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A. Jüngel, J. Milisic:
"Macroscopic Quantum Models With and Without Collisions";
in: "Proceedings of the Sixth International Workshop on Mathematical Aspects of Fluid and Plasma", issued by: K. Aoki, P. Degond, R. Illner; Bulletin of the Institute of Mathematics Academia Sinica (New Series), Taiwan, 2007, ISSN: 0304-9825, 251 - 279.

Recent progress on the derivation of macroscopic quantum models,
particularly used in semiconductor device modeling, is
reviewed. The first part of the survey is concerned with collisionless
models, namely quantum hydrodynamic equations. These models
are derived from the mixed-state Schr\"odinger system or from the
Wigner equation. In the second part, starting from a Wigner-Boltzmann-type
equation, quantum diffusion models like the viscous quantum hydrodynamic
and the quantum drift-diffusion equations are derived. For these
quantum diffusion models,
new numerical results for a simple semiconductor
resonant tunneling diode are presented.
Moreover, some hybrid macroscopic-microscopic models for semiconductor
devices are reviewed.

Siehe englisches Abstract.

Quantum hydrodynamic equations, quantum drift-diffusion equations, moment method, semiconductor, viscosity, hybrid models