Time-dependent scattering theory of N-body quantum systems

Reviews in Mathematical Physics

Volumn 12, Issue 8, 2000, Pages 1033-1084

  Hunziker, W ^a   Sigal, I M ^a  

^a NONE

Author keywords

[No Author keywords available]

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EID: 0034376103     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X0000040X     Document Type: Article

References (55)

1. S. Agmon, Lectures on Exponential Decay of Solutions of Second Order Elliptic Equations, Princeton Univ. Press, 1982.
2. 0-Groups, Commutator Methods and Spectral Theory for N-Body Hamiltonians", Progress in Mathematical Physics 135, Birkhäuser, 1996.
3. E. Balslev and J.-M. Combes, "Spectral properties of many-body Schrödinger operators with dilation analytic interactions", Commun. Math. Phys. 22 (1971) 280-294
4. A. Boutet de Monvel, V. Georgescu and A. Soffer, "N-body Hamiltonians with hard core interactions", Rev. Math. Phys. 6 (1994) 515-596.
5. H. Cycon, R. Froese, W. Kirsch and B. Simon, "Schrödinger Operators", Texts and Monographs in Physics, Springer-Verlag, Berlin, Heidelberg, New York, 1987.
6. E. B. Davies, "Spectral Theory and Differential Operators", Cambridge Univ. Press, 1995.
7. P. Deift and B. Simon, "A time-dependent approach to the completeness of N-particle quantum systems", Comm. Pure Appl. Math. 30 (1977) 573-578.
8. J. Dereziński, "Asymptotic completeness for long-range N-body systems. Main ideas of a proof", in Schrödinger Operators, the Quantum Mechanical Many-Body Problem, ed. E. Balslev, Lecture Notes in Physics 403 (1992) 56-72.
9. J. Dereziński, "Asymptotic completeness for N-particle long-range quantum systems", Ann. Math. 138 (1993) 427-476.
10. J. Dereziński and C. Gérard, "A remark on the asymptotic catering of N-body systems", in Schrödinger Operators, the Quantum Mechanical Many-Body Problem, ed. E. Balslev, Lecture Notes in Physics 403 (1992) 73-84.
11. J. Dereziński and C. Gérard, Scattering Theory of Classical and Quantum N-Particle Systems, Texts and Monographs in Physics. Springer-Verlag, 1997
12. V. Enss, "A note on Hunziker's theorem", Commun. Math. Phys. 52 (1977) 233-238.
13. V. Enss, "Asymptotic completeness for quantum mechanical potential scattering", Commun. Math. Phys. 61 (1978) 285-291.
14. V. Enss, "Completeness of three-body scattering", in Dynamics and Processes, eds. P. Blanchard and L. Streit, Lecture Notes in Math. 103, 62-88, Springer Verlag, 1983.
15. V. Enss, "Quantum scattering theory for two-and three-body systems with potentials of short-and long-range", in Schrödinger Operators, ed. S. Graffi, Lecture Notes in Mathematics, 1159, 39-178. Springer-Verlag, Berlin and New York, 1985.
16. L. D. Faddeev, "Mathematical problems of the quantum theory of scattering for a three-particle system", Publications of the Steklov Mathematical Institute 69, Leningrad (1983) (in Russian), and Israel program for scientific translations, Jerusalem (1965).
17. L. D. Faddeev, "Mathematical problems of the quantum theory of scattering for a three-particle system", Publications of the Steklov Mathematical Institute 69, Leningrad (1983) (in Russian), and Israel program for scientific translations, Jerusalem (1965).
18. G. M. Graf, "Asymptotic completeness for N-body short-range quantum systems: a new proof", Commun. Math. Phys. 132 (1990) 73-101.
19. G. M. Graf, private communication.
20. M. Griesemer, "N-body systems with singular potentials", Ann. Inst. H. Poincaré 69 (1998) 135-187.
21. R. Haag, "Quantum field theories with composite particles and asymptotic conditions", Phys. Rev. 112 (1958) 669-673.
22. R. Haag, "The framework of quantum field theory", Nuovo Cim. Suppl. 14 (1959) 131-152.
23. M. N. Hack, "Wave operators in multichannel scattering", Nuovo Cim. 13 (1959) 231-236.
24. B. Helffer and J. Sjöstrand, "Equation de Schrödinger avec champ magnétique et équation de Harper", in Schrödinger operators, eds. H. Holden and A. Jensen, Lecture notes in Physics 345, Springer Verlag, 1989.
