Semiclassical, t asymptotics and dispersive effects for Hartree-Fock systems
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 32 (1998) no. 6, p. 699-713
@article{M2AN_1998__32_6_699_0,
     author = {Gasser, I. and Illner, R. and Markowich, Peter A. and Schmeiser, C.},
     title = {Semiclassical, $t\rightarrow \infty $ asymptotics and dispersive effects for Hartree-Fock systems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {32},
     number = {6},
     year = {1998},
     pages = {699-713},
     zbl = {0924.35125},
     mrnumber = {1652601},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1998__32_6_699_0}
}
Gasser, I.; Illner, R.; Markowich, P. A.; Schmeiser, C. Semiclassical, $t\rightarrow \infty $ asymptotics and dispersive effects for Hartree-Fock systems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 32 (1998) no. 6, pp. 699-713. http://www.numdam.org/item/M2AN_1998__32_6_699_0/

[CG] J. M. Chadam and R. T. Glassey, Global existence of solutions to the Cauchy problem for time dependent Hartree equations, J.M.P. 16(5), pp. 1122-1130, 1975. | MR 413843 | Zbl 0299.35084

[DF] J. P. Dlas and M. Figueira, Conservation laws and time decay for the solutions of some nonlinear Schrödinger-Hartree equations and systems, J. Math. Anal. Appl. 84, pp. 486-508, 1981. | MR 639678 | Zbl 0481.35057

[GMMP] P. Gerard, P. A. Markowich, N. J. Mauser and F. Poupaud, Homogenization limits and Wigner transforms, Comm. Pure Appl. Math. 50, No. 4, pp. 323-379, 1997. | MR 1438151 | Zbl 0881.35099

[GV] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations. II. Scattenng theory, general case, J. Funct. Anal. 32, pp. 33-71, 1979. | MR 533219 | Zbl 0396.35029

[ILZ] R. Illner, P. F. Zweifel and H. Lange, Uniqueness and asymptotic behaviour of solutions of the Wigner-Poisson and the SchrödungerPoisson Systems, M2AS 17, pp. 349-376, 1994. | MR 1273317 | Zbl 0808.35116

[LPa] P. L. Lions et T. Paul, Sur les mesures de Wigner, Revista Matematica Iberoamericana 9, pp. 553-618, 1993. | MR 1251718 | Zbl 0801.35117

[LPe] P. L. Lions et B. Perthame, Global solutions of Vlasov-Poisson type equations, preprint n. 8824, Ceremade, 1995.

[LPel] P. L. Lions et B. Perthame, Lemme de moments, de moyenne et de dispersion, C. R. Acad. Sci. Paris, 314, Serie 1, pp. 801-806, 1992. | MR 1166050 | Zbl 0761.35085

[M] P. A. Markowich, On the equivalence of the Schrödinger and the Quantum Liouville equation, M2AS 11, pp. 459-469, 1989. | MR 1001097 | Zbl 0696.47042

[MM] P. A. Markowich and N. J. Mauser, The classical limit of a self-consistent quantum-Vlasov equation in 3d, M3AS 3, pp. 109-124, 1993. | MR 1203274 | Zbl 0772.35061

[P] B. Perthame, Time decay, propagation of low moments and dispersive effects of kinetic equations, Com. PDE 21, No. 3-4, pp. 659-686, 1996. | MR 1387464 | Zbl 0852.35139

[RS] M. Reed and B. Simon, Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness, Academic Press, New York, 1975. | MR 493420 | Zbl 0308.47002

[S] J. C. Slater, A simplification of the Hartree-Fock method, Phys. Rev. 81(3), pp. 385-390, 1951. | Zbl 0042.23202

[W] E. Wigner, On the Quantum Correction for the Thermodynamic Equilibrium, Phys. Rev. 40, pp. 749-759, 1932. | JFM 58.0948.07