Scattering theory for 3-particle systems in constant magnetic fields: dispersive case
Annales de l'Institut Fourier, Volume 46 (1996) no. 3, p. 801-876
We develop a scattering theory for quantum systems of three charged particles in a constant magnetic field. For such systems, we generalize our earlier results in that we make no additional assumptions on the electric charges of subsystems. The main difficulty is the analysis of the scattering channels corresponding to the motion of the bound states of the neutral subsystems in the directions transversal to the field. The effective kinetic energy of this motion is given by certain dispersive Hamiltonians; therefore we refer to this case as dispersive. Under suitable assumptions on the regularity of the eigenvalues of the reduced Hamiltonians, we obtain the Mourre estimate for general long-range systems, and asymptotic completeness for short-range and Coulomb systems.
Nous développons la théorie de la diffusion pour des systèmes quantiques de trois particules chargées en présence d’un champ magnétique constant. Nous généralisons nos travaux précèdents en ne faisant pas d’autres hypothèses sur les charges des sous systèmes. La difficulté principale est dans l’analyse des canaux de diffusion correspondant au mouvement des états liés des sous systèmes neutres transversalement au champ magnétique. L’énergie cinétique effective de ce mouvement est donnée par certains hamiltoniens dispersifs. Sous des hypothèses convenables sur la régularité des valeurs propres des hamiltoniens réduits, nous obtenons une estimation de Mourre ainsi que la complétude asymptotique pour des interactions à courte portée et de type de Coulomb.
@article{AIF_1996__46_3_801_0,
     author = {G\'erard, Christian and \L aba, Izabella},
     title = {Scattering theory for 3-particle systems in constant magnetic fields: dispersive case},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {46},
     number = {3},
     year = {1996},
     pages = {801-876},
     doi = {10.5802/aif.1532},
     zbl = {0853.35098},
     mrnumber = {97j:81377},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1996__46_3_801_0}
}
Gérard, Christian; Łaba, Izabella. Scattering theory for 3-particle systems in constant magnetic fields: dispersive case. Annales de l'Institut Fourier, Volume 46 (1996) no. 3, pp. 801-876. doi : 10.5802/aif.1532. http://www.numdam.org/item/AIF_1996__46_3_801_0/

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