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

Ben Abdallah, Naoufel; Méhats, Florian; Negulescu, Claudia

Commun. Math. Sci. 4, No. 3, 621-650 (2006).

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

Keywords:

Schrödinger equation; Boltzmann equation; subband model; collision operator; diffusion limit; spherical harmonic expansion model; energy-transport model