On the Spectrum of an Hamiltonian in Fock Space. Discrete Spectrum Asymptotics View Full Text


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Article Info

DATE

2007-02-14

AUTHORS

Sergio Albeverio, Saidakhmat N. Lakaev, Tulkin H. Rasulov

ABSTRACT

A model operator H associated with the energy operator of a system describing three particles in interaction, without conservation of the number of particles, is considered. The location of the essential spectrum of H is described. The existence of infinitely many eigenvalues (resp. the finiteness of eigenvalues) below the bottom τess(H) of the essential spectrum of H is proved for the case where the associated Friedrichs model has a threshold energy resonance (resp. a threshold eigenvalue). For the number N(z) of eigenvalues of H lying below z < τess(H) the following asymptotics is found \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lim\limits_{z \to \tau_{\rm ess}(H)-0}\frac{N(z)}{|\log |z-\tau_{\rm ess}(H)||}={U}_0 (0<{U}_0 <\infty).$$\end{document} More... »

PAGES

191-220

References to SciGraph publications

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  • 1993-09. The Efimov effect. Discrete spectrum asymptotics in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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  • 2003-08. Asymptotics of the Discrete Spectrum of the Three-Particle Schrödinger Difference Operator on a Lattice in THEORETICAL AND MATHEMATICAL PHYSICS
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  • 2003-01. Efimov's Effect in a Model of Perturbation Theory of the Essential Spectrum in FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
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    URI

    http://scigraph.springernature.com/pub.10.1007/s10955-006-9240-6

    DOI

    http://dx.doi.org/10.1007/s10955-006-9240-6

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