Nanometer Vortices

An exact complex mapping is used to show the close relationship between the Schroedinger equation for a charged particle in an external ̄eld, the Landau-Ginsburg equation for the order parameter in a superconductor, and the equation for the evolution of vorticity in a Navier-Stokes compressible, viscous, °uid. The absolute square of the wave function, or complex order paramter, is exactly equal to the vorticity distribution (including topological vorticity defects) in a °uid with a viscosity coe±cient de ̄ned as o = h=21⁄4m0. This cohomological, but classical, interpretation of the wave function, o®ers an alternative to the Copenhagen dogma, and has application to the understanding of what recently have been described as superconducting vortices. However, the objects of experimental interest are better described as domains of quantized circulation, not vorticity. The vorticity distribution will contain topological circulation defects of null vorticity, for which the circulation integral around a closed path is quantized by deRham's theorems.