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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 198, Number 3, Pages 418–432
DOI: https://doi.org/10.4213/tmf9582 (Mi tmf9582) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Threshold phenomena in the spectrum of the two-particle Schrödinger operator on a lattice

S. N. Lakaev, A. T. Boltaev

Samarkand State University, Samarkand, Uzbekistan
Full-text PDF (463 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf9582
Abstract: For a broad class of short-range pairwise attraction potentials, we study threshold phenomena in the spectrum of the two-particle Schrödinger operator associated with the energy operator of the s–d exchange model. We prove that the bound state (eigenvalue) either exists or does not exist depending on the exchange interaction parameter, the system quasimomentum, and dimension of the lattice.
Keywords: discrete Schrödinger operator, two-particle system, energy operator, dispersion relation, virtual level, eigenvalue, lattice.
Funding agency Grant number
Russian Foundation for Basic Research OT-F4-66
This research was supported by the Foundation for Basic Research of the Uzbekistan Republic (Grant No. OT-F4-66).
Received: 24.04.2018
Revised: 02.07.2018
English version:
Theoretical and Mathematical Physics, 2019, Volume 198, Issue 3, Pages 363–375
DOI: https://doi.org/10.1134/S0040577919030036
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. N. Lakaev, A. T. Boltaev, “Threshold phenomena in the spectrum of the two-particle Schrödinger operator on a lattice”, TMF, 198:3 (2019), 418–432; Theoret. and Math. Phys., 198:3 (2019), 363–375
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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