For example the quantum properties have regular or disordered characteristics depending on whether the underlying classical system has regular or chaotic dynamics. In contrast, Bohmian trajectories in semiclassical systems have little in common with the trajectories of the classical counterpart, creating a dynamical mismatch relative to the quantum-classical correspondence visible in these systems. Our aim is to describe this mismatch (explicit illustrations are given), explain its origin, and examine some of the consequences for the status of Bohmian trajectories in semiclassical systems. We argue in particular that semiclassical systems put stronger constraints on the empirical acceptability and plausibility of Bohmian trajectories because the usual arguments given to dismiss the mismatch between the classical and the BB motions are weakened by the occurrence of classical trajectories in the quantum wavefunction of such systems.