Complétude asymptotique des systèmes à N corps à courte portée

Christian Gérard

Séminaire Bourbaki (1989-1990)

  • Volume: 32, page 179-201
  • ISSN: 0303-1179

How to cite


Gérard, Christian. "Complétude asymptotique des systèmes à $N$ corps à courte portée." Séminaire Bourbaki 32 (1989-1990): 179-201. <>.

author = {Gérard, Christian},
journal = {Séminaire Bourbaki},
keywords = {-particle Hamiltonian; asymptotic completeness; short range interactions},
language = {fre},
pages = {179-201},
publisher = {Société Mathématique de France},
title = {Complétude asymptotique des systèmes à $N$ corps à courte portée},
url = {},
volume = {32},
year = {1989-1990},

AU - Gérard, Christian
TI - Complétude asymptotique des systèmes à $N$ corps à courte portée
JO - Séminaire Bourbaki
PY - 1989-1990
PB - Société Mathématique de France
VL - 32
SP - 179
EP - 201
LA - fre
KW - -particle Hamiltonian; asymptotic completeness; short range interactions
UR -
ER -


  1. [Ag] S. Agmon - Lectures on exponential decay of solutions of second order elliptic equations, Math. NotesPrinceton Univ. Press1982. Zbl0503.35001MR745286
  2. [BGM] A. Boutet de Monvel-Berthier, V. Georgescu, M. Mantoiu - Mourre's theory in a Besov space setting, C.R.A.S. t310 (1990). Zbl0694.47035
  3. [Com] J.-M. Combes - Relatively compact interactions in many particles systems, Comm. Math. Phys.12(1969). Zbl0174.28304MR1552563
  4. [Do] J.D. Dollard - Quantum mechanical scattering for short-range and Coulomb interactions, Rocky Mountain J. Math.1(1971). Zbl0226.35074MR270673
  5. [De] J. Derezinski - A new proof of propagation theorem for N-body Quantum systems, Com. Math. Phys.122(1989). Zbl0677.47006MR994502
  6. [DL] F. Dyson- A. Lenard - Stability of matter I,II, J. Math. Phys.8 (1967), 9(1969). Zbl0948.81665
  7. [E1] V. Enss - Quantum scattering theory for two and three-body systems with potentials of short and long range, in : Schrödinger Operators, S.Graffi ed. SpringerLN Math.1159 (1985). Zbl0585.35023MR824987
  8. [E2] V. Enss - Long range scattering for two and three body quantum systems, Actes du Congrès de Saint Jean de Monts (1989). Zbl0734.35069MR1030815
  9. [FH] R. Froese, I. Herbst - A new proof of the Mourre estimate, Duke Math. J49 (1982). Zbl0514.35025MR683011
  10. [Ge] C. Gérard - The Mourre estimate for regular dispersive N-body systems, Preprint de l'Ecole Polytechnique (1990). 
  11. [G] G.M. Graf - Asymptotic completeness for N-body shortrange quantum systems : a new proof, Preprint ETH (1989). 
  12. [Hö] L. Hörmander - On the existence and regularity of solutions of linear pseudodifferential equations, L'Enseign. Math.17 (1971). Zbl0224.35084
  13. [Ka1 T. Kato - On the existence of solutions of the Helium wave equation, Trans. Amer. Math. Soc.70 (1951). Zbl0044.42702MR41011
  14. [Ka2] T. Kato - Smooth operators and commutators, Studia Math.31 (1968). Zbl0215.48802MR234314
  15. [LL] L. Landau, E. Lifschitz - Mécanique QuantiqueEditions MirMoscou1967. MR347251
  16. [L] E.H. Lieb - The stability of matter : from atoms to stars, Bull. de l'A.M.S. Vol 22(1) (1990). Zbl0698.35135MR1014510
  17. [LT] E. Lieb, W. Thirring - Bound for the kinetic energy of fermions which proves the stability of matter, Phys. Rev. Lett.35 (1975). 
  18. [M] E. Mourre - Absence of singular continuous spectrum for certain selfadjoint operators, Comm. Math. Phys.78 (1981). Zbl0489.47010MR603501
  19. [Pe] D.B. Pearson - Singular continuous measures in scattering theory, Comm. in Math. Phys.60 (1978). Zbl0451.47013MR484145
  20. [PSS] P. Perry, I.M. Sigal, B. Simon - Spectral analysis of N-body Schrödinger operators, Ann. of Math.114 (1981). Zbl0477.35069MR634428
  21. [RS] M. Reed, B. Simon - Methods of Modern Mathematical Physics II, III, Academic Press (1975) (1979). Zbl0308.47002MR751959
  22. [SS1] I.M. Sigal, A. Soffer - N-particle scattering problem: asymptotic completeness for short range systems, Ann. Math.126 (1987). Zbl0646.47009MR898052
  23. [SS2] I.M. Sigal, A. Soffer - Long range many-body scattering: asymptotic clustering for Coulomb type systems, Invent. Math.99 (1990). Zbl0702.35197MR1029392

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