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A. Jüngel, J. Lopez, J. Montejo-Gamez:
"A new derivation of the quantum Navier-Stokes equations in the Wigner-Fokker-Planck approach";
in: "ASC Report 14/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

A quantum Navier-Stokes system for the particle, momentum, and energy
densities are formally derived from the Wigner-Fokker-Planck equation using
a moment method. The viscosity term depends on the particle density with a
shear viscosity coefficient which equals the quantum diffusion coefficient of the
Fokker-Planck collision operator. The main idea of the derivation is the use of a
so-called osmotic momentum operator, which is the sum of the phase-space momentum
and the gradient operator. In this way, a Chapman-Enskog expansion of
the Wigner function, which typically leads to viscous approximations, is avoided.
Moreover, we show that the osmotic momentum emerges from local gauge theory.

Quantum Navier-Stokes model · Wigner-Fokker-Planck equations · moment method · osmotic momentum · local gauge transformation

http://www.asc.tuwien.ac.at/preprint/2011/asc14x2011.pdf