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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 135, Number 3, Pages 478–503
DOI: https://doi.org/10.4213/tmf197
(Mi tmf197)
 

This article is cited in 38 scientific papers (total in 38 papers)

Essential and Discrete Spectra of the Three-Particle Schrödinger Operator on a Lattice

S. N. Lakaev, M. I. Muminov

A. Navoi Samarkand State University
References:
Abstract: We consider the system of three quantum particles (two are bosons and the third is arbitrary) interacting by attractive pair contact potentials on a three-dimensional lattice. The essential spectrum is described. The existence of the Efimov effect is proved in the case where either two or three two-particle subsystems of the three-particle system have virtual levels at the left edge of the three-particle essential spectrum for zero total quasimomentum ($K=0$). We also show that for small values of the total quasimomentum ($K\ne 0$), the number of bound states is finite.
Keywords: essential spectrum, virtual level, channel operator, discrete spectrum, Weyl inequality, Hilbert–Schmidt operator.
Received: 23.07.2002
English version:
Theoretical and Mathematical Physics, 2003, Volume 135, Issue 3, Pages 849–871
DOI: https://doi.org/10.1023/A:1024087105686
Bibliographic databases:
Language: Russian
Citation: S. N. Lakaev, M. I. Muminov, “Essential and Discrete Spectra of the Three-Particle Schrödinger Operator on a Lattice”, TMF, 135:3 (2003), 478–503; Theoret. and Math. Phys., 135:3 (2003), 849–871
Citation in format AMSBIB
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\paper Essential and Discrete Spectra of the Three-Particle Schr\"odinger Operator on a Lattice
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\pages 478--503
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\transl
\jour Theoret. and Math. Phys.
\yr 2003
\vol 135
\issue 3
\pages 849--871
\crossref{https://doi.org/10.1023/A:1024087105686}
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Linking options:
  • https://www.mathnet.ru/eng/tmf197
  • https://doi.org/10.4213/tmf197
  • https://www.mathnet.ru/eng/tmf/v135/i3/p478
  • This publication is cited in the following 38 articles:
    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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    References:74
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