Macroscopic Quantum Models With and Without Collisions

Recent progress on the derivation of macroscopic quantum models 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 Schrödinger 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 resonant tunneling diode are presented. Moreover, some hybrid macroscopicmicroscopic models are reviewed.

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