A quantum particle subject to a time-dependent force appears as if it were a collisionless turbulent fluid with a tensorial pressure given by a known equation of state. Such a fluid may possess topological singularities such as line vortices and sheet vortices, which are frozen in the fluid. Creation and destruction of these vortices are only possible when the forcing potential is singular. In addition, when the initial data are of large scale, the quantum fluctuations have a tendency to become steepened, characteristic of the classical compressible fluid in forming shock waves, and the nonlinear steepening is halted by the wave dispersion in generating an abundance of short waves. Chaotic quantum dynamics is expected to be governed by the interplay between wave steepening and vortex interactions.
