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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 178, Number 3, Pages 390–402
DOI: https://doi.org/10.4213/tmf8544
(Mi tmf8544)
 

This article is cited in 4 scientific papers (total in 4 papers)

Positivity of eigenvalues of the two-particle Schrödinger operator on a lattice

S. N. Lakaev, Sh. U. Alladustov

Samarkand State University, Samarkand, Uzbekistan
Full-text PDF (472 kB) Citations (4)
References:
Abstract: We consider the family H(k) of two-particle discrete Schrödinger operators depending on the quasimomentum of a two-particle system kTd, where Td is a d-dimensional torus. This family of operators is associated with the Hamiltonian of a system of two arbitrary particles on the d-dimensional lattice Zd, d3, interacting via a short-range attractive pair potential. We prove that the eigenvalues of the Schrödinger operator H(k) below the essential spectrum are positive for all nonzero values of the quasimomentum kTd if the operator H(0) is nonnegative. We establish a similar result for the eigenvalues of the Schrödinger operator H+(k), kTd, corresponding to a two-particle system with repulsive interaction.
Keywords: discrete Schrödinger operator, system quasimomentum, Hamiltonian, repulsive interaction, virtual level, eigenvalue, lattice.
Received: 25.04.2013
Revised: 29.07.2013
English version:
Theoretical and Mathematical Physics, 2014, Volume 178, Issue 3, Pages 336–346
DOI: https://doi.org/10.1007/s11232-014-0146-1
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. N. Lakaev, Sh. U. Alladustov, “Positivity of eigenvalues of the two-particle Schrödinger operator on a lattice”, TMF, 178:3 (2014), 390–402; Theoret. and Math. Phys., 178:3 (2014), 336–346
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf8544
  • https://doi.org/10.4213/tmf8544
  • https://www.mathnet.ru/eng/tmf/v178/i3/p390
  • This publication is cited in the following 4 articles:
    1. S. N. Lakaev, S. Kh. Abdukhakimov, “Threshold effects in a two-fermion system on an optical lattice”, Theoret. and Math. Phys., 203:2 (2020), 648–663  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. S. N. Lakaev, A. T. Boltaev, “Threshold phenomena in the spectrum of the two-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 198:3 (2019), 363–375  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Sh. Yu. Kholmatov, Z. I. Muminov, “Existence of bound states of N-body problem in an optical lattice”, J. Phys. A-Math. Theor., 51:26 (2018), 265202  crossref  mathscinet  isi  scopus
    4. I. P. Popov, “Gruppovaya skorost volnovogo paketa, obrazovannogo dvumya svobodnymi identichnymi chastitsami s raznymi nerelyativistskimi skorostyami”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2015, no. 3(35), 69–72  mathnet  crossref  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:762
    Full-text PDF :218
    References:109
    First page:55
     
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