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Comptes Rendus Mathématique
Volume 334, n° 4
pages 283-288 (2002)
Doi : S1631-073X(02)02263-X
Received : 5 Mars 2001 ; 
A mathematical model for the transient evolution of a resonant tunneling diode
Modélisation d'une diode à effet tunnel résonant en régime transitoire
 

Naoufel Ben Abdallah , Olivier Pinaud
Mathématiques pour l'industrie et la physique, UMR 5640, Université P. Sabatier, UFR MIG, 118, route de Narbonne, 31062 Toulouse cedex 4, France 

Note presented by Pierre-Louis Lions

Abstract

A mathematical model of quantum transient transport is derived and analyzed. The model describes the evolution of electrons injected into the “device” by reservoirs having a stationary statistics. The electrostatic potential in the device is modified by electron presence through electrostatic interaction. The wave functions are computed in the device region and satisfy non homogeneous open boundary conditions at the device edges. A priori estimates are deduced from the “dissipative properies” of the boundary conditions and from the repulsive character of the electrostatic interaction. To cite this article: N. Ben Abdallah, O. Pinaud, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 283-288.

The full text of this article is available in PDF format.
Résumé

Un modèle de transport quantique transitoire est dérivé et analysé. Il décrit l'évolution des fonctions d'onde d'un système d'électrons injectés dans une zone active à partir de réservoirs selon une statistique stationnaire. Le potentiel électrostatique est modifié, dans la région active, par l'interaction électrostatique due à la présence des électrons. Les équations de Schrödinger sont résolues uniquement dans la zone active et sont munies de conditions aux limites transparentes non homogènes aux extrémités de cette même zone. Les estimations a priori sont déduites des « propriétés dissipatives » des conditions aux limites et de la repulsivité de l'interaction électrostatique. Pour citer cet article : N. Ben Abdallah, O. Pinaud, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 283-288.

The full text of this article is available in PDF format.


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