Chaos and ergodicity in a partially integrable 3d Bohmian system: a comparison with 2d systems

Abstract

In the present paper we study the Bohmian dynamics of a partially integrable 3d Bohmian system whose trajectories evolve on spherical surfaces. By use of spherical coordinates (R, ϕ, θ) we study the behaviour of unstable fixed points that generate chaos on the (ϕ, θ) plane and discuss the differences between them and those of planar 2d systems. Finally, we show for the first time that the chaotic trajectories of this system are ergodic although the number of its nodes is very small (two). Thus we can observe ergodicity not only in multinodal 2d systems but also in partially integrable systems with few nodes due to their curved geometry.