Comment on the article ``On the existence of the N-body Efimov effect'' by X.P. Wang
type: Item
instance of: scholarly article
title: Comment on the article ``On the existence of the N-body Efimov effect'' by X.P. Wang
title: On the existence of the \(N\)-body Efimov effect.
zbMATH Open document ID: 1251.81089
zbMATH Open document ID: 1059.81061
DOI: 10.1016/S0022-1236(03)00170-8
DOI: 10.1016/J.JFA.2012.06.009
author: Dmitry K. Gridnev
author: Xue Ping Wang
published in: Journal of Functional Analysis
publication date: 2012-08-30T00:00:00Z
publication date: 2004-06-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/1204.5609
Mathematics Subject Classification ID: 81U10
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 46E39
zbMATH DE Number: 6073999
zbMATH DE Number: 2073660
zbMATH Keywords: Schrödinger operators
zbMATH Keywords: Efimov effect
zbMATH Keywords: number of negative eigenvalues
zbMATH Keywords: \(N\)-body potential scattering theory
MaRDI profile type: Publication
OpenAlex ID: W2056661155
arXiv ID: 1204.5609
review text: The author considers the Efimov effect for the \(N\)-body problem with \(N\geq 4\) for the Schrödinger equation in \({\mathbb R}{^ 3},\) where the potential consists of the sum of two-body interaction terms depending only on the separation distance. Under appropriate restrictions, it is shown that there may be an infinite number of discrete eigenvalues below \(E_ 0\) for the whole system as a result of the contributions from the eigenvalues and resonances at \(E_ 0\) of the \((N-1)\)-particle system, where \(E_ 0\) is the threshold energy separating the discrete and continuous spectra. The proof uses the ideas from \textit{A. V. Sobolev} [Commun. Math. Phys. 156, No. 1, 101--126 (1993; Zbl 0785.35070)] and exploits the conditions on the finiteness of number of discrete eigenvalues by \textit{W. D. Evans} and \textit{R. T. Lewis} [Trans. Am. Math. Soc. 322, No. 2, 593--626 (1990; Zbl 0732.35062)].
reviewed by: Tuncay Aktosun
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description: scientific article; zbMATH DE number 2073660
alternative label: On the existence of the \(N\)-body Efimov effect.