High energy asymptotics for N-body scattering matrices with arbitrary channels

 Access to full text

 Full (PDF)

1. [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. Zbl0335.35013MR466902
2. [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. MR542070
3. [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. Zbl0491.47005MR656835
4. [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. MR1240535
5. [5] H. Cycon, R. Froese, W. Kirsch and B. Simon, Schrödinger Operators, Texts and Monographs in Physics, Springer Verlag, 1987. Zbl0619.47005
6. [6] V. Enss and B. Simon, Finite total cross-sections in nonrelativistic quantum mechanics, Commun. in Math. Phys., Vol. 76, 1980, pp. 177-209. Zbl0471.35065MR587510
7. [7] C. Gérard, H. Isozaki and E. Skibsted, Commutator algebra and resolvent estimates, preprint 1993. Zbl0814.35086MR1275395
8. [8] W. Hunziker, Potential scattering at high energies, Helv. Phys. Acta, Vol. 36, 1963, pp. 838-856. MR180135
9. [9] H. Isozaki, Structure of S-matrices for three body Schrödinger operators, Comm. Math. Phys., Vol. 146, 1992, pp. 241-258. Zbl0748.35026MR1165182
10. [10] H.T. Ito, High energy behavior of total scattering cross sections for 3-body quantum systems, preprint 1992. MR1245017
11. [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. Zbl0769.35045MR1183366
12. [12] L.D. Landau and E.M. Lifchitz, Quantum Mechanics, Nonrelativistic Theory, Pergmon Press, Oxford, 1965. Zbl0178.57901
13. [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. [14] M. Reed and B. Simon, Methods of Modern Mathematical Physics, IV. Analysis of Operators, Academic Press, New York, 1978. Zbl0401.47001MR493421
15. [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. Zbl0801.35100MR1169349
16. [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. Zbl0648.35066MR912158
17. [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. MR1291643
18. [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. Zbl0646.47009MR898052
19. [19] E. Skibsted, Smoothness of N-body scattering amplitudes, Rev. Math. Phys., Vol. 4(4), 1992, pp. 619-658. Zbl0781.35047MR1197552
20. [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. Zbl0607.35070MR839284
21. [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. Zbl0776.35045MR1188806
22. [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. Zbl0810.35073MR1255046
23. [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. Zbl0875.35023
24. [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. Zbl0839.35113MR1233849
25. [25] X.P. Wang, On the uniqueness of inverse scattering for N-body systems, Inverse Problems, Vol. 10, 1994, pp. 765-784. Zbl0803.35169MR1278586
26. [26] D.R. Yafaev, The eikonal approximation for the Schrödinger equation, Proc. of the Steklov Inst. Math., Vol. 179(2), 1989, pp. 251-266. Zbl0693.35125MR964920
27. [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. Zbl0672.35054MR936527
28. [28] D.R. Yafaev, Resolvent estimates and scattering matrix for N-particle hamiltonians, preprint Univ. Rennes 1, September 1993. 
29. [29] K. Yajima, The quasiclassical limit of scattering amplitude - L2 approach for short range potentials-, Japan J. Math., Vol. 13, 1987, pp. 77-126. Zbl0648.35067MR914315