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Mat. Zametki, 2008, Volume 83, Issue 1, Pages 86–94 (Mi mz4337)  

This article is cited in 6 scientific papers (total in 6 papers)

On the Structure of the Essential Spectrum of a Model Many-Body Hamiltonian

T. H. Rasulov

A. Navoi Samarkand State University

Abstract: In this paper, we study the essential spectrum of a model lattice Hamiltonian describing a system with fluctuating number of particles ($0\le n\le2$) in the quasimomentum representation. The spectral properties are described in terms of the boundary values of a function of a complex variable, whose meaning is that of the kernel of the Schur complement
$$ H_{11}-z-H_{12}(H_{22}-z)^{-1}H_{12}^*. $$


Keywords: Schur complement, quasimomentum representation, many-body problem, fluctuating number of particles, essential spectrum

DOI: https://doi.org/10.4213/mzm4337

Full text: PDF file (452 kB)
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English version:
Mathematical Notes, 2008, 83:1, 80–87

Bibliographic databases:

UDC: 517.984
Received: 20.03.2006

Citation: T. H. Rasulov, “On the Structure of the Essential Spectrum of a Model Many-Body Hamiltonian”, Mat. Zametki, 83:1 (2008), 86–94; Math. Notes, 83:1 (2008), 80–87

Citation in format AMSBIB
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\paper On the Structure of the Essential Spectrum of a Model Many-Body Hamiltonian
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\yr 2008
\vol 83
\issue 1
\pages 86--94
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\pages 80--87
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  • https://doi.org/10.4213/mzm4337
  • http://mi.mathnet.ru/eng/mz/v83/i1/p86

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. T. H. Rasulov, “Investigation of the spectrum of a model operator in a Fock space”, Theoret. and Math. Phys., 161:2 (2009), 1460–1470  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. T. H. Rasulov, “Study of the essential spectrum of a matrix operator”, Theoret. and Math. Phys., 164:1 (2010), 883–895  mathnet  crossref  crossref  adsnasa  isi
    3. Rasulov T.H., “Investigations of the essential spectrum of a Hamiltonian in Fock space”, Appl. Math. Inform. Sci., 4:3 (2010), 395–412  mathscinet  isi
    4. Muminov Z. Ismail F. Rasulov J., “The Faddeev Equation and the Essential Spectrum of a Model Operator Associated With the Hamiltonian of a Nonconserved Number of Particles”, Adv. Math. Phys., 2014, 943868  crossref  mathscinet  zmath  isi  scopus
    5. Muminov M.I., Rasulov T.H., “on the Eigenvalues of a 2 X 2 Block Operator Matrix”, Opusc. Math., 35:3 (2015), 371–395  crossref  mathscinet  zmath  isi  scopus
    6. T. H. Rasulov, “Branches of the essential spectrum of the lattice spin-boson model with at most two photons”, Theoret. and Math. Phys., 186:2 (2016), 251–267  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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