Quantum cohomology demonstates an exact 11 correspondence between the
Schroedinger equation for a charged particle of mass m in an electromagnetic
field (generated by potentials) and the NavierStokes equation (NOT the usual
Euler approximations) for the vorticity of a compressible, viscous
fluid! The result can be obtained by applying a certain complex mapping to the
2dimensional time dependent Schroedinger equation, then separating the
resulting equations into real and imaginary parts.
The complex square of the wave function can be identified with the Enstrophy
(square of the fluid vorticity) distribution in the fluid representation. This
exact result of a well defined transformation is not at all equivalent to the
Madelung to Takabashi Eulerian fluid dynamic analogies, which historically have
been used for interpreting quantum evolution.
In addition, the transformation result indicates the existence of a primitive
viscosity dissipation coefficient in the quantum system, equal to the ratio of
Planck's constant divided by the "particle" mass: viscosity = h/m.
The elemental "particle" mass is attributed to the inertia of an
elemental Vortex in the hydrodynamic representation, and is similar to the
"hole" mass in crystalline lattices.
Such results were obtained a number of years ago as a curiosity, but now they
have current applicability to the problems of understanding dissipation
phenomena in Type II superconductors, for the Enstrophy distribution in the
fluid representation maps to the Magnetic field penetration distributions in the
quantum representation.
