  We study the topological properties of the quantum phase space current in the
Husimi representation, focusing on the dynamical differences, induced by these
properties, between the quantum and the classical flows. We show that the zeros
of the Husimi function are stagnation points of the current and have a nonzero
topological charge. Due to overall charge conservation, new stagnation points
with opposite charge appear in pairs in the Husimi current and they have
important roles in dynamical processes. As an example we show the topological
effect of the zeros in the transmission rate of particle through a potential
barrier.
