Contents Online

# Communications in Mathematical Sciences

## Volume 4 (2006)

### Number 3

### Adiabatic quantum-fluid transport models

Pages: 621 – 650

DOI: http://dx.doi.org/10.4310/CMS.2006.v4.n3.a8

#### Authors

#### Abstract

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.

#### Keywords

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.