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Asymptotic completeness of -particle long-range scattering
Author(s):
I. M.
Sigal;
A.
Soffer
Journal:
J. Amer. Math. Soc.
7
(1994),
307-334.
MSC:
Primary 81U10;
Secondary 47A40, 47N50
MathSciNet review:
1233895
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Abstract:
We prove asymptotic completeness for -particle long-range system with potentials vanishing as , where , at infinity.
References:
-
- [CFKS]
- H. Cycon, R. Froese, W. Kirsch, and B. Simon, Schrödinger operators, Springer-Verlag, Berlin, Heidelberg, and New York, 1987. MR 883643 (88g:35003)
- [Der1]
- J. Derezinski, A new proof of the propagation theorem for
-body quantum systems, Comm. Math. Phys. 122 (1989), 203-231. MR 994502 (91a:81218) - [Der2]
- -, Algebraic approach to the
-body long-range scattering, Rev. Math. Phys. 3 (1991), 1-62. MR 1110555 (93d:81186) - [Der3]
- -, Private communication, July 1991.
- [En1]
- V. Enss, Asymptotic observables on scattering states, Comm. Math. Phys. 89 (1983), 245-268. MR 709466 (84j:81110)
- [En2]
- -, Quantum scattering theory for two- and three-body systems with potentials of short- and long-range, Schrödinger Operators (S. Graffi, ed.), Lecture Notes in Math., vol. 1159, Springer-Verlag, Berlin and New York, 1985. MR 824987 (87c:81169)
- [En3]
- -, Two- and three-body quantum scattering: completeness revisited, Symposium: ``Partial Differential Equations'' (Holzhou, 1988) (M. Demuth and B.-W. Schultze, eds.), Teubner-Texte Math., Teubner, Leipzig, 1989, pp. 108-120. MR 1105802
- [GerDer]
- C. Gérard and J. Derezinski, A remark on asymptotic clustering for
-particle quantum systems, preprint, École Polytech., Paris, 1991. - [Gr]
- G.-M. Graf, Asymptotic completeness for
-body short-range quantum systems: a new proof, Comm. Math. Phys. 132 (1990), 73-101. MR 1069201 (91i:81100) - [Mo]
- E. Mourre, Opérateurs conjugués et propriétés de propagation, Comm. Math. Phys. 91 (1983), 279-300. MR 723552 (86h:47031)
- [RS]
- M. Reed and B. Simon, Methods of modern mathematical physics. II, Academic Press, San Diego, CA, 1979. MR 751959 (85e:46002)
- [Sig1]
- I. M. Sigal, Mathematical questions of quantum many-body problem, Seminaire sur les équations aux derivées partielles, 1986-1987, Exposé No. XXIII, École Polytech., Palaiseau, 1987. MR 920041 (89c:81181)
- [Sig2]
- -, On the long-rang scattering, Duke Math. J. 60 (1990), no. 2. MR 1047762 (91h:35246)
- [SigSof1]
- I. M. Sigal and A. Soffer, The
-particle scattering problem: asymptotic completeness for short-range systems, Anal. Math. 126 (1987), 35-108. MR 898052 (88m:81137) - [SigSof2]
- -, Asymptotic completeness of multiparticle scattering, Differential Equations and Mathematical Physics (Knowles and Saito, eds.), Lecture Notes in Math., vol. 1285, Springer-Verlag, Berlin, Heidelberg, and New York, 1987. MR 921295 (89h:81248)
- [SigSof3]
- -, Long-range many-body scattering. Asymptotic clustering for Coulomb-type potential, Invent. Math. 99 (1990), 115-143. MR 1029392 (91e:81114)
- [SigSof4]
- -, Local decay and velocity bounds, preprint.
- [SigSof5]
- -, Asymptotic completeness for Coulomb-type
-body systems, preprint, Princeton, 1991. - [SigSof6]
- -, Asymptotic completeness for
particle systems with the Coulomb-type interactions, Duke Math. J. 71 (1993), 243-298. MR 1230292 (94i:81141) - [SS]
- A. G. Sigalov and I. M. Sigal, Description of the spectrum of the energy operator of quantum mechanical systems invariant under permutations of identical particles, Theoret. and Math. Phys. 5 (1970), 990-1005.
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Additional Information:
DOI:
10.1090/S0894-0347-1994-1233895-8
PII:
S0894-0347-1994-1233895-8
Copyright of article:
Copyright
1994,
American Mathematical Society
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