Classical and Bohmian trajectories in integrable and non integrable systems

TL;DR

This paper compares classical and quantum trajectories in the Hénon-Heiles system, revealing that Bohmian trajectories exhibit chaos in both integrable and non-integrable cases, with different onset times.

Contribution

It provides a detailed comparison of classical and Bohmian quantum trajectories in integrable and non-integrable Hénon-Heiles systems, highlighting differences in chaos emergence.

Findings

Bohmian trajectories are chaotic in both cases.

Chaos appears at different times in integrable vs. non-integrable systems.

Invariant curves differ between classical and quantum analyses.

Abstract

In the present paper we study the classical and the quantum H\'enon-Heiles systems. In particular we make a comparison between the classical and the quantum trajectories of the integrable and of the non integrable H\'enon Heiles Hamiltonian. From a classical standpoint, we study theoretically and numerically the form of the invariant curves in the Poincar\'e surfaces of section for several values of the coupling parameter of the integrable case and compare them with those of the non integrable case. Then we study the corresponding Bohmian trajectories and we find that they are chaotic in both cases, but chaos emerges at different times.