Semiclassical, t → ∞ asymptotics and dispersive effects for Hartree-Fock systems

I. Gasser; R. Illner; P. A. Markowich; C. Schmeiser

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1998)

  • Volume: 32, Issue: 6, page 699-713
  • ISSN: 0764-583X

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Gasser, I., et al. "Semiclassical, $t\rightarrow \infty $ asymptotics and dispersive effects for Hartree-Fock systems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 32.6 (1998): 699-713. <http://eudml.org/doc/193893>.

@article{Gasser1998,
author = {Gasser, I., Illner, R., Markowich, P. A., Schmeiser, C.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Hartree-Fock; semiclassical limit; decay estimates; dispersive effects; Vlasov equation},
language = {eng},
number = {6},
pages = {699-713},
publisher = {Dunod},
title = {Semiclassical, $t\rightarrow \infty $ asymptotics and dispersive effects for Hartree-Fock systems},
url = {http://eudml.org/doc/193893},
volume = {32},
year = {1998},
}

TY - JOUR
AU - Gasser, I.
AU - Illner, R.
AU - Markowich, P. A.
AU - Schmeiser, C.
TI - Semiclassical, $t\rightarrow \infty $ asymptotics and dispersive effects for Hartree-Fock systems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1998
PB - Dunod
VL - 32
IS - 6
SP - 699
EP - 713
LA - eng
KW - Hartree-Fock; semiclassical limit; decay estimates; dispersive effects; Vlasov equation
UR - http://eudml.org/doc/193893
ER -

References

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  2. [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. Zbl0481.35057MR639678
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  4. [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. Zbl0396.35029MR533219
  5. [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. Zbl0808.35116MR1273317
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  7. [LPe] P. L. LIONS et B. PERTHAME, Global solutions of Vlasov-Poisson type equations, preprint n. 8824, Ceremade, 1995. 
  8. [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. Zbl0761.35085MR1166050
  9. [M] P. A. MARKOWICH, On the equivalence of the Schrödinger and the Quantum Liouville equation, M2AS 11, pp. 459-469, 1989. Zbl0696.47042MR1001097
  10. [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. Zbl0772.35061MR1203274
  11. [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. Zbl0852.35139MR1387464
  12. [RS] M. REED and B. SIMON, Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness, Academic Press, New York, 1975. Zbl0308.47002MR493420
  13. [S] J. C. SLATER, A simplification of the Hartree-Fock method, Phys. Rev. 81(3), pp. 385-390, 1951. Zbl0042.23202
  14. [W] E. WIGNER, On the Quantum Correction for the Thermodynamic Equilibrium, Phys. Rev. 40, pp. 749-759, 1932. Zbl58.0948.07JFM58.0948.07

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