Communications in Mathematical Sciences
Volume 4 (2006)
Adiabatic quantum-fluid transport models
Pages: 621 – 650
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.
Schrödinger equation; Boltzmann equation; subband model; collision operator; diffusion limit; spherical harmonic expansion model; energy-transport model
2010 Mathematics Subject Classification
Primary 82D37. Secondary 76X05, 76Y05, 78A35, 82B40.