A Kohn-Sham system at zero temperature

Journal of Physics A: Mathematical and Theoretical

Volumn 41, Issue 38, 2008, Pages

  Cornean, H ^a   Hoke, K ^b   Neidhardt, H ^b   Racec, P N ^b   Rehberg, J ^b  

^a AALBORG UNIVERSITY   (Denmark)

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54749148789     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/38/385304     Document Type: Article

References (41)

1. Ambrosetti A and Ruiz D 2008 Multiple bound states for the Schrödinger-Poisson system Comm. Contemp. Math. 10 391-404
2. Andreu F, Caselles V and Mazón J M 2005 The Cauchy problem for a strongly degenerate quasilinear equation J. Eur. Math. Soc. (JEMS) 7 361-93
3. Andreu F, Caselles V, Mazón J M and Moll S 2006 Finite propagation speed for limited flux diffusion equations Arch. Ration. Mech. Anal. 182 269-97
4. Ayers P W 2008 The dependence on and continuity of the energy and other molecular properties with respect to the number of electrons J. Math. Chem. 43 285-303
5. Bokanowski O, López J L, Sánchez Ó and Soler J 2006 Long time behaviour to the Schrödinger-Poisson- systems Mathematical Physics of Quantum Mechanics (Lecture Notes in Phys. vol 690) (Berlin: Springer) pp 217-32
6. Bokanowski O, López J L and Soler J 2003 On an exchange interaction model for quantum transport: the Schrödinger-Poisson-Slater system Math. Models Methods Appl. Sci. 13 1397-412
7. Cahay M, McLennan M, Datta S and Lundstrom M S 1987 Importance of space-charge effects in resonant tunneling devices Appl. Phys. Lett. 50 612-4
8. Chan G K-L 1999 A fresh look at ensembles: derivative discontinuities in density functional theory J. Chem. Phys. 110 4710-23
9. Cohen M H and Wasserman A 2006 On hardeness and electronegativity equalization in chemical reactivity theory J. Stat. Phys. 125 1121-39
10. Cohen M H and Wasserman A 2007 On the foundation of chemical reactivity theory J. Phys. Chem. A 111 2229-42
11. Cornean H D, Jensen A and Moldoveanu V 2005 A rigorous proof of the Landauer-Büttiker formula J. Math. Phys. 46 042106
12. D'Aprile T and Wei J 2005 On bound states concentrating on spheres for the Maxwell-Schrödinger equation SIAM J. Math. Anal. 37 321-42
13. Dirac P A M 1930 Note on exchange phenomena in the Thomas atom Proc. Cambridge 26 376-85
14. Frensley W R 1990 Boundary conditions for open quantum systems driven far from equilibrium Rev. Mod. Phys. 62 745-91
15. Gajewski H 1993 Analysis und Numerik von Ladungstransport in Halbleitern Report 6 (Berlin: WIAS)
16. Hohenberg P and Kohn W 1964 Inhomogeneous electron gas Phys. Rev. 136 B864-71
17. Kaiser H-Chr, Neidhardt H and Rehberg J 2007 Monotonicity properties of the quantum mechanical particle density Monatshefte für Mathematik (Berlin: WIAS) p 1275 at press (Preprint)
18. Kaiser H-Chr and Rehberg J 1999 About a one-dimensional stationary Schrödinger-Poisson system with Kohn-Sham potential Z. Angew. Math. Phys. 50 423-58
19. Kaiser H-Chr and Rehberg J 2000 About a stationary Schrödinger- Poisson system with Kohn-Sham potential in a bounded two- or three-dimensional domain Nonlinear Anal. (Ser. A: Theory Methods) 41 33-72
20. Kato T 1966 Perturbation theory for linear operators Die Grundlehren der mathematischen Wissenschaften vol 132 (New York: Springer)
21. Kerkhoven T 1994 Mathematical modeling of quantum wires in periodic heterojunction structures Semiconductors: part II. (The IMA Volumes in Mathematics and its Applications vol 59) (New York: Springer) pp 237-53
22. Kerkhoven T 1996 Numerical nanostructure modeling Z. Angew. Math. Mech. 76 (Suppl. 2) 297-300
23. Kohn W and Sham L J 1965 Self-consistent equations including exchange and correlation effects Phys. Rev. 140 A1133-8
24. Levy M 1982 Electron densities in search of Hamiltonians Phys. Rev. A 26 1200-8
25. Lieb E H 1983 Density functionals for Coulomb systems Int. J. Quantum Chem. 24 243-77
26. Lieb E H and Simon B 1977 The Hartree-Fock theory for Coulomb systems Commun. Math. Phys. 53 185-94
27. Lions P-L 1987 Solutions of Hartree-Fock equations for Coulomb systems Commun. Math. Phys. 109 33-97
28. Mermin N D 1965 Thermal properties of the inhomogeneous electron gas Phys. Rev. 137 A1441-3
29. Nier F 1991 Etude mathématique et numêrique de modèles cinétiques quantiques issus de la physique des semi-conducteurs Master's Thesis Ecole Polytechnique
30. Nier F 1993 A variational formulation of Schrödinger-Poisson systems in dimension d ≤ 3 Commun. Part Differ. Equ 18 1125-47
31. Perdew J P, Parr R G, Levy M and Balduz J L 1982 Density-functional theory for fractional particle number: derivative discontinuities of the energy Phys. Rev. Lett. 49 1691-4
32. Prodan E and Nordlander P 2003 On the Kohn-Sham equations with periodic background potentials J. Stat. Phys. 111 967-92
33. Racec P N, Wulf U and Kuera J 2000 Integration of quantum transport models in classical device simulators Solid-State Electron. 44 881-6
34. Ruiz David 2006 The Schrödinger-Poisson equation under the effect of a nonlinear local term J. Funct. Anal. 237 655-74
35. Sánchez Ó and Soler J 2004 Long-time dynamics of the Schrödinger-Poisson-Slater system J. Stat. Phys. 114 179-204
36. Slater J C 1951 A Simplification of the Hartree-Fock method Phys. Rev. 81 385-90
37. Su J, Wang Z-Qi and Willem M 2007 Weighted Sobolev embedding with unbounded and decaying radial potentials J. Differ. Equ 238 201-19
38. Wang Zh and Zhou H-S 2007 Positive solution for a nonlinear stationary Schrödinger-Poisson system in Discrete Contin. Dyn. Syst. 18 809-16
39. Zeidler E 1990 Nonlinear Functional Analysis and Its Applications: part II/B. (New York: Springer) (Nonlinear monotone operators)
40. Zhang Y and Yang W 2000 Perspective on 'Density-functional theory for fractional particle number: derivative of the energy' Theor. Chem. Acc. 103 346-8
41. +-GaAs structures and comparison with measurements J. Appl. Phys. 64 3581-8