A quantum-transport model for semiconductors : the Wigner-Poisson problem on a bounded Brillouin zone
M2AN - Modélisation mathématique et analyse numérique, Volume 24 (1990) no. 6, pp. 697-709.
@article{M2AN_1990__24_6_697_0,
     author = {Degond, Pierre and Markowich, Peter A.},
     title = {A quantum-transport model for semiconductors : the {Wigner-Poisson} problem on a bounded {Brillouin} zone},
     journal = {M2AN - Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {697--709},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {24},
     number = {6},
     year = {1990},
     zbl = {0742.35046},
     mrnumber = {1080715},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1990__24_6_697_0/}
}
TY  - JOUR
AU  - Degond, Pierre
AU  - Markowich, Peter A.
TI  - A quantum-transport model for semiconductors : the Wigner-Poisson problem on a bounded Brillouin zone
JO  - M2AN - Modélisation mathématique et analyse numérique
PY  - 1990
DA  - 1990///
SP  - 697
EP  - 709
VL  - 24
IS  - 6
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1990__24_6_697_0/
UR  - https://zbmath.org/?q=an%3A0742.35046
UR  - https://www.ams.org/mathscinet-getitem?mr=1080715
LA  - en
ID  - M2AN_1990__24_6_697_0
ER  - 
%0 Journal Article
%A Degond, Pierre
%A Markowich, Peter A.
%T A quantum-transport model for semiconductors : the Wigner-Poisson problem on a bounded Brillouin zone
%J M2AN - Modélisation mathématique et analyse numérique
%D 1990
%P 697-709
%V 24
%N 6
%I AFCET - Gauthier-Villars
%C Paris
%G en
%F M2AN_1990__24_6_697_0
Degond, Pierre; Markowich, Peter A. A quantum-transport model for semiconductors : the Wigner-Poisson problem on a bounded Brillouin zone. M2AN - Modélisation mathématique et analyse numérique, Volume 24 (1990) no. 6, pp. 697-709. http://www.numdam.org/item/M2AN_1990__24_6_697_0/

[1] M. Cessenat, Théorèmes de Trace pour des Espaces des Fonctions de la Neutronique. C.R. Acad. Sc. Paris, tome 300, série l, n°3, 1985. | MR | Zbl

[2] R. Dautray and J. L. Lions, Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques. Tome 3, Masson, Paris, 1985. | MR

[3] F. Golse, P. L. Lions, B. Perthame and R. Sentis, Regularity of the Moments of the Solution of a Transport Equation. J. Funct. Anal. 88, pp. 110-125, 1988. | MR | Zbl

[4] J. C. Guillot, J. Ralston and E. Trubowitz, Semi-Classical Asymptotics in Solid State Physics. Communications in Math. Phys., vol. 116, n°3, pp. 401-415, 1988. | MR | Zbl

[5] C. Kittel, Introduction to Solid States Physics, J. Wiley and Sons, New York, 1968. | Zbl

[6] P. A. Markowich and C. Ringhofer, An Analysis of the Quantum Liouville Equation. To appear in ZAMM, 1988. | MR | Zbl

[7] P. A. Markowich, On the Equivalence of the Schrödinger and the Quantum Liouville Equations. To appear in Math. Meth. In the Appl. Sci., 1988. | MR | Zbl

[8] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer Verlag, New York-Berlin-Heidelberg-Tokyo, 1983. | MR | Zbl

[9] V. I. Tatarskii, The Wigner Representation of Quantum Mechanics. Sov. Phys. Usp., vol. 26, n°4, pp. 311-327, 1983. | MR

[10] A. Arnold,P. Degond, P. A. Markowich and H. Steinrück, The Wigner-Poisson Equation in a Crystal, to appear in : Applied Mathematics Letters, 1989. | MR | Zbl

[11] P. Degond, P. A. Markowich and H. Steinrück, A Mathematical Derivation of the Wigner-Poisson Problem on a bounded Brillouin Zone from the Schrödinger Equation, manuscript.