High energy asymptotics for N-body scattering matrices with arbitrary channels
Annales de l'I.H.P. Physique théorique, Volume 65 (1996) no. 1, p. 81-108
@article{AIHPA_1996__65_1_81_0,
     author = {Wang, Xue Ping},
     title = {High energy asymptotics for N-body scattering matrices with arbitrary channels},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {65},
     number = {1},
     year = {1996},
     pages = {81-108},
     zbl = {0858.35096},
     mrnumber = {1407167},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1996__65_1_81_0}
}
Wang, X. P. High energy asymptotics for N-body scattering matrices with arbitrary channels. Annales de l'I.H.P. Physique théorique, Volume 65 (1996) no. 1, pp. 81-108. http://www.numdam.org/item/AIHPA_1996__65_1_81_0/

[1] S. Agmon and L. Hörmander, Asymptotic properties of solutions of differential equations with simple characteristics, J. Analyse Math., Vol. 30, 1976, pp. 1-38. | MR 466902 | Zbl 0335.35013

[2] W.O. Amrein, D.B. Pearson and K.B. Sinha, Bounds on the total scattering cross section for N-body systems, Nuovo Cimento, Vol. 52A, 1979, pp. 115-131. | MR 542070

[3] W.O. Amrein and K.B. Sinha, On three-body scattering cross sections, J. Phys. A: Math. Gen., Vol. 15, 1982, pp. 1567-1586. | MR 656835 | Zbl 0491.47005

[4] A. Bommier, Régularité et prolongement méromorphe de la matrice de diffusion pour les problèmes à N-corps à longue portée, Thèse de Doctorat, École Polytechnique, 1993. | MR 1240535

[5] H. Cycon, R. Froese, W. Kirsch and B. Simon, Schrödinger Operators, Texts and Monographs in Physics, Springer Verlag, 1987. | Zbl 0619.47005

[6] V. Enss and B. Simon, Finite total cross-sections in nonrelativistic quantum mechanics, Commun. in Math. Phys., Vol. 76, 1980, pp. 177-209. | MR 587510 | Zbl 0471.35065

[7] C. Gérard, H. Isozaki and E. Skibsted, Commutator algebra and resolvent estimates, preprint 1993. | MR 1275395

[8] W. Hunziker, Potential scattering at high energies, Helv. Phys. Acta, Vol. 36, 1963, pp. 838-856. | MR 180135

[9] H. Isozaki, Structure of S-matrices for three body Schrödinger operators, Comm. Math. Phys., Vol. 146, 1992, pp. 241-258. | MR 1165182 | Zbl 0748.35026

[10] H.T. Ito, High energy behavior of total scattering cross sections for 3-body quantum systems, preprint 1992. | MR 1245017 | Zbl 0847.35097

[11] H.T. Ito and H. Tamura, Semi-classical asymptotics for total scattering cross sections of 3-body systems, J. Math. Kyoto Univ., Vol. 32, 1992, pp. 533-555. | MR 1183366 | Zbl 0769.35045

[12] L.D. Landau and E.M. Lifchitz, Quantum Mechanics, Nonrelativistic Theory, Pergmon Press, Oxford, 1965. | Zbl 0178.57901

[13] R. Novikov, Le problème de scattering inverse pour les systèmes à trois corps, exposé au Séminaire des E.D.P., Univ. de Nantes, Mai 1994.

[14] M. Reed and B. Simon, Methods of Modern Mathematical Physics, IV. Analysis of Operators, Academic Press, New York, 1978. | MR 493421 | Zbl 0401.47001

[15] D. Robert, Asymptotique de la phase de diffusion à haute énergie pour des perturbations du second ordre du Laplacien, Ann. Sci. École Norm. Sup., Vol. 25, 1992, pp. 107-134. | Numdam | MR 1169349 | Zbl 0801.35100

[16] D. Robert and H. Tamura, Semiclassical estimates for resolvents and asymptotics for total scattering cross sections, Ann. Inst. H. Poincaré, Vol. 46, 1987, pp. 415-442. | Numdam | MR 912158 | Zbl 0648.35066

[17] D. Robert and X.P. Wang, Pointwise semiclassical asymptotics for total cross sections in N-body problems, preprint 1992, Univ. Nantes, in "Spectral and Scattering Theory", M. Ikawa ed., Marcel Dekker. | MR 1291643 | Zbl 0831.35148

[18] I.M. Sigal and A. Soffer, The N-particle scattering problem: asymptotic completeness for short range systems, Ann. of Math., Vol. 126, 1987, pp. 35-108. | MR 898052 | Zbl 0646.47009

[19] E. Skibsted, Smoothness of N-body scattering amplitudes, Rev. Math. Phys., Vol. 4(4), 1992, pp. 619-658. | MR 1197552 | Zbl 0781.35047

[20] A.V. Sobolev and D.R. Yafaev, On the quasiclassical limit of total scattering cross-section in non-relativistic quantum mechanics, Ann. Inst. H. Poincaré, Vol. 44, 1986, pp. 195-210. | Numdam | MR 839284 | Zbl 0607.35070

[21] X.P. Wang, On the three-body long-range scattering problems, Letters in Math. Phys., Vol. 25, 1992, pp. 267-276.Detailed version: Propagation estimates and asymptotic completeness in three-body long-range scattering, J. of Funct. Analysis, Vol. 125(1), 1994, pp. 1-36. | MR 1188806 | Zbl 0823.35138 | Zbl 0776.35045

[22] X.P. Wang, Microlocal resolvent estimates of N-body Schrödinger operators, J. of the Fac. Sc., Univ. Tokyo, Sect. IA, Mathematics, Vol. 40(2), 1993, pp. 337-385. | MR 1255046 | Zbl 0810.35073

[23] X.P. Wang, Sections efficaces dans le problème à N-corps, Exposé No. IX au Séminaire EDP à l'École Polytechnique, Palaiseau, Décembre 1992. | Numdam | Zbl 0875.35023

[24] X.P. Wang, Total cross sections in N-body problems: Finiteness and high energy asymptotics, Commun. Math. Phys., Vol. 156, 1993, pp. 333-354. | MR 1233849 | Zbl 0839.35113

[25] X.P. Wang, On the uniqueness of inverse scattering for N-body systems, Inverse Problems, Vol. 10, 1994, pp. 765-784. | MR 1278586 | Zbl 0803.35169

[26] D.R. Yafaev, The eikonal approximation for the Schrödinger equation, Proc. of the Steklov Inst. Math., Vol. 179(2), 1989, pp. 251-266. | MR 964920 | Zbl 0693.35125

[27] D.R. Yafaev, Quasiclassical asymptotics of the scattering cross-section for the Schrödinger equation, Math. USSR Izv., Vol. 32(1), 1989, pp. 141-165. | MR 936527 | Zbl 0672.35054

[28] D.R. Yafaev, Resolvent estimates and scattering matrix for N-particle hamiltonians, preprint Univ. Rennes 1, September 1993. | Zbl 0823.47010

[29] K. Yajima, The quasiclassical limit of scattering amplitude - L2 approach for short range potentials-, Japan J. Math., Vol. 13, 1987, pp. 77-126. | MR 914315 | Zbl 0648.35067