Origin of chaos in 3-d Bohmian trajectories

TL;DR

This paper investigates the origins of chaos in three-dimensional Bohmian trajectories of a quantum system, revealing a 3D analogue of known 2D chaos mechanisms involving nodal point-X-point complexes.

Contribution

It extends the understanding of chaos mechanisms in Bohmian trajectories from 2D to 3D, identifying a foliation of nodal and X-points as the chaos-generating structure.

Findings

Existence of a 3D foliation of nodal and X-points.

Chaotic trajectories result from encounters with these structures.

Mechanism analogous to 2D systems is confirmed in 3D.

Abstract

We study the 3-d Bohmian trajectories of a quantum system of three harmonic oscillators. We focus on the mechanism responsible for the generation of chaotic trajectories. We demonstrate the existence of a 3-d analogue of the mechanism found in earlier studies of 2-d systems, based on moving 2-d `nodal point - X-point complexes'. In the 3-d case, we observe a foliation of nodal point - X-point complexes, forming a `3-d structure of nodal and X-points'. Chaos is generated when the Bohmian trajectories are scattered at one or more close encounters with such a structure.