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

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Teoreticheskaya i Matematicheskaya Fizika, 1979, Volume 39, Number 1, Pages 83–93 (Mi tmf2602)

This article is cited in 10 scientific papers (total in 10 papers)

Bound states of a cluster operator

S. N. Lakaev, R. A. Minlos

Full-text PDF (1302 kB) Citations (10)

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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).

Received: 21.08.1978

English version:
Theoretical and Mathematical Physics, 1979, Volume 39, Issue 1, Pages 336–342
DOI: https://doi.org/10.1007/BF01018946

Bibliographic databases:

Language: Russian

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://mathscinet.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}

Linking options:

https://www.mathnet.ru/eng/tmf2602

https://www.mathnet.ru/eng/tmf/v39/i1/p83

This publication is cited in the following 10 articles:

G. A. Agafonkin, “Spektralnye svoistva modeli Fridrikhsa s involyutsiei”, Matem. zametki, 117:1 (2025), 3–15
Nargiza A. Tosheva, 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, 030003
Yu. Kh. Eshkabilov, D. J. Kulturaev, “On discrete spectrum of one two-particle lattice Hamiltonian”, Ufa Math. J., 14:2 (2022), 97–107
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
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
Eshkabilov Yu.Kh., “O beskonechnosti chisla otritsatelnykh sobstvennykh znachenii modeli fridriskha”, Nanosistemy: fizika, khimiya, matematika, 3:6 (2012), 16–24
Yu. Kh. Eshkabilov, “On infinity of the discrete spectrum of operators in the Friedrichs model”, Siberian Adv. Math., 22:1 (2012), 1–12
Albeverio, S, “Schrodinger operators on lattices. The Efimov effect and discrete spectrum asymptotics”, Annales Henri Poincare, 5:4 (2004), 743
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
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

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

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Abstract page:	388
Full-text PDF :	131
References:	71
First page:	3

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