Asymptotic behavior of regularized scattering phases for long range perturbations

Jean-Marc Bouclet

Journées équations aux dérivées partielles (2002)

  • page 1-12
  • ISSN: 0752-0360

Abstract

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We define scattering phases for Schrödinger operators on ℝ d as limit of arguments of relative determinants. These phases can be defined for long range perturbations of the laplacian; therefore they can replace the spectral shift function (SSF) of Birman-Krein’s theory which can just be defined for some special short range perturbations (we shall recall this theory for non specialists). We prove the existence of asymptotic expansions for these phases, which generalize results on the SSF.

How to cite

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Bouclet, Jean-Marc. "Asymptotic behavior of regularized scattering phases for long range perturbations." Journées équations aux dérivées partielles (2002): 1-12. <http://eudml.org/doc/93429>.

@article{Bouclet2002,
abstract = {We define scattering phases for Schrödinger operators on $\mathbb \{R\}^d$ as limit of arguments of relative determinants. These phases can be defined for long range perturbations of the laplacian; therefore they can replace the spectral shift function (SSF) of Birman-Krein’s theory which can just be defined for some special short range perturbations (we shall recall this theory for non specialists). We prove the existence of asymptotic expansions for these phases, which generalize results on the SSF.},
author = {Bouclet, Jean-Marc},
journal = {Journées équations aux dérivées partielles},
language = {eng},
pages = {1-12},
publisher = {Université de Nantes},
title = {Asymptotic behavior of regularized scattering phases for long range perturbations},
url = {http://eudml.org/doc/93429},
year = {2002},
}

TY - JOUR
AU - Bouclet, Jean-Marc
TI - Asymptotic behavior of regularized scattering phases for long range perturbations
JO - Journées équations aux dérivées partielles
PY - 2002
PB - Université de Nantes
SP - 1
EP - 12
AB - We define scattering phases for Schrödinger operators on $\mathbb {R}^d$ as limit of arguments of relative determinants. These phases can be defined for long range perturbations of the laplacian; therefore they can replace the spectral shift function (SSF) of Birman-Krein’s theory which can just be defined for some special short range perturbations (we shall recall this theory for non specialists). We prove the existence of asymptotic expansions for these phases, which generalize results on the SSF.
LA - eng
UR - http://eudml.org/doc/93429
ER -

References

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