On the finiteness of the discrete spectrum of a \(3\times 3\) operator matrix
type: Item
instance of: scholarly article
zbMATH Open document ID: 1363.81012
publication date: 2016-09-27T00:00:00Z
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 47N50
zbMATH DE Number: 6630282
zbMATH Keywords: operator matrix
zbMATH Keywords: lattice system
zbMATH Keywords: spin-boson Hamiltonian
author: T. Kh. Rasulov
MaRDI profile type: Publication
title: On the finiteness of the discrete spectrum of a \(3\times 3\) operator matrix
published in: Methods of Functional Analysis and Topology
review text: The author considers an operator matrix \(H\) associated with the lattice system describing three particles in interaction without conservation of the number of particles; this is a lattice analog of the spin-boson Hamiltonian (see [\textit{R. Minlos} and \textit{H. Spohn}, in: Topics in statistical and theoretical physics. F. A. Berezin memorial volume. Transl. ed. by A. B. Sossinsky. Providence, RI: American Mathematical Society. 159--193 (1996; Zbl 0881.47049)]. The main results deal with the structure of the essential and point spectra of \(H\). In particular, the author finds conditions guaranteeing the finiteness of the number of discrete eigenvalues located below the bottom of the three-particle branch of the essential spectrum.
reviewed by: Anatoly N. Kochubei
description: scientific article; zbMATH DE number 6630282