A dynamical systems approach to Bohmian trajectories

TL;DR

This paper applies dynamical systems theory to classify and understand the complex behaviors of Bohmian trajectories influenced by vortices, aiming to ground the study of their stochasticity with a systematic framework.

Contribution

It introduces a systematic classification method for Bohmian trajectory behaviors using dynamical systems theory, advancing the understanding of quantum chaos.

Findings

Vortices induce chaos in Bohmian trajectories.

Dynamical systems theory provides a framework for classifying trajectory behaviors.

Application to harmonic oscillator illustrates the approach.

Abstract

Vortices are known to play a key role in the dynamics of the quantum trajectories defined within the framework of the de Broglie-Bohm formalism of quantum mechanics. It has been rigourously proved that the motion of a vortex in the associated velocity field can induce chaos in these trajectories, and numerical studies have explored the rich variety of behaviors that due to their influence can be observed. In this paper, we go one step further and show how the theory of dynamical systems can be used to construct a general and systematic classification of such dynamical behaviors. This should contribute to establish some firm grounds on which the studies on the intrinsic stochasticity of Bohm's quantum trajectories can be based. An application to the two dimensional isotropic harmonic oscillator is presented as an illustration.