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Macroscopic quantum models with and without collisions. (English) Zbl 1128.76069

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

MSC:

76Y05 Quantum hydrodynamics and relativistic hydrodynamics
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
82D37 Statistical mechanics of semiconductors
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