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

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

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English version:
Mathematical Notes, 2008, 83:1, 80–87

Bibliographic databases:

UDC: 517.984

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
\Bibitem{Ras08} \by T.~H.~Rasulov \paper On the Structure of the Essential Spectrum of a Model Many-Body Hamiltonian \jour Mat. Zametki \yr 2008 \vol 83 \issue 1 \pages 86--94 \mathnet{http://mi.mathnet.ru/mz4337} \crossref{https://doi.org/10.4213/mzm4337} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2400001} \zmath{https://zbmath.org/?q=an:1156.47061} \transl \jour Math. Notes \yr 2008 \vol 83 \issue 1 \pages 80--87 \crossref{https://doi.org/10.1134/S0001434608010100} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000254056300010} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-48849091796} 

• http://mi.mathnet.ru/eng/mz4337
• 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
Related articles on Google Scholar: Russian articles, English articles

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
2. T. H. Rasulov, “Study of the essential spectrum of a matrix operator”, Theoret. and Math. Phys., 164:1 (2010), 883–895
3. Rasulov T.H., “Investigations of the essential spectrum of a Hamiltonian in Fock space”, Appl. Math. Inform. Sci., 4:3 (2010), 395–412
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
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
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
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