Vortex dynamics and their interactions in quantum trajectories

Abstract

Vortices are known to play a key role in many important processes in physics and chemistry. Here, we study vortices in connection with the quantum trajectories that can be defined in the framework provided by the de Broglie-Bohm formalism of quantum mechanics. In a previous work, it was shown that the presence of a single moving vortex is enough to induce chaos in these trajectories. Here, this situation is explored in more detail by discussing the relationship between Lyapunov exponents and the parameters characterizing the vortex dynamics. We also consider the issue when more than one vortex exists. In this case, the interaction among them can annihilate or create pairs of vortices with opposite vorticity. This phenomenon is analyzed from a dynamical point of view, showing how the size of the regular regions in phase space grows, as vortices disappear. © 2007 IOP Publishing Ltd.