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Few-Body Systems

, 60:46 | Cite as

Four-Boson Continuous Scale Symmetry Breaking

  • T. FredericoEmail author
  • W. de Paula
  • A. Delfino
  • M. T. Yamashita
  • Lauro Tomio
Article
  • 22 Downloads
Part of the following topical collections:
  1. Ludwig Faddeev Memorial Issue

Abstract

We show that the homogeneous Faddeev–Yakubovski formalism for the bound state of four identical bosons with zero-range interaction in the unitary limit (infinite two-body scattering length) presents scale invariance in the ultraviolet (UV) region. By resorting to an approximate form of the integral equations in the UV limit (considering exclusively an attractive pairwise zero-range interaction), we demonstrate that a pair of log-periodic solutions, with a cycle distinct from the three-boson one, exists with a four-body scale required to define the phase between them.

Notes

Acknowledgements

The authors thank the following agencies for partial support: Conselho Nacional de Desenvolvimento Científico e Tecnológico [Procs. 313236/2018-6 and 438562/2018-6 (WP), 310205/2017-4(AD), 308486/2015-3(TF), 306191/2014-8(LT), 302075/2016-0(MTY) and INCT-FNA Proc.464898/2014-5], Fundação de Amparo à Pesquisa do Estado de São Paulo [Projs. 2017/05660-0(LT and TF), 2016/01816-2 (MTY)], and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Grant 88881.030363/2013-01 (MTY) and 88881.309870/2018-01 (WP and LT). This study was financed in part by CAPES - Finance Code 001.

