Critical points and trajectories of the Bohmian quantum flow

In the present work we study the critical points of the Bohmian quantum flow, namely the nodal point and its associated X-point, which are responsible for the generation of chaos in Bohmian trajectories. In the first part of the paper we find an analytical equation for the position of the X-point in a planar 2-d Bohmian system with a single nodal point and test its accuracy numerically. We then calculate its asymptotic curves and comment on the way they affect the evolution of the nearby Bohmian trajectories. In the second part we present our first results on the position of the X-point and its asymptotic curves in a 3d partially integrable system, where the Bohmian trajectories evolve on spherical surfaces.