Viscosity, Mass and Planck's Constant.

Quantum cohomology demonstates an exact 1-1 correspondence between the Schroedinger equation for a charged particle of mass m in an electromagnetic field (generated by potentials) and the Navier-Stokes 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 2-dimensional 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.


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Last update 01/23/2009
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