On the structure of the essential spectrum of a model many-body Hamiltonian
type: Item
instance of: scholarly article
title: On the structure of the essential spectrum of a model many-body Hamiltonian
zbMATH Open document ID: 1156.47061
DOI: 10.1134/S0001434608010100
published in: Mathematical Notes
publication date: 2008-10-16T00:00:00Z
review text: The author study the spectrum of a model lattice Hamiltonian \(H\) \[ H= \begin{pmatrix} H_{00} & H_{01} & 0 \\ H_{10} & H_{11} & H_{12} \\ 0 & H_{21} & H_{22} \end{pmatrix}, \] describing a system with fluctuating number of particles. The spectral properties of the model are derived in term of the boundary-values of a complex function defined as the kernel of the operator \(H_{11}-z-H_{12}(H_{22}-z)^{-1} H_{12}^*\).
reviewed by: Bernard Ducomet
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 81V70
zbMATH DE Number: 5352320
zbMATH Keywords: Schur complement
zbMATH Keywords: quasimomentum representation
zbMATH Keywords: many-body problem
zbMATH Keywords: fluctuating number of particles
zbMATH Keywords: essential spectrum
author: T. Kh. Rasulov
MaRDI profile type: Publication
cites work: Q4341441
cites work: Spectrum and scattering in a ``spin-boson'' model with not more than three photons
cites work: Q3976402
cites work: On Efimov's effect in a system of three identical quantum particles
cites work: Q4191141
cites work: A model in the theory of perturbations of the essential spectrum of multiparticle operators
cites work: Efimov's effect in a model of perturbation theory of the essential spectrum
cites work: Q3976398
cites work: Q4725190
description: scientific article; zbMATH DE number 5352320