Advertisement

Three strongly correlated charged bosons in a one-dimensional harmonic trap: natural orbital occupancies

  • P. KościkEmail author
Regular Article

Abstract

We study a one-dimensional system composed of three charged bosons confined in an external harmonic potential. More precisely, we investigate the ground-state correlation properties of the system, paying particular attention to the strong-interaction limit. We explain for the first time the nature of the degeneracies appearing in this limit in the spectrum of the reduced density matrix. An explicit representation of the asymptotic natural orbitals and their occupancies is given in terms of some integral equations.

Keywords

Mesoscopic and Nanoscale Systems 

References

  1. 1.
    N. Nielsen, I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge), 2000 Google Scholar
  2. 2.
    A. Harju, S. Siljamäki, R.M. Nieminen, Phys. Rev. B 65, 075309 (2002) ADSCrossRefGoogle Scholar
  3. 3.
    A. Puente, L. Serra, R. Nazmitindov, Phys. Rev. B 69, 125315 (2004) ADSCrossRefGoogle Scholar
  4. 4.
    N. Simonović, R. Nazmitindov, Phys. Rev. B 67, 041305 (2003) ADSCrossRefGoogle Scholar
  5. 5.
    O. Ciftja, M.G. Faruk, J. Phys.: Condens. Matter 18, 2623 (2006) ADSCrossRefGoogle Scholar
  6. 6.
    D. Manzano et al., J. Phys. A Math. Theor. 43, 275301 (2010) ADSCrossRefMathSciNetGoogle Scholar
  7. 7.
    R. Yañez, A. Plastino, J. Dehesa, Eur. Phys. J. D 56, 141 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    P.A. Bouvrie et al., Eur. Phys. J. D 66, 15 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    H. Laguna, R. Sagar, J. Phys. A Math. Theor. 45, 025307 (2012) ADSCrossRefGoogle Scholar
  10. 10.
    H. Laguna, R. Sagar, Phys. Rev. A 84, 012502 (2011) ADSCrossRefGoogle Scholar
  11. 11.
    P. Kościk, A. Okopińska, Phys. Lett. A 374, 3841 (2010) ADSzbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    P. Kościk, Phys. Lett. A 375, 458 (2011) ADSCrossRefGoogle Scholar
  13. 13.
    P. Kościk, A. Okopińska, J. Phys. A Math. Theor. 40, 1045 (2007) ADSzbMATHCrossRefGoogle Scholar
  14. 14.
    P. Kościk, A. Okopińska, Eur. Phys. J. B 85, 93 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    B. Sun, M. Pindzola, Phys. Lett. A 373, 3833 (2009) ADSzbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    J. Wang, C.K. Law, M.C. Chu, Phys. Rev. A 72, 022346 (2005) ADSCrossRefGoogle Scholar
  17. 17.
    S. Zöllner, H. Meyer, P. Schmelcher, Phys. Rev. A 74, 053612 (2006) ADSCrossRefGoogle Scholar
  18. 18.
    S. Zöllner, H. Meyer, P. Schmelcher, Phys. Rev. A 74, 063611 (2006) ADSCrossRefGoogle Scholar
  19. 19.
    M.D. Girardeau, E.M. Wright, J.M. Triscari, Phys. Rev. A 63, 033601 (2001) ADSCrossRefGoogle Scholar
  20. 20.
    B. Sun, D. Zhou, L. You, Phys. Rev. A 73, 012336 (2006) ADSCrossRefGoogle Scholar
  21. 21.
    M. Girardeau, J. Math. Phys. 1, 516 (1960)ADSzbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Y. He, C. Bao, J. Phys. B At. Mol. Opt. Phys. 34, 1641 (2001) ADSCrossRefGoogle Scholar
  23. 23.
    T. Schneider, R. Blümel, J. Phys. B At. Mol. Opt. Phys. 32, 5017 (1999) ADSCrossRefGoogle Scholar
  24. 24.
    Y. Kim, A. Zubarev, Phys. Rev. A 64, 013603 (2001) ADSCrossRefGoogle Scholar
  25. 25.
    A. Gonzalez et al., Phys. Rev. B 59, 1653 (1999) ADSCrossRefGoogle Scholar
  26. 26.
    G. Morigi, H. Walther, Eur. Phys. J. D 13, 261 (2001)ADSCrossRefGoogle Scholar
  27. 27.
    G.E. Astrakharchik, M.D. Girardeau, Phys. Rev. B 83, 153303 (2011) ADSCrossRefGoogle Scholar
  28. 28.
    J. Ciosłowski, K. Pernal, J. Chem. Phys. 125, 064106 (2006) ADSCrossRefGoogle Scholar
  29. 29.
    J. Wineland et al., Phys. Rev. Lett. 59, 2935 (1987) ADSCrossRefGoogle Scholar
  30. 30.
    R. Grobe, K. Rzążewski, J.H. Eberly, J. Phys. B 27, L503 (1994) ADSCrossRefGoogle Scholar
  31. 31.
    J.S. Dehesa et al., J. Phys. B At. Mol. Opt. Phys. 45, 015504 (2012) ADSCrossRefGoogle Scholar
  32. 32.
    G. Ghirardi, L. Marinatto, Phys. Rev. A 70, 012109 (2004) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of PhysicsJan Kochanowski UniversityKielcePoland

Personalised recommendations