About a stationary Schrödinger-Poisson system with Kohn-Sham potential in a bounded two- or three-dimensional domain

Nonlinear Analysis, Theory, Methods and Applications

Volumn 41, Issue 1, 2000, Pages 33-72

  Kaiser, Hans Christoph ^a   Rehberg, Joachim ^a  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CARRIER CONCENTRATION; ELECTRON GAS; ELECTROSTATICS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; SEMICONDUCTOR QUANTUM DOTS; SEMICONDUCTOR QUANTUM WELLS; SEMICONDUCTOR QUANTUM WIRES;

KOHN-SHAM POTENTIAL; STATIONARY SCHRODINGER-POISSON SYSTEM;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0034230627     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00261-2     Document Type: Article

References (41)

1. G. Albinus, H.-Chr. Kaiser, J. Rehberg, On Stationary Schrödinger-Poisson Equations, Preprint 66, Institute for Applied Analysis and Stochastics, Berlin, 1993.
2. A. Arnold, U. Giering, An analysis of the Marshak conditions for matching Boltzmann and Euler equations, Math. Models Methods Appl. Sci. 7(4) (1997) 557-577.
3. N. Ben Abdallah, P. Degond, P.A. Markowich, On a one-dimensional Schrödinger-Poisson scattering model, Z. Angew. Math. Phys. 48 (1997) 135-155.
4. M.S. Birman, M.Z. Solomjak, Double Stieltjes operator integrals III, Problems of Mathematical Physics, vol. 6, Izdat. Leningrad. Univ., 1973, pp. 27-53 (in Russian).
5. M.S. Birman, M.Z. Solomjak, On double Stieltjes operator integrals, Dokl. Akad. Nauk SSSR 165 (1965) 1223-1226 (in Russian).
6. Ph. Caussignac, B. Zimmermann, R. Ferro, Finite element approximation of electrostatic potential in one dimensional multilayer structures with quantized electronic charge, Computing 45 (1990) 251-264.
7. R. Courant, D. Hilbert, Methoden der Mathematischen Physik, Springer, Berlin, 1993.
8. J. Dieudonné, Grundzüge der Modernen Analysis, vol. 2, Deutscher Verlag der Wissenschaften, Berlin, 1975.
9. W.R. Frensley, Boundary conditions for open quantum systems driven far from equilibrium, Rev. Modern Phys. 62 (1990) 745.
10. H. Gajewski, Analysis und numerik von ladungstransport in halbleitern, GAMM Mitteilungen 16 (1993) 35.
11. H. Gajewski, K. Gröger, K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974.
12. H. Gajewski et al., ToSCA-Two-dimensional Semiconductor Analysis Package, Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, D-10117 Berlin.
13. I.M. Gamba, C.S. Morawetz, A viscous approximation for a 2-d steady semiconductor or transonic gas dynamic flow: Existence theorem for potential flow, Commun. Pure Appl. Math. XLIX (1996) 999-1049.
14. P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman, Boston, 1985.
15. l, p-estimate for solutions to mixed boundary value problems for second order elliptic differential equations, Math. Ann. 283 (1989) 679-687.
16. R. Hünlich, Private communication, 1996.
17. H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, Macroscopic Current Induced Boundary Conditions for Schrödinger Operators, in preparation.
18. H.-Chr. Kaiser, J. Rehberg, About a one-dimensional stationary Schrödinger-Poisson system with Kohn-Sham potential, Zeit. Angew. Math. Phys. (2 AMP), to appear.
19. H.-Chr. Kaiser, J. Rehberg, About a Stationary Schrödinger-Poisson System with Kohn-sham Potential in Nanoelectronics, Preprint 339, Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, D-10117 Berlin, Germany, 1997, with an appendix about the Kohn-Sham systen by Udo Krause.
20. H.-Chr. Kaiser, J. Rehberg, Matching the Phenomenological and the Quantum Mechanical Description of Semiconductor Devices, in preparation.
21. H.-Chr. Kaiser, J. Rehberg, On stationary Schrödinger-Poisson equations, Zeitschrift für Angewandte Mathematik und Mechanik-ZAMM 75 (1995) 467-468.
22. H.-Chr. Kaiser, J. Rehberg, On stationary Schrödinger-Poisson equations modelling an electron gas with reduced dimension, Math. Methods Appl. Sci. 20 (1997) 1283-1312.
23. T. Kato, Perturbation Theory for Linear Operators, vol. 132 of Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, 1984.
24. T. Kerkhoven, Mathematical modelling of quantum wires in periodic heterojunction structures, in: Semiconductors Part II, the IMA Volumes in Mathematics and its Applications, vol. 59, Springer, New York, 1994, pp. 237-253.
25. T. Kerkhoven, Numerical nanostructure modeling, Zeitschrift für Angewandte Mathematik und Mechanik-ZAMM 76(Suppl. 2) (1996) S297-S300; Proc. 3rd Int. Congr. on Industrial and Applied Mathematics, ICIAM 95, Hamburg, Germany, 3-7 July 1995.
26. T. Kerkhoven, Numerical nanostructure modeling, Zeitschrift für Angewandte Mathematik und Mechanik-ZAMM 76(Suppl. 2) (1996) S297-S300; Proc. 3rd Int. Congr. on Industrial and Applied Mathematics, ICIAM 95, Hamburg, Germany, 3-7 July 1995.
27. A. Klar, Asymptotic-induced domain decomposition methods for kinetic and drift-diffusion semiconductor equations, SIAM Sci. Comp. 19 (1998) 2032-2050.
28. C.S. Lent, D.J. Kirkner, The quantum transmitting boundary method, J. Appl. Phys. 67 (1990) 6353.
29. P.A. Markowich, C.A. Ringhofer, C. Schmeiser, Semiconductor Equations, Springer, Wien, 1990.
30. W. Mazja, Sobolev Spaces, Leningrad University, 1985.
31. F. Nier, A stationary Schrödinger-Poisson system arising from the modelling of electronic devices, Forum Mathematicum 2 (1990) 489.
32. F. Nier, A variational formulation of Schrödinger-Poisson systems in dimensions d ≤ 3, Commun. Partial Differential Equations 18 (1993) 1125-1147.
33. F. Nier, Etude Mathématique et Numérique de Modèles Cinétiques Quantiques Issus de la Physique des Semi-conducteurs, Master's Thesis, Ecole Polytechnique, 1991.
34. F. Nier, The dynamics of some quantum open systems with short-range nonlinearities, Nonlinearity 11 (1998) 1127-1172.
35. M. Reed, B. Simon, Methods of Modern Mathematical Physics IV: Analysis of Operators, Academic Press, New York, 1978.
36. L. Recke, J.A. Griepentrog, Solution Regularity for Linear Elliptic Boundary Value Problems with Non-smooth Data and Smoothness of the Coefficient-to-solution-map, to appear.
37. R. Temam, Navier-Stokes Equations-Theory and Numerical Analysis, North-Holland, Amsterdam, New York, Oxford, 1979.
38. G. Wachutka, A., Fleszar, F. Màca, M. Scheffler, Self-consistent green-function method for the calculation of electronic properties of localized defects at surfaces and in the bulk, J. Phys.: Condens. Matter 4 (1992) 2831-2844.
39. C. Weisbuch, B. Vinter, Quantum Semiconductor Structures: Fundamentals and Applications, Academic Press, Boston, 1991.
40. J. Wloka, Partielle Differentialgleichungen, Teubner Verlagsgesellschaft Leipzig, 1982.
41. H.-J. Wünsche, Private communication, April 1995.