@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] The one-dimensional periodic Bloch-Poisson equation, M3AS, 1, 83-112. | MR | Zbl
, , , 1991,[2] An operator splitting method forthe Wigner-Poisson problem, to appear in SIAM J. Num. Anal. | MR | Zbl
, , 1995,[3] 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.
, , 1990,[4] 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
, 1985,[5] 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
, , 1990,[6] Absorbing boundary conditions for the numerical simulation of waves, Math. Comp., 31, 629-651. | MR | Zbl
, , 1977,[7] Wigner function model of a resonant-tunneling semiconductor device, Phys. Rev. B, 36, 1570-1580.
, 1987,[8] 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
, , 1990,[9] Error analysis for absorbing boundary conditions, Numer. Math., 51, 459-467. | MR | Zbl
, , 1987,[10] Selfconsistent study of the resonant tunneling diode, Phys. Rev. B., 39, 7720-7735.
, , , , 1989,[11] Initial boundary value problems for hyperbolic Systems, Comm. Pure Appl. Math., 23,277-298. | MR | Zbl
, 1970,[12] Initial-Boundary Value Problems and the Navier-Stokes Equations, Academic Press, San Diego. | MR | Zbl
, , 1989,[13] An analysis of the quantum Liouville equation, Z. angew. Math. Mech., 69, 121-127. | MR | Zbl
, , 1989,[14] Semiconductor Equations, Springer-Verlag, Wien, New York. | MR | Zbl
, , , 1990,[15] Asymptotic analysis of a scaled Wigner equation and quantum scattering, To appear in M3AS.
, 1993,[16] Absorbing boundary conditions for the simulation of quantum transport phenomena, Transport Theory and Statistical Physics, 18, 331-346. | MR | Zbl
, , , 1989,[17] Autour de l'Approximation Semi-classique, Birkhauser, Boston. | MR | Zbl
, 1987,[18] Pseudodifferential Operators and Spectral Theory, Springer-Verlag, Berlin, Heidelberg. | MR | Zbl
, 1987,[19] The one-dimensional Wigner-Poisson problem and its relation to the Schrödinger-Poisson problem, SIAM J. Math. Anal., 22, 957-972. | MR | Zbl
, 1991,[20] The Wigner representation of quantum mechanics, Sov. Phys. Usp., 26, 311-327. | MR
, 1983,