On absorbing boundary conditions for quantum transport equations
ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 7, pp. 853-872.
@article{M2AN_1994__28_7_853_0,
     author = {Arnold, A.},
     title = {On absorbing boundary conditions for quantum transport equations},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {853--872},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {28},
     number = {7},
     year = {1994},
     mrnumber = {1309417},
     zbl = {0821.45002},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1994__28_7_853_0/}
}
TY  - JOUR
AU  - Arnold, A.
TI  - On absorbing boundary conditions for quantum transport equations
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1994
SP  - 853
EP  - 872
VL  - 28
IS  - 7
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1994__28_7_853_0/
LA  - en
ID  - M2AN_1994__28_7_853_0
ER  - 
%0 Journal Article
%A Arnold, A.
%T On absorbing boundary conditions for quantum transport equations
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1994
%P 853-872
%V 28
%N 7
%I AFCET - Gauthier-Villars
%C Paris
%U http://www.numdam.org/item/M2AN_1994__28_7_853_0/
%G en
%F M2AN_1994__28_7_853_0
Arnold, A. On absorbing boundary conditions for quantum transport equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 7, pp. 853-872. http://www.numdam.org/item/M2AN_1994__28_7_853_0/

[1] A. Arnold, P. A. Markowich, N. Mauser, 1991, The one-dimensional periodic Bloch-Poisson equation, M3AS, 1, 83-112. | MR | Zbl

[2] A. Arnold, C. Ringhofer, 1995, An operator splitting method forthe Wigner-Poisson problem, to appear in SIAM J. Num. Anal. | MR | Zbl

[3] F. A. Buot, K. L. Jensen, 1990, Lattice Weyl-Wigner formulation of exact many-body quantum-transport theory and applications to novel solid-state quantum-based devices, Phys. Rev. B., 42, 9429-9457.

[4] M. Cessenat, 1985, Théorèmes de trace pour des espaces de fonctions de la neutronique, C. R. Acad. Sc. Paris, tome 300, série I, n° 3, 89-92. | MR | Zbl

[5] P. Degond, P. A. Markowich, 1990, A quantum transport model for semiconductors : the Wigner-Poisson problem on a bounded Brillouin zone, Modélisation Mathématique et Analyse Numérique, 24, 697-710. | Numdam | MR | Zbl

[6] B. Engquist, A. Majda, 1977, Absorbing boundary conditions for the numerical simulation of waves, Math. Comp., 31, 629-651. | MR | Zbl

[7] W. R. Frensley, 1987, Wigner function model of a resonant-tunneling semiconductor device, Phys. Rev. B, 36, 1570-1580.

[8] T. Ha-Duong, P. Joly, 1990, On the stability analysis of boundary conditions for the wave equation by energy methods, Part I: The homogeneous case, Rapports de Recherche 1306, INRIA. | Zbl

[9] L. Halpern, J. Rauch, 1987, Error analysis for absorbing boundary conditions, Numer. Math., 51, 459-467. | MR | Zbl

[10] N. Kluksdahl, A. M. Kriman, D. K. Ferry, C. Ringhofer, 1989, Selfconsistent study of the resonant tunneling diode, Phys. Rev. B., 39, 7720-7735.

[11] H. O. Kreiss, 1970, Initial boundary value problems for hyperbolic Systems, Comm. Pure Appl. Math., 23,277-298. | MR | Zbl

[12] H. O. Kreiss, J. Lorenz, 1989, Initial-Boundary Value Problems and the Navier-Stokes Equations, Academic Press, San Diego. | MR | Zbl

[13] P. A. Markowich, C. Ringhofer, 1989, An analysis of the quantum Liouville equation, Z. angew. Math. Mech., 69, 121-127. | MR | Zbl

[14] P. A. Markowich, C. Ringhofer, C. Schmeiser, 1990, Semiconductor Equations, Springer-Verlag, Wien, New York. | MR | Zbl

[15] F. Nier, 1993, Asymptotic analysis of a scaled Wigner equation and quantum scattering, To appear in M3AS.

[16] C. Ringhofer, D. Ferry, N. Kluksdahl, 1989, Absorbing boundary conditions for the simulation of quantum transport phenomena, Transport Theory and Statistical Physics, 18, 331-346. | MR | Zbl

[17] D. Robert, 1987, Autour de l'Approximation Semi-classique, Birkhauser, Boston. | MR | Zbl

[18] M. A. Shubin, 1987, Pseudodifferential Operators and Spectral Theory, Springer-Verlag, Berlin, Heidelberg. | MR | Zbl

[19] H. Steinrück, 1991, The one-dimensional Wigner-Poisson problem and its relation to the Schrödinger-Poisson problem, SIAM J. Math. Anal., 22, 957-972. | MR | Zbl

[20] V. I. Tatarskii, 1983, The Wigner representation of quantum mechanics, Sov. Phys. Usp., 26, 311-327. | MR