Anharmonic quantum mechanical systems do not feature phase-space trajectories
Phase-space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical systems do not allow for a trajectory-based description of their phase-space dynamics. This invalidates some approaches to quantum phase-space studies. We first demonstrate the absence of trajectories in general terms. We then give an explicit proof for all quantum phase-space distributions with negative values: we show that the generation of coherences in anharmonic quantum mechanical systems is responsible for the occurrence of singularities in their phase-space velocity fields, and vice versa. This explains numerical problems repeatedly reported in the literature, and provides deeper insight into the nature of quantum phase-space dynamics.