  The behaviour of classical mechanical systems is characterised by their phase
portraits, the collections of their trajectories. Heisenberg's uncertainty
principle precludes the existence of sharply defined trajectories, which is why
traditionally only the time evolution of wave functions is studied in quantum
dynamics. These studies are quite insensitive to the underlying structure of
quantum phase space dynamics. We identify the flow that is the quantum analog
of classical particle flow along phase portrait lines. It reveals hidden
features of quantum dynamics and extra complexity. Being constrained by
conserved flow winding numbers, it also reveals fundamental topological order
in quantum dynamics that has so far gone unnoticed.
