Integrals of motion in 3-d Bohmian Trajectories

TL;DR

This paper explores the role of integrals of motion in 3D Bohmian trajectories, analyzing how they influence chaos, order, and the structure of quantum trajectories, with implications for understanding quantum chaos.

Contribution

It extends previous work by examining both partial and full integrability in 3D Bohmian systems and discusses their physical significance.

Findings

Identification of integral surfaces governing trajectories

Distinction between ordered and chaotic trajectories based on integrability

Implications for quantum chaos understanding

Abstract

Chaos in Bohmian Quantum Mechanics is an open field of research. In general, most of the 3-d Bohmian trajectories are free to wander around the 3-d space. However there are cases where the evolution of the trajectories is dictated by exact or approximate integrals of motion. A first case corresponds to partial integrability, where the trajectories (ordered and chaotic) evolve on certain integral surfaces. A second case corresponds to ordered trajectories. In this paper we extend our previous work in 3-d Bohmian Chaos by using both forms of integrability and discuss their physical implications.