References

  1. 1.
    L.D. Faddeev, Z. Eksp, Teor. Fiz. 39, 1459 (1960)Google Scholar
  2. 2.
    O.A. Yakubovsky, Sov. J. Nucl. Phys. 5, 937 (1967)Google Scholar
  3. 3.
    G.S. Danilov, JETP 40, 698 (1961)Google Scholar
  4. 4.
    G.S. Danilov, Sov. Phys. JETP 13, 349 (1961)Google Scholar
  5. 5.
    G. Skorniakov, K. Ter-Martirosian, Sov. Phys. JETP 4, 648 (1957)Google Scholar
  6. 6.
    V. Efimov, Phys. Lett. B 33, 563 (1970)ADSCrossRefGoogle Scholar
  7. 7.
    V. Efimov, Sov. J. Nucl. Phys. 12, 589 (1971)Google Scholar
  8. 8.
    V. Efimov, Nat. Phys. 5, 533 (2009)CrossRefGoogle Scholar
  9. 9.
    V. Efimov, Few Body Syst. 60, 15 (2019)ADSCrossRefGoogle Scholar
  10. 10.
    T. Kraemer et al., Nature 440, 315 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    R. Grimm, Few Body Syst. 60, 23 (2019)ADSCrossRefGoogle Scholar
  12. 12.
    H. Feshbach, Theoretical Nuclear Physics (Wiley, New York, 1992)Google Scholar
  13. 13.
    E. Timmermans, P. Tommasini, M. Hussein, A. Kerman, Phys. Rep. 315, 199–230 (1999)ADSCrossRefGoogle Scholar
  14. 14.
    T. Köhler, K. Göral, P.S. Julienne, Rev. Mod. Phys. 78, 1311 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    L.H. Thomas, Phys. Rev. 47, 903 (1935)ADSCrossRefGoogle Scholar
  16. 16.
    S.K. Adhikari, A. Delfino, T. Frederico, I.D. Goldman, L. Tomio, Phys. Rev. A 37, 3666 (1988)ADSCrossRefGoogle Scholar
  17. 17.
    M.T. Yamashita, L. Tomio, A. Delfino, T. Frederico, Europhys. Lett. 75, 555 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    M.R. Hadizadeh, M.T. Yamashita, L. Tomio, A. Delfino, T. Frederico, Phys. Rev. Lett. 107, 135304 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    J. von Stecher, J.P. D’Incao, C.H. Greene, Nat. Phys. 5, 417 (2009)CrossRefGoogle Scholar
  20. 20.
    F. Ferlaino, S. Knoop, M. Berninger, W. Harm, J.P. D’Incao, H.-C. Nägerl, R. Grimm, Phys. Rev. Lett. 102, 140401 (2009)ADSCrossRefGoogle Scholar
  21. 21.
    M. Zaccanti, B. Deissler, C. D’Errico, M. Fattori, M. Jona-Lasinio, S. Müller, G. Roati, M. Inguscio, G. Modugno, Nat. Phys. 5, 586 (2009)CrossRefGoogle Scholar
  22. 22.
    S.E. Pollack, D. Dries, R.G. Hulet, Science 326, 1683 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    F. Ferlaino, A. Zenesini, M. Berninger, B. Huang, H.-C. Nägerl, R. Grimm, Few Body Syst. 51, 113 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    H.W. Hammer, L. Platter, Eur. Phys. J. A 32, 113 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    A. Deltuva, Phys. Rev. A 82, 040701(R) (2010)ADSCrossRefGoogle Scholar
  26. 26.
    D. Blume, Rep. Prog. Phys. 75, 046401 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    A. Deltuva, Few Body Syst. 54, 569 (2013)ADSCrossRefGoogle Scholar
  28. 28.
    N.T. Zinner, A.S. Jensen, J. Phys. G 40, 053101 (2013)ADSCrossRefGoogle Scholar
  29. 29.
    H.W. Hammer, A. Nogga, A. Schwenk, Rev. Mod. Phys. 85, 197 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    A. Kievsky, N.K. Timofeyuk, M. Gattobigio, Phys. Rev. A 90, 032504 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    R. Álvarez-Rodríguez, A. Deltuva, A. Kievsky, M. Gattobigio, Phys. Rev. A 93, 062701 (2016)ADSCrossRefGoogle Scholar
  32. 32.
    U. van Kolck, Few Body Syst. 58, 112 (2017)ADSCrossRefGoogle Scholar
  33. 33.
    C.H. Greene, P. Giannakeas, J. Perez-Rios, Rev. Mod. Phys. 89, 035006 (2017)ADSCrossRefGoogle Scholar
  34. 34.
    P. Naidon, S. Endo, Rep. Prog. Phys. 80, 056001 (2017)ADSCrossRefGoogle Scholar
  35. 35.
    S.M. Yoshida, S. Endo, J. Levinsen, M.M. Parish, Phys. Rev. X 8, 011024 (2018)Google Scholar
  36. 36.
    D. Blume, Phys. Rev. A 99, 013613 (2019)ADSCrossRefGoogle Scholar
  37. 37.
    B. Bazak, J. Kirscher, S. König, M. Pavón Valderrama, N. Barnea, U. van Kolck, Phys. Rev. Lett. (2019). arXiv:1812.00387 [cond-mat.quant-gas]
  38. 38.
    M.R. Hadizadeh, M.T. Yamashita, L. Tomio, A. Delfino, T. Frederico, Phys. Rev. A 85, 023610 (2012)ADSCrossRefGoogle Scholar
  39. 39.
    M.R. Hadizadeh, M. Yamashita, L. Tomio, A. Delfino, T. Frederico, Phys. Rev. A 87, 013620 (2013)ADSCrossRefGoogle Scholar
  40. 40.
    W. de Paula, A. Delfino, T. Frederico, L. Tomio, Interwoven limit cycles in the spectra of mass imbalanced many-boson system. arXiv:1903.10321 [quant-ph]
  41. 41.
    P. Naidon, Few Body Syst. 59, 64 (2018)ADSCrossRefGoogle Scholar
  42. 42.
    E.R. Christensen, A.S. Jensen, E. Garrido, Few Body Syst. 59, 136 (2018)ADSCrossRefGoogle Scholar
  43. 43.
    M.T. Yamashita, Few Body Syst. 60, 22 (2019)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.DCTAInstituto Tecnológico de AeronáuticaSão José dos CamposBrazil
  2. 2.Instituto de FísicaUniversidade Federal FluminenseNiteróiBrazil
  3. 3.Instituto de Física TeóricaUniversidade Estadual PaulistaSão PauloBrazil

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