Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(e) ISSN 0894-0347(p)

     

Asymptotic completeness of $ N$-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
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We prove asymptotic completeness for $ N$-particle long-range system with potentials vanishing as $                 O({\left\vert x \right\vert^{ - \mu }})$, where $ \mu \geq 1 - {2^{ - N -                 2}}$, 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 $ N$-body quantum systems, Comm. Math. Phys. 122 (1989), 203-231. MR 994502 (91a:81218)

[Der2]
-, Algebraic approach to the $             N$-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 $             N$-particle quantum systems, preprint, École Polytech., Paris, 1991.

[Gr]
G.-M. Graf, Asymptotic completeness for $ N$-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 $             N$-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 $ 3$-body systems, preprint, Princeton, 1991.

[SigSof6]
-, Asymptotic completeness for $ N \leq 4$ 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.

Similar Articles:

Retrieve articles in Journal of the American Mathematical Society with MSC: 81U10, 47A40, 47N50

Retrieve articles in all Journals with MSC: 81U10, 47A40, 47N50


Additional Information:

DOI: 10.1090/S0894-0347-1994-1233895-8
PII: S0894-0347-1994-1233895-8
Copyright of article: Copyright 1994, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia