Symmetries and singular behaviors with Bohmian trajectories

TL;DR

This paper explores how Bohmian mechanics provides insights into phase-driven phenomena in quantum and optical systems, analyzing singular behaviors like Airy beam self-acceleration and self-focusing.

Contribution

It demonstrates the utility of Bohmian trajectories in understanding phase-related effects and singular behaviors in quantum and optical contexts.

Findings

Bohmian mechanics clarifies the role of phase in quantum dynamics.

Analysis of Airy beams reveals their self-accelerating and shape-invariant properties.

Spontaneous self-focusing is explained through phase-driven velocity fields.

Abstract

Quantum mechanics is able to predict challenging behaviors even in the simplest physical scenarios. These behaviors are possible because of the important dynamical role that phase plays in the evolution of quantum systems, and are very similar, on the other hand, to effects observable in analogous optical systems. This work focuses on how Bohmian mechanics proves to be a rather convenient theoretical framework to analyze phase-based phenomena, since the phase constitutes the central element in this hydrodynamical formulation of quantum mechanics. More specifically, it allows us to understand how spatial phase variations give rise to velocity fields that eventually rule the dynamical behavior of quantum systems, and that, when integrated in time locally (i.e., taking into account specific positions), they provide us with a neat local (point by point) description of the system evolution in the configuration space. Indeed, it will also be seen that this idea transcends the quantum realm and can be profitably used to describe the behavior of optical analogs with rather singular behaviors. With this purpose, two interesting phenomena that take place in free space are considered, namely, the self-acceleration and shape-invariance of Airy beams, and spontaneous self-focusing.