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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 179, Number 3, Pages 387–405
DOI: https://doi.org/10.4213/tmf8577 (Mi tmf8577) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Spectral properties of three-electron systems in the Hubbard model

S. M. Tashpulatov

Institute for Nuclear Physics, Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan
Full-text PDF (443 kB) Citations (11)
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DOI: https://doi.org/10.4213/tmf8577
Abstract: We investigate spectral properties of a three-electron system in the Hubbard model framework. We prove that the essential spectrum of the system in a quartet state consists of a single segment and the three-electron bound state is absent. We show that the essential spectrum of the system in doublet states is the union of at most three segments. We also prove that three-electron bound states exist in doublet states.
Keywords: Hubbard model, three-electron system, quartet state, triplet state, doublet state, singlet state, essential spectrum, discrete spectrum, three-electron bound state, discrete Schrödinger operator.
Received: 22.07.2013
Revised: 02.12.2013
English version:
Theoretical and Mathematical Physics, 2014, Volume 179, Issue 3, Pages 712–728
DOI: https://doi.org/10.1007/s11232-014-0173-y
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. M. Tashpulatov, “Spectral properties of three-electron systems in the Hubbard model”, TMF, 179:3 (2014), 387–405; Theoret. and Math. Phys., 179:3 (2014), 712–728
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    1. R. T. Parmanova, “First triplet four-electron state in the impurity Hubbard model. Three-dimensional case”, Theoret. and Math. Phys., 222:3 (2025), 497–510  mathnet  crossref  crossref
    2. Sa'dulla Tashpulatov, Rukhsat Parmanova, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 3045, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 2024, 030005  crossref
    3. S. M. Tashpulatov, “Struktura suschestvennogo spektra i diskretnyi spektr operatora energii shestielektronnykh sistem v modeli Khabbarda. Chetvertoe tripletnoe sostoyanie”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXV», Voronezh, 26-30 aprelya 2024 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 236, VINITI RAN, M., 2024, 31–48  mathnet  crossref
    4. S. M. Tashpulatov, “Structure of essential spectrum and discrete spectra of the energy operator of five-electron systems in the Hubbard model. Fourth quartet state”, Dalnevost. matem. zhurn., 23:1 (2023), 112–133  mathnet  crossref
    5. S. M. Tashpulatov, “The Structure of the Essential Spectrum and the Discrete Spectrum of the Energy Operator for Six-Electron Systems in the Hubbard Model. The Second Singlet State”, Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S279–S299  mathnet  crossref  crossref  mathscinet  elib
    6. S. M. Tashpulatov, R. T. Parmanova, “Struktura suschestvennogo spektra i diskretnyi spektr operatora energii chetyrekhelektronnykh sistem v primesnoi modeli Khabbarda. Trete tripletnoe sostoyanie”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 27 yanvarya — 1 fevralya 2023 g. Chast 3, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 229, VINITI RAN, M., 2023, 53–82  mathnet  crossref
    7. S. M. Tashpulatov, “Spectra of the Energy Operator of Three-Electron Systems in the Impurity Hubbard Model. Second Doublet State”, J Math Sci, 265:1 (2022), 103  crossref
    8. S. M. Tashpulatov, Trends in Mathematics, Operator Theory and Differential Equations, 2021, 275  crossref
    9. S. M. Tashpulatov, “Spektr operatora energii v trekhelektronnykh sistemakh s primesyu v modeli Khabbarda. Vtoroe dubletnoe sostoyanie”, Sovremennye problemy matematiki i fiziki, SMFN, 65, no. 1, Rossiiskii universitet druzhby narodov, M., 2019, 109–123  mathnet  crossref
    10. S. M. Tashpulatov, “The structure of essential spectra and discrete spectrum of four-electron systems in the Hubbard model in a singlet state”, Lobachevskii J. Math., 38:3, SI (2017), 530–541  crossref  mathscinet  zmath  isi  scopus
    11. S. M. Tashpulatov, “Spectra of the energy operator of four-electron systems in the triplete state in the Hubbard model”, Algebra, Analysis and Quantum Probability, Journal of Physics Conf. Ser., 697, eds. S. Ayupov, V. Chilin, N. Ganikhodjaev, F. Mukhamedov, I. Rakhimov, IOP Publishing Ltd, 2016, 012025  crossref  isi  scopus
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