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TMF, 1979, Volume 39, Number 1, Pages 83–93 (Mi tmf2602)  

This article is cited in 7 scientific papers (total in 7 papers)

Bound states of a cluster operator

S. N. Lakaev, R. A. Minlos


Abstract: The bound states of a self-adjoint cluster operator with maximal single-particle spectrum are studied. It is shown that under certain conditions this spectrum can disappear, being absorbed by the continuous two-particle spectrum. It is shown that this phenomenon can occur in the spectrum of the transfer matrix of certain two-dimensional Gibbs lattice fields (for example, in the so-called eight-vertex model).

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English version:
Theoretical and Mathematical Physics, 1979, 39:1, 336–342

Bibliographic databases:

Received: 21.08.1978

Citation: S. N. Lakaev, R. A. Minlos, “Bound states of a cluster operator”, TMF, 39:1 (1979), 83–93; Theoret. and Math. Phys., 39:1 (1979), 336–342

Citation in format AMSBIB
\Bibitem{LakMin79}
\by S.~N.~Lakaev, R.~A.~Minlos
\paper Bound states of a~cluster operator
\jour TMF
\yr 1979
\vol 39
\issue 1
\pages 83--93
\mathnet{http://mi.mathnet.ru/tmf2602}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=536468}
\transl
\jour Theoret. and Math. Phys.
\yr 1979
\vol 39
\issue 1
\pages 336--342
\crossref{https://doi.org/10.1007/BF01018946}


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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. V. A. Malyshev, “Cluster expansions in lattice models of statistical physics and the quantum theory of fields”, Russian Math. Surveys, 35:2 (1980), 1–62  mathnet  crossref  mathscinet  adsnasa  isi
    2. S. N. Lakaev, Sh. M. Tilavova, “Merging of eigenvalues and resonances of a two-particle Schrödinger operator”, Theoret. and Math. Phys., 101:2 (1994), 1320–1331  mathnet  crossref  mathscinet  zmath  isi
    3. Albeverio, S, “Schrodinger operators on lattices. The Efimov effect and discrete spectrum asymptotics”, Annales Henri Poincare, 5:4 (2004), 743  isi
    4. Yu. Kh. Eshkabilov, “On infinity of the discrete spectrum of operators in the Friedrichs model”, Siberian Adv. Math., 22:1 (2012), 1–12  mathnet  crossref  mathscinet  elib
    5. Yu. Kh. Eshkabilov, R. R. Kucharov, “Essential and discrete spectra of the three-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 170:3 (2012), 341–353  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. Eshkabilov Yu.Kh., “O beskonechnosti chisla otritsatelnykh sobstvennykh znachenii modeli fridriskha”, Nanosistemy: fizika, khimiya, matematika, 3:6 (2012), 16–24  elib
    7. R. R. Kucharov, Yu. Kh. Eshkabilov, “On the number of negative eigenvalues of a partial integral operator”, Siberian Adv. Math., 25:3 (2015), 179–190  mathnet  crossref  mathscinet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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