On an exchange interaction model for quantum transport: The Schrödinger-Poisson-Slater system

Mathematical Models and Methods in Applied Sciences

Volumn 13, Issue 10, 2003, Pages 1397-1412

  Bokanowski, Olivier ^a   López, José L ^b   Soler, Juan ^b  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

Exchange interaction; Minimal energy solution; Mixed state Schr dinger Poisson system; Slater approach; Strichartz estimates

Indexed keywords

EID: 0344494858     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202503002969     Document Type: Article

References (21)

1. V. Bach, Accuracy of mean field approximations for atoms and molecules, Commun. Math. Phys. 155 (1993) 295-310.
2. O. Bokanowski, B. Grébert and N. Mauser, Approximations de l'énergie cinétique en fonction de la densité pour un modèle de Coulomb périodique, C. R. Acad. Sci., Math. Phys. 329 (1999) 85-90.
3. O. Bokanowski, B. Grébert and N. Mauser, Local density approximations for the energy of a periodic Coulomb model, Math. Models Methods Appl. Sci. 13 (2003) 1185-1217.
4. O. Bokanowski and N. Mauser, Local approximation for the Hartree-Fock exchange potential: A deformation approach, Math. Models Methods Appl. Sci. 9 (1999) 941-961.
5. N. Burq, P. Gérard and N. Tzvetkov, Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds, preprint.
6. 2 solutions to the Schrödinger-Poisson system: Existence, uniqueness, time behaviour, and smoothing effects, Math. Models Methods Appl. Sci. 8 (1997) 1051-1083.
7. T. Cazenave, An introduction to nonlinear Schrödinger equations, Textos de Métodos Matemáticos Vol. 26 (Universidade Federal do Rio de Janeiro, 1993), 2nd edition.
8. P. A. M. Dirac, Note on exchange phenomena in the Thomas-Fermi atom, Proc. Cambridge Philos. Soc. 26 (1931) 376-385.
9. G. Friesecke, Pair correlation and exchange phenomena in the free electron gas, Comm. Math. Phys. 184 (1997) 143-171.
10. I. Gasser, R. Illner, P. A. Markowich and C. Schmeiser, Semiclassical, t → ∞ asymptotics and dispersive effects for Hartree-Fock systems, Maths. Methods Anal. Numer. 32 (1998) 699-713.
11. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. A140 (1965) 1133.
12. C. Le Bris, Some results on the Thomas-Fermi-Dirac-von Weizsäcker model, Diff. Int. Equations 6 (1993) 337-353.
13. C. LeBris and E. Cancès, On the time-dependent Hartree-Fock equations coupled with a classical nuclear dynamics, Math. Models Methods Appl. Sci. 9 (1999) 963-990.
14. E. H. Lieb, Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation, Studies Appl. Math. 57 (1977) 93-105.
15. E. H. Lieb, Thomas-Fermi and related theories of atoms and molecules, Rev. Mod. Phys. 53 (1981) 603-640.
16. E. H. Lieb and B. Simon, The Hartree-Fock theory for Coulomb systems, Comm. Math. Phys. 53 (1977) 185-194.
17. P. L. Lions, Solution of Hartree-Fock equations for Coulomb systems, Comm. Math. Phys. 109 (1987) 33-97.
18. R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford Univ. Press, 1989).
19. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations (Springer-Verlag, 1983).
20. O. Sánchez and J. Soler, Long-time dynamics of the Schödinger-Poisson-Slater system, to appear in J. Stat. Phys.
21. J. C. Slater, A simplification of the Hartree-Fock method, Phys. Rev. 81 (1951) 385-390.