Scattering for a dispersive charge transfer model

Lech Zielinski

Annales de l'I.H.P. Physique théorique (1997)

  • Volume: 67, Issue: 4, page 339-386
  • ISSN: 0246-0211

How to cite

top

Zielinski, Lech. "Scattering for a dispersive charge transfer model." Annales de l'I.H.P. Physique théorique 67.4 (1997): 339-386. <http://eudml.org/doc/76772>.

@article{Zielinski1997,
author = {Zielinski, Lech},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {wave operators; asymptotic completeness},
language = {eng},
number = {4},
pages = {339-386},
publisher = {Gauthier-Villars},
title = {Scattering for a dispersive charge transfer model},
url = {http://eudml.org/doc/76772},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Zielinski, Lech
TI - Scattering for a dispersive charge transfer model
JO - Annales de l'I.H.P. Physique théorique
PY - 1997
PB - Gauthier-Villars
VL - 67
IS - 4
SP - 339
EP - 386
LA - eng
KW - wave operators; asymptotic completeness
UR - http://eudml.org/doc/76772
ER -

References

top
  1. [1] W.O. Amrein, A. Boutet de Monvel and V. Georgescu, C0-groups, commutator methods and spectral theory of N-body hamiltonians, Birkhäuser1996. Zbl0962.47500MR1388037
  2. [2] G. Arsu, Spectral analysis for simply characteristic operators by Mourre's method, Operator theory: advances and applications, Vol. 43, 1990, pp. 89-99, Birkhäuser, VerlagBasel. Zbl0702.47003MR1090118
  3. [3] A. Boutet de Monvel, V. Georgescu, Spectral theory and scattering theory by the conjugate operator method, Algebra and Analysis, Vol. 4, No. 3, 1991, pp. 73-116. Zbl0780.47010MR1190772
  4. [4] J. Derezinski, The Mourre estimate for dispersive N-body Schrödinger operators, Trans. Amer. Math. Soc., Vol. 317, 1990, pp. 773-798. Zbl0691.47004MR970265
  5. [5] J. Derezinski, Asymptotic completeness for long range quantum systems, Ann. of Math., Vol.. 138, 1993, pp. 427-476. Zbl0844.47005MR1240577
  6. [6] J. Derezinski and C. Gérard, Asymptotic completeness of N-particle systems, Springer-Verlag, 1996. 
  7. [7] V. Enss, Asymptotic completeness for quantum mechanical potential scattering I, Short range potentials, Comm. Math. Phys., Vol. 61, 1978, pp. 285-291. Zbl0389.47005MR523013
  8. [8] W.G. Faris, Self-adjoint operators, Lect. Notes Math., Vol. 433, edited by A. DOLD and B. ECKMANN. 
  9. [9] C. Gérard, Mourre estimate for regular dispersive systems, Ann. Inst. H. Poincaré, Physique Théorique, 54/1, 1991, pp. 59-88. Zbl0724.35083MR1102972
  10. [10] G.M. Graf, Phase space analysis of the charge transfer model, Helv. Phys. Acta, Vol. 63, 1990, pp. 107-138. Zbl0741.35050MR1045931
  11. [11] G.M. Graf, Asymptotic completeness for N-body short range systems, Comm. Math. Phys., Vol. 132, 1991, pp. 73-104. Zbl0726.35096MR1069201
  12. [12] G.A. Hagedorn, Asymptotic completeness for the impact parameter approximation to the three particle Scattering, Ann. Inst. H. Poincaré, A36, 1982, pp. 19-40. Zbl0482.47003MR653016
  13. [13] L. Hörmander, The analysis of linear partial differential operators, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, Vol. 1, 2, 1983, Vol. 3, 4, 1985. Zbl0521.35002MR404822
  14. [14] Pl. Muthuramalingam, A time dependent scattering theory for a class of simply characteristic operators with short range local potentials, J. London Math. Soc., Vol. 32, 2, 1985, pp. 259-264. Zbl0557.47007MR811784
  15. [15] I.M. Sigal and A. Soffer, The N-particle scattering problem: asymptotic completeness for the short-range quantum systems, Ann. of Math., Vol. 125, 1987, pp. 35-108. Zbl0646.47009MR898052
  16. [16] I.M. Sigal and A. Soffer, Asymptotic completeness of N-particle long-range scattering, J. Amer. Math. Soc., Vol. 7, 1994, pp. 307-334. Zbl0811.35091MR1233895
  17. [17] U. Wüller, Asymptotische Vollständigkeit beim Charge-Transfer-Modell, Ph. D. Thesis, Berlin, 1988. Zbl0669.35093
  18. [18] K. Yajima, A multi-channel scattering theory for some time dependent hamiltonians, Charge Transfer Problem, Comm. Math. Phys., Vol. 75, 1980, pp. 153-178. Zbl0437.47008MR582506
  19. [19] L. Zielinski, Complétude asymptotique pour un modèle du transfert de charge, Ann. Inst. H. Poincaré, Physique Théorique, Vol. 58, 1993, pp. 363-411. Zbl0791.35114MR1241703
  20. [20] L. Zielinski, A proof of asymptotic completeness for N-body Schrödinger operators, Comm. in P.D.E., Vol. 19, 3-4, 1994, pp. 455-522. Zbl0812.35118MR1265807
  21. [21] L. Zielinski, Wave operators of Deift-Simon type for a class of Schrödinger evolutions I, J. of Math. Phys., Geom. and Analysis, Vol. 3, 1996, pp. 169-213. Zbl0870.35077MR1483821

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.