Vortices are known to play a key role in the dynamics of the quantum trajectories defined within the framework of the de Broglie-Bohm formalism of quantum mechanics. It has been rigourously proved that the motion of a vortex in the associated velocit
y field can induce chaos in these trajectories, and numerical studies have explored the rich variety of behaviors that due to their influence can be observed. In this paper, we go one step further and show how the theory of dynamical systems can be used to construct a general and systematic classification of such dynamical behaviors. This should contribute to establish some firm grounds on which the studies on the intrinsic stochasticity of Bohms quantum trajectories can be based. An application to the two dimensional isotropic harmonic oscillator is presented as an illustration.
The interaction of streamers in nitrogen-oxygen mixtures such as air is studied. First, an efficient method for fully three-dimensional streamer simulations in multiprocessor machines is introduced. With its help, we find two competing mechanisms how
two adjacent streamers can interact: through electrostatic repulsion and through attraction due to nonlocal photo-ionization. The non-intuitive effects of pressure and of the nitrogen-oxygen ratio are discussed. As photo-ionization is experimentally difficult to access, we finally suggest to measure it indirectly through streamer interactions.
