@article{M2AN_1994__28_7_853_0,
author = {Arnold, A.},
title = {On absorbing boundary conditions for quantum transport equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {28},
year = {1994},
pages = {853-872},
mrnumber = {1309417},
zbl = {0821.45002},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_1994__28_7_853_0}
}
Arnold, A. On absorbing boundary conditions for quantum transport equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 28 (1994) pp. 853-872. http://gdmltest.u-ga.fr/item/M2AN_1994__28_7_853_0/
[1] , , , 1991, The one-dimensional periodic Bloch-Poisson equation, M3AS, 1, 83-112. | MR 1105009 | Zbl 0828.34073
[2] , , 1995, An operator splitting method forthe Wigner-Poisson problem, to appear in SIAM J. Num. Anal. | MR 1360463 | Zbl 0860.65143
[3] , , 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] , 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 777741 | Zbl 0648.46028
[5] , , 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 1080715 | Zbl 0742.35046
[6] , , 1977, Absorbing boundary conditions for the numerical simulation of waves, Math. Comp., 31, 629-651. | MR 436612 | Zbl 0367.65051
[7] , 1987, Wigner function model of a resonant-tunneling semiconductor device, Phys. Rev. B, 36, 1570-1580.
[8] , , 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 0829.35063
[9] , , 1987, Error analysis for absorbing boundary conditions, Numer. Math., 51, 459-467. | MR 902101 | Zbl 0656.35076
[10] , , , , 1989, Selfconsistent study of the resonant tunneling diode, Phys. Rev. B., 39, 7720-7735.
[11] , 1970, Initial boundary value problems for hyperbolic Systems, Comm. Pure Appl. Math., 23,277-298. | MR 437941 | Zbl 0193.06902
[12] , , 1989, Initial-Boundary Value Problems and the Navier-Stokes Equations, Academic Press, San Diego. | MR 998379 | Zbl 0689.35001
[13] , , 1989, An analysis of the quantum Liouville equation, Z. angew. Math. Mech., 69, 121-127. | MR 990011 | Zbl 0682.46047
[14] , , , 1990, Semiconductor Equations, Springer-Verlag, Wien, New York. | MR 1063852 | Zbl 0765.35001
[15] , 1993, Asymptotic analysis of a scaled Wigner equation and quantum scattering, To appear in M3AS.
[16] , , , 1989, Absorbing boundary conditions for the simulation of quantum transport phenomena, Transport Theory and Statistical Physics, 18, 331-346. | MR 1026635 | Zbl 0703.35163
[17] , 1987, Autour de l'Approximation Semi-classique, Birkhauser, Boston. | MR 897108 | Zbl 0621.35001
[18] , 1987, Pseudodifferential Operators and Spectral Theory, Springer-Verlag, Berlin, Heidelberg. | MR 883081 | Zbl 0616.47040
[19] , 1991, The one-dimensional Wigner-Poisson problem and its relation to the Schrödinger-Poisson problem, SIAM J. Math. Anal., 22, 957-972. | MR 1112058 | Zbl 0738.35077
[20] , 1983, The Wigner representation of quantum mechanics, Sov. Phys. Usp., 26, 311-327. | MR 730012