On absorbing boundary conditions for quantum transport equations

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1. [1] A. ARNOLD, P. A. MARKOWICH, N. MAUSER, 1991, The one-dimensional periodic Bloch-Poisson equation, M3AS, 1, 83-112. Zbl0828.34073MR1105009
2. [2] A. ARNOLD, C. RINGHOFER, 1995, An operator splitting method forthe Wigner-Poisson problem, to appear in SIAM J. Num. Anal. Zbl0860.65143MR1360463
3. [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. [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. Zbl0648.46028MR777741
5. [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. Zbl0742.35046MR1080715
6. [6] B. ENGQUIST, A. MAJDA, 1977, Absorbing boundary conditions for the numerical simulation of waves, Math. Comp., 31, 629-651. Zbl0367.65051MR436612
7. [7] W. R. FRENSLEY, 1987, Wigner function model of a resonant-tunneling semiconductor device, Phys. Rev. B, 36, 1570-1580. 
8. [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. Zbl0829.35063
9. [9] L. HALPERN, J. RAUCH, 1987, Error analysis for absorbing boundary conditions, Numer. Math., 51, 459-467. Zbl0656.35076MR902101
10. [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. [11] H. O. KREISS, 1970, Initial boundary value problems for hyperbolic Systems, Comm. Pure Appl. Math., 23,277-298. Zbl0193.06902MR437941
12. [12] H. O. KREISS, J. LORENZ, 1989, Initial-Boundary Value Problems and the Navier-Stokes Equations, Academic Press, San Diego. Zbl0689.35001MR998379
13. [13] P. A. MARKOWICH, C. RINGHOFER, 1989, An analysis of the quantum Liouville equation, Z. angew. Math. Mech., 69, 121-127. Zbl0682.46047MR990011
14. [14] P. A. MARKOWICH, C. RINGHOFER, C. SCHMEISER, 1990, Semiconductor Equations, Springer-Verlag, Wien, New York. Zbl0765.35001MR1063852
15. [15] F. NIER, 1993, Asymptotic analysis of a scaled Wigner equation and quantum scattering, To appear in M3AS. Zbl0870.45003
16. [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. Zbl0703.35163MR1026635
17. [17] D. ROBERT, 1987, Autour de l'Approximation Semi-classique, Birkhauser, Boston. Zbl0621.35001MR897108
18. [18] M. A. SHUBIN, 1987, Pseudodifferential Operators and Spectral Theory, Springer-Verlag, Berlin, Heidelberg. Zbl0616.47040MR883081
19. [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. Zbl0738.35077MR1112058
20. [20] V. I. TATARSKII, 1983, The Wigner representation of quantum mechanics, Sov. Phys. Usp., 26, 311-327. MR730012