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 Navier-Stokes fluid.

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.

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