It is remarkable that in two spatial dimensions there exists a well defined
mapping between the Schroedinger equation for a charged particle in an
electromagnetic field, the Landau-Ginsburg order parameter theory for a
superconductor, and the viscous, compressible time dependent evolution of a
The square of the wave function becomes equal to the normal field component of the vorticity distribution in the fluid, a point of view that is in contrast to the "position probability" theory of the Born-Copenhagen school.
Recent work on nanometer superconducting structures, as well as optical
"vortices" in laser beams, has re- stimulated interest in these ideas. The
original motivation was to explain the onset of turbulence in fluid flow in
terms of the production of vortex defect pairs.