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.


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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