Can Bohmian trajectories account for quantum recurrences having classical periodicities?

Abstract

Quantum systems in specific regimes display recurrences at the period of the periodic orbits of the corresponding classical system. We investigate the excited hydrogen atom in a magnetic field -- a prototypical system of 'quantum chaos' -- from the point of view of the de Broglie Bohm (BB) interpretation of quantum mechanics. The trajectories predicted by BB theory are computed and contrasted with the time evolution of the wavefunction, which shows pronounced features at times matching the period of closed orbits of the classical hydrogen in a magnetic field problem. Individual BB trajectories do not possess these periodicities and cannot account for the quantum recurrences. These recurrences can however be explained by BB theory by considering the ensemble of trajectories compatible with an initial statistical distribution, although none of the trajectories of the ensemble are periodic, rendering unclear the dynamical origin of the classical periodicities.