Origin of chaos in 3-d Bohmian trajectories

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 [1,2], 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.