## Adiabatic quantum-fluid transport models.(English)Zbl 1296.82064

Summary: Coupled quantum-fluid models are derived by means of a diffusion approximation from adiabatic quantum-kinetic models. These models describe the electron transport of a bidimensional electron gas. Particles are confined in one direction (denoted by $$z$$) while transport occurs in an orthogonal direction (denoted by $$x$$). The length-scale in the $$z$$ direction is comparable to the de Broglie wavelength, while the $$x$$-length scale is much bigger. The aim of this paper is to investigate the diffusion limit from quantum-kinetic to quantum-fluid models, which are numerically more interesting. Transitions between sub-bands are considered in the Fermi Golden rule setting.

### MSC:

 82D37 Statistical mechanics of semiconductors 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 78A35 Motion of charged particles 82B40 Kinetic theory of gases in equilibrium statistical mechanics
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