Bommier, Antoine 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 Ann. Inst. Henri Poincaré, Phys. Théor. 59, No. 3, 237-267 (1993). 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) Cited in 5 Documents MSC: 35Q40 PDEs in connection with quantum mechanics 81V70 Many-body theory; quantum Hall effect Keywords:\(N\)-body theory; diffusion matrix × Cite Format Result Cite Review PDF Full Text: Numdam EuDML 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 · doi:10.1007/BF01206033 [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 · doi:10.1215/S0012-7094-92-06719-6 [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 · doi:10.1016/0022-1236(84)90104-6 [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 · doi:10.2307/1999899 [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 · doi:10.1007/BF01211163 [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 · doi:10.1142/S0129055X92000248 [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 · doi:10.2307/2001538 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.