Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Absence of the efimov effect in a homogeneous magnetic field

  • 32 Accesses

  • 3 Citations

Abstract

A system of three identical particles in a homogeneous magnetic field is studied. It is shown that the Hamiltonian of this system with short-range potentials after the separation of the center of mass motion has a finite discrete spectrum for each fixed type m of the rotational (SO(2)) symmetry.

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

References

  1. 1.

    Efimov, V.: Yadernaya Fiz. 12 (1970), 1080–1091.

  2. 2.

    Yafaev, D.: Mat. Sb. 94 (1974), 567–593.

  3. 3.

    Ovchinnikov, Y. N. and Sigal, I. M., Ann. Phys. 123 (1979), 274–295.

  4. 4.

    Tamura, H.: J. Funct. Anal. 95 (1991), 433–459.

  5. 5.

    Vugalter, S. and Zhislin, G.: Comm. Math. Phys. 87 (1982), 89–103.

  6. 6.

    Vugalter, S. and Zhislin, G.: Lett. Math. Phys. 25 (1992), 299–306.

  7. 7.

    Zhislin, G.: Teor. i Mat. Fiz. 21 (1974), 60–73.

  8. 8.

    Vugalter, S. and Zhislin, G.: Funk. Analiz i Prilozh. 25 (1991), 83–86.

  9. 9.

    Vugalter, S. and Zhislin, G.: Algebra i Analiz 5(2) (1993), 108–125.

  10. 10.

    Birman, M. Sh.: Mat. Sbornik 55 (1961), 125–173.

Download references

Author information

Additional information

Supported by the Erwin Schrödinger Institute, Austria, International Science Foundation Grant No. 9400 and Russian Grant of the State Committee for High Education RF-94-27-1022.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Vugalter, S. Absence of the efimov effect in a homogeneous magnetic field. Lett Math Phys 37, 79–94 (1996). https://doi.org/10.1007/BF00400141

Download citation

Mathematics Subject Classification (1991)

  • 81V10

Key words

  • Efimov effect
  • homogeneous magnetic field
  • decomposition of configuration space