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.

References in corpus (6)

• Computing the wavefunction from trajectories: particle and wave pictures in quantum mechanics and their relation
• Bohmian description of a decaying quantum system
• Observation of diffractive orbits in the spectrum of excited NO in a magnetic field
• Dynamics of quantum trajectories in chaotic systems
• Generic Bohmian Trajectories of an Isolated Particle
• Rydberg wavepackets in terms of hidden-variables: de Broglie-Bohm trajectories

Cited by in corpus (4)

• Applied Bohmian Mechanics
• Bohmian mechanics, the quantum-classical correspondence and the classical limit: the case of the square billiard
• Are Bohmian trajectories real? On the dynamical mismatch between de Broglie-Bohm and classical dynamics in semiclassical systems
• The theory of the Double Solution: Dynamical issues in quantum systems in the semiclassical regime