Asymptotic behavior of regularized scattering phases for long range perturbations | Zendy

JeanMarc Bouclet | Zendy

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Asymptotic behavior of regularized scattering phases for long range perturbations

Author(s) -

JeanMarc Bouclet

Publication year - 2002

Publication title -

journées équations aux dérivées partielles

Language(s) - English

Resource type - Journals

eISSN - 2118-9366

pISSN - 0752-0360

DOI - 10.5802/jedp.600

Subject(s) - range (aeronautics) , limit (mathematics) , scattering , laplace operator , asymptotic analysis , spectral theory , function (biology) , mathematics , statistical physics , mathematical analysis , physics , quantum mechanics , materials science , hilbert space , evolutionary biology , composite material , biology

We define scattering phases for Schrödinger operators on Rd as limit of arguments of relative determinants. These phases can be defined for long range perturbations of the Laplacian and therefore they can replace the usual spectral shift function (SSF) of Birman-Krein’s theory, which can be defined for only special short range perturbations (relatively trace class perturbations). We prove the existence of asymptotic expansions for these phases, which generalize results on the SSF.

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