  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
absenceof 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.
