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Properties of the diffusion matrix, 2-clusters 2-clusters, for \(N\) body problems with long range interactions. (Propriétés de la matrice de diffusion, 2-amas 2-amas, pour les problèmes à \(N\) corps à longue portée.) (French) Zbl 0804.35111
This paper studies the regularity of the 2-clusters 2-clusters diffusion amplitude for \(N\) body problems with long range interactions.
Reviewer: L.-I.Anita (Iaşi)

MSC:
35Q40 PDEs in connection with quantum mechanics
81V70 Many-body theory; quantum Hall effect
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References:
[1] R. Froese et I. Herbst , Exponential Bounds and Absence of Positive Eigenvalues for N-Body Schrödinger Operators , Com. Math. Phys. , vol. 87 , 1982 , p. 429 - 447 . Article | MR 682117 | Zbl 0509.35061 · Zbl 0509.35061
[2] C. Gérard , Sharp Propagation Estimates for N-particle Systems , 1991 , Duke. Math. Journal , vol. 67 , 1992 , p. 483 - 515 . Article | MR 1181310 | Zbl 0760.35049 · Zbl 0760.35049
[3] L. Hörmander , The Analysis of Partial Differential Operators , vol. 3 , Springer-Verlag , New York , 1985 . Zbl 0601.35001 · Zbl 0601.35001
[4] B. Helffer et J. Sjöstrand , Equation de Schrôdinger avec champ magnétique et équation de Harper , Springer , Lecture Notes in Physics , n^\circ 345 , 1989 , p. 118 - 197 . MR 1037319 | Zbl 0699.35189 · Zbl 0699.35189
[5] H. Isozaki et H. Kitada , Scattering Matrices for Two-Body Schrödinger Operators, Scientific Papers of the College of Arts and Sciences , Tokyo University , vol. 35 , 1985 , p. 81 - 107 . MR 847881 | Zbl 0615.35065 · Zbl 0615.35065
[6] H. Isozaki et H. Kitada , Micro-Local Resolvent Estimates for 2-Body Schrödinger Operators , J. Funct. Anal. , vol. 57 , 1984 , p. 270 - 300 . MR 756171 | Zbl 0568.35022 · Zbl 0568.35022
[7] A. Jensen , Propagation Estimates for Schrôdinger Type Operators , Trans. Am. Math. Soc. , vol. 291 - 1 , 1985 , p. 129 - 144 . MR 797050 | Zbl 0577.35089 · Zbl 0577.35089
[8] E. Mourre , Opérateurs conjugués et propriétés de propagation , Com. Math. Phys. , vol. 91 , 1981 , p. 279 - 300 . Article | MR 723552 | Zbl 0543.47041 · Zbl 0543.47041
[9] M. Reed et B. Simon , Methods of Modern Mathematical Physics , vol. 1 - 4 , Academic , London 1975 , 1978 , 1979 et 1980 . MR 751959 · Zbl 0308.47002
[10] E. Skibsted , Smoothness of N-body scattering amplitudes , Rev. Math. Phys. , vol. 4 , n^\circ 4 , 1992 , p. 619 - 658 . MR 1197552 | Zbl 0781.35047 · Zbl 0781.35047
[11] X.P. Wang , Asymptotiques Semi-classiques pour les Opérateurs de Schrôdinger et de Dirac , Thèse d’état , 1986 , non publiée.
[12] X.P. Wang , Time-delay operators in semiclassical limit. II. Short-Range Potentials , Trans. Am. Math. Soc. , vol. 322 - 1 , 1990 , p. 395 - 414 . MR 987170 | Zbl 0714.35064 · Zbl 0714.35064
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