25. K. Hepp, "On the quantum mechanical N-body problem", Helv. Phys. Acta 42 (1969) 425-458.
26. W. Hunziker, "Mathematical theory of multi-particle quantum systems, Lect. Notes in Theor. Physics X, eds. A. Barut and W. Britten, Gordon and Brach, N.Y., 1968.
27. W. Hunziker and I. M. Sigal, "The general theory of N-body quantum systems", in Mathematical Quantum Theory: II. Schrödinger Operators, eds. J. Feldman et al., CRM Proc. and Lecture Notes 8, Amer. Math. Soc., 1995.
28. A. Iftimovici, "On asymptotic completeness for Agmon type Hamiltonians", C. R. Acad. Sci. Paris 314, Série I (1992) 337-342.
29. V. Ivrii and I. M. Sigal, "Asymptotics of the ground state energies of large Coulomb systems", Ann. Math. 138 (2) (1993) 143-335.
30. J. M. Jauch, "Theory of the scattering operator II, multichannel scattering", Helv. Phys. Acta 31 (1958) 661-684.
31. R. J. Iorio, Jr. and M. O'Carroll, "Asymptotic completeness of multiparticle Schrödinger Hamiltonians with weak potentials", Commun. Math. Phys. 27 (1972) 137-145.
32. T. Kato, "Fundamental properties of Hamiltonian operators of Schrödinger type", Trans. Amer. Math. Soc. 70 (1951) 195-211.
33. T. Kato, "Smooth operators and commutators", Studia Math. XXXI (1968) 535-546.
34. R. Lavine, "Commutators and scattering theory I: Repulsive interactions", Commun. Math. Phys. 20 (1971) 301-323.
35. R. Lavine, "Completeness of the wave operators in the repulsive N-body problem", J. Math. Phys. 14 (1973) 376-379.
36. E. Mourre, "Absence of singular continuous spectrum for certain self-adjoint operators", Commun. Math. Phys. 78 (1981) 391-408.
37. E. Mourre, "Opérateurs conjugués et propriétés de propagation", Commun. Math. Phys. 91 (1983) 279-300.
38. P. Perry, I. M. Sigal and B. Simon, "Spectral analysis of N-body Schrödinger operators", Ann. Math. 114 (1981) 519-567.
39. C. R. Putnam, "Commutation Properties of Hilbert Space Operators and Related Topics", Springer Verlag, 1967.
40. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. I-IV, Academic Press.
41. D. Ruelle, "On the asymptotic condition in quantum field theory", Helv. Phys. Acta 35 (1962) 147-163.
42. D. Ruelle, "A remark on bound states in potential scattering theory", Nuovo Cimento A61 (1969) 655-662.
43. I. M. Sigal, Mathematical Foundations of Quantum Scattering Theory for Multiparticle Systems, Memoirs of the Amer. Math. Soc. N209, 1978.
44. I.M. Sigal, "Geometric methods in the quantum many body problem: Non-existence of very negative ions", Commun. Math. Phys. 85 (1982) 309-324.
45. I. M. Sigal and A. Soffer, "The N-particle scattering problem: asymptotic completeness for short-range systems", Ann. Math. 126 (1987) 35-108.
46. I. M. Sigal and A. Soffer, "Local decay and minimal velocity bounds", preprint, Princeton, 1988.
47. I. M. Sigal and A. Soffer, "Long-range many-body scattering. Asymptotic clustering for Coulomb-type potentials", Invent. Math. 99 (1990) 115-143.
48. I. M. Sigal and A. Soffer, "Asymptotic completeness for N ≤ 4 particle systems with Coulomb-type interactions", Duke Math. J. 71 (1993) 243-298.
49. I. M. Sigal and A. Soffer, "Asymptotic completeness of N-Particle long range systems", J. AMS 7 (1994) 307-333.
50. B. Simon "Resonances in N-body quantum systems with dilation analytic potentials and the foundations time-dependent perturbation theory", Ann. Math. 97 (1973) 247-274.
51. B. Simon, "Geometric methods in multiparticle quantum systems", Commun. Math. Phys. 55 (1977) 259-274.
52. E. Skibsted, "Propagation estimates for N-body Schrödinger operators", Commun. Math. Phys. 142 (1991) 67-98.
53. H. Tamura, "Asymptotic completeness for N-body Schrödinger operators with short-range interactions", Commun. P.D.E. 16 (1991) 1129-1154.
54. D. R. Yafaev, "Radiation conditions and scattering theory for N-particle Hamiltonians", Commun. Math. Phys. 154 (1993) 523-554.
55. L. Zielinski, "A Proof of asymptotic completeness for N-Body Schrödinger operators", Commun. P.D.E. 19 (1994) 455-522.