Existence and analyticity of bound states of a two-particle Schrödinger operator on a lattice View Full Text


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Article Info

DATE

2012-03

AUTHORS

S. N. Lakaev, S. S. Ulashov

ABSTRACT

We consider the two-particle discrete Schrödinger operator Hμ(K) corresponding to a system of two arbitrary particles on a d-dimensional lattice ℤd, d ≥ 3, interacting via a pair contact repulsive potential with a coupling constant μ > 0 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K \in \mathbb{T}^d$$\end{document} is the quasimomentum of two particles). We find that the upper (right) edge of the essential spectrum can be either a virtual level (for d = 3, 4) or an eigenvalue (for d ≥ 5) of Hμ (K). We show that there exists a unique eigenvalue located to the right of the essential spectrum, depending on the coupling constant μ and the two-particle quasimomentum K. We prove the analyticity of the corresponding eigenstate and the analyticity of the eigenvalue and the eigenstate as functions of the quasimomentum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K \in \mathbb{T}^d$$\end{document} in the domain of their existence. More... »

PAGES

326-340

References to SciGraph publications

  • 2004-08. Schrödinger Operators on Lattices. The Efimov Effect and Discrete Spectrum Asymptotics in ANNALES HENRI POINCARÉ
  • 1993-07. On Efimov's effect in a system of three identical quantum particles in FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
  • 2005-11-24. The Threshold Effects for the Two-Particle Hamiltonians on Lattices in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2006-06. Repulsively bound atom pairs in an optical lattice in NATURE
  • 1993-09. The Efimov effect. Discrete spectrum asymptotics in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1007/s11232-012-0033-6

    DOI

    http://dx.doi.org/10.1007/s11232-012-0033-6

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    https://app.dimensions.ai/details/publication/pub.1025079917


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