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

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Matematicheskie Zametki, 2008, Volume 83, Issue 1, Pages 86–94
DOI: https://doi.org/10.4213/mzm4337 (Mi mzm4337)

This article is cited in 8 scientific papers (total in 8 papers)

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

T. H. Rasulov

A. Navoi Samarkand State University

Full-text PDF (452 kB) Citations (8)

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

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.

Received: 20.03.2006

English version:
Mathematical Notes, 2008, Volume 83, Issue 1, Pages 80–87
DOI: https://doi.org/10.1134/S0001434608010100

Bibliographic databases:

UDC: 517.984

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/mzm4337

https://doi.org/10.4213/mzm4337

https://www.mathnet.ru/eng/mzm/v83/i1/p86

This publication is cited in the following 8 articles:

T. Kh. Rasulov, Kh. M. Lapitov, “Opisanie spektra odnoi operatornoi matritsy chetvertogo poryadka”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 27:3 (2023), 427–445
Hakimboy M. Latipov, Tulkin H. Rasulov, PHYSICAL MESOMECHANICS OF CONDENSED MATTER: Physical Principles of Multiscale Structure Formation and the Mechanisms of Nonlinear Behavior: MESO2022, 2899, PHYSICAL MESOMECHANICS OF CONDENSED MATTER: Physical Principles of Multiscale Structure Formation and the Mechanisms of Nonlinear Behavior: MESO2022, 2023, 030006
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
Muminov M.I., Rasulov T.H., “on the Eigenvalues of a 2 X 2 Block Operator Matrix”, Opusc. Math., 35:3 (2015), 371–395
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
T. H. Rasulov, “Study of the essential spectrum of a matrix operator”, Theoret. and Math. Phys., 164:1 (2010), 883–895
Rasulov T.H., “Investigations of the essential spectrum of a Hamiltonian in Fock space”, Appl. Math. Inform. Sci., 4:3 (2010), 395–412
T. H. Rasulov, “Investigation of the spectrum of a model operator in a Fock space”, Theoret. and Math. Phys., 161:2 (2009), 1460–1470

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	80
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