Skip to main content
SpringerLink
Log in

Spectrum of the Three-Particle Schrödinger Difference Operator on a Lattice

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

For a three-particle operator on a lattice, we study the properties of its spectrum that depend on pairwise interactions and are determined by a parameter characterizing the intensity of interaction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. V. N. Efimov, “Bound states of three resonance interacting particles,” Nuclear Physics, 12 (1970), no. 5, 1080–1091.

    Google Scholar 

  2. S. P. Merkur'ev and L. D. Faddeev, Quantum Scattering Theory for Several-Particle Systems [in Russian], Nauka, Moscow, 1985.

    Google Scholar 

  3. R. D. Amado and J. V. Noble, “Efimov's effect: a new pathology of three-particle systems. II,” Phys. Rev. D, 5 (1971), no. 8, 1992–2002.

    Google Scholar 

  4. D. R. Yafaev, “Theory of the discrete spectrum of the three-particle Schrödinger operator,” Mat. Sb. [Math. USSR-Sb.], 9 (136) (1974), no. 4 (8), 567–592.

    Google Scholar 

  5. Yu. N. Ovchinnikov and I. M. Sigal, “Number of bound states of three-body systems and Efimov's effect,” Ann. Physics, 123 (1989), 274–295.

    Google Scholar 

  6. H. Tamura, “The Efimov effect of three-body Schrödinger operators,” J. Funct. Anal., 95 (1991), 433–459.

    Google Scholar 

  7. A. V. Sobolev, “The Efimov Effect. Discrete Spectrum Asymptotics,” Commun. Math. Phys., 156 (1993), 101–126.

    Google Scholar 

  8. D. C. Mattis, “The few-body problem on lattice,” Rev. Modern Phys., 58 (1986), no. 2, 361–379.

    Google Scholar 

  9. V. A. Malyshev and R. A. Minlos, “Cluster operators,” Trudy Sem. Petrovsk., (1983), no. 9, 63–80.

  10. A. I. Mogilner, “The problem of few quasi-particles in solid-state physics,” in: Applications of Self-Adjoint Extensions in Quantum Physics (P. Exner and P. Seba, editors), vol. 324, Lecture Notes in Phys., Springer-Verlag, Berlin, 1988.

    Google Scholar 

  11. S. N. Lakaev, “The Efimov effect in a system of three identical quantum particles,” Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.], 27 (1993), no. 3, 15–28.

    Google Scholar 

  12. M. Reed and B. Simon, Methods of Modern Mathematical Physics, vol. 4, Analysis of Operators, Academic Press, New York, 1979.

    Google Scholar 

  13. Zh. I. Abdullaev and S. N. Lakaev, “Finiteness of the discrete spectrum of the three-particle Schrödinger operator on a lattice,” Teoret. Mat. Fiz. [Theoret. and Math. Phys.], 111 (1997), no. 1, 94–108.

    Google Scholar 

  14. D. R. Yafaev, “Singular spectrum in a three-particle system,” Mat. Sb. [Math. USSR-Sb.], 106 (148) (1978), no. 4 (8), 622–640.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Samarkand University, Russia

    S. N. Lakaev & Zh. I. Abdullaev

Authors
  1. S. N. Lakaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zh. I. Abdullaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lakaev, S.N., Abdullaev, Z.I. Spectrum of the Three-Particle Schrödinger Difference Operator on a Lattice. Mathematical Notes 71, 624–633 (2002). https://doi.org/10.1023/A:1015831803838

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015831803838

Search

Navigation