Scattering theory for 3-particle systems in constant magnetic fields : dispersive case

Christian Gérard; Izabella Łaba

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 3, page 801-876
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Gérard, Christian, and Łaba, Izabella. "Scattering theory for 3-particle systems in constant magnetic fields : dispersive case." Annales de l'institut Fourier 46.3 (1996): 801-876. <http://eudml.org/doc/75196>.

@article{Gérard1996,
abstract = {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.},
author = {Gérard, Christian, Łaba, Izabella},
journal = {Annales de l'institut Fourier},
keywords = {magnetic Hamiltonians; asymptotic completeness},
language = {eng},
number = {3},
pages = {801-876},
publisher = {Association des Annales de l'Institut Fourier},
title = {Scattering theory for 3-particle systems in constant magnetic fields : dispersive case},
url = {http://eudml.org/doc/75196},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Gérard, Christian
AU - Łaba, Izabella
TI - Scattering theory for 3-particle systems in constant magnetic fields : dispersive case
JO - Annales de l'institut Fourier
PY - 1996
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 3
SP - 801
EP - 876
AB - 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.
LA - eng
KW - magnetic Hamiltonians; asymptotic completeness
UR - http://eudml.org/doc/75196
ER -

References

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