Adiabatic quantum fluid transport models

Naoufel Ben Abdallah (1) , Florian Méhats (2) , Claudia Negulescu (1)

1 MIP - Mathématiques pour l'Industrie et la Physique
2 IRMAR - Institut de Recherche Mathématique de Rennes

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 subbands are considered in the Fermi Golden rule setting.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Naoufel Ben Abdallah, Florian Méhats, Claudia Negulescu. Adiabatic quantum fluid transport models. Communications in Mathematical Sciences, 2006, 4 (3), pp.621-650. ⟨hal-00378453⟩