Existence and analyticity of eigenvalues of a two-channel molecular resonance model View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2011-12

AUTHORS

S. N. Lakaev, Sh. M. Latipov

ABSTRACT

We consider a family of operators Hγμ(k), k ∈ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{T}^d $\end{document}:= (−π,π]d, associated with the Hamiltonian of a system consisting of at most two particles on a d-dimensional lattice ℤd, interacting via both a pair contact potential (μ > 0) and creation and annihilation operators (γ > 0). We prove the existence of a unique eigenvalue of Hγμ(k), k ∈ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{T}^d $\end{document}, or its absence depending on both the interaction parameters γ,μ ≥ 0 and the system quasimomentum k ∈ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{T}^d $\end{document}. We show that the corresponding eigenvector is analytic. We establish that the eigenvalue and eigenvector are analytic functions of the quasimomentum k ∈ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{T}^d $\end{document} in the existence domain G ⊂ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{T}^d $\end{document}. More... »

PAGES

1658-1667

References to SciGraph publications

  • 1992-04. Bound states and resonances ofN-particle discrete Schrödinger operator in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2005-11-24. The Threshold Effects for the Two-Particle Hamiltonians on Lattices in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2007-02-14. On the Spectrum of an Hamiltonian in Fock Space. Discrete Spectrum Asymptotics in JOURNAL OF STATISTICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11232-011-0143-6

    DOI

    http://dx.doi.org/10.1007/s11232-011-0143-6

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1030666622


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