Anomalous effects in a trapped Bose-Einstein condensate

Regular Article

Abstract

We study the anomalous density in an ultra-cold trapped bose gas in a variational framework, for both zero and finite temperature. We show that it is finite in 1D, while it is logarithmically and linearly divergent in 2D and 3D. The renormalization that we adopt is more reliable and compatible with the variational scheme. The main outcome is that the anomalous and non condensate densities are of the same order of magnitude and should therefore be treated on an equal footing.

Keywords

Cold Matter and Quantum Gas 

References

  1. 1.
    M. Benarous, Ann. Phys. 320, 226 (2005) ADSCrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    R. Balian, M. Vénéroni, Ann. Phys. 187, 29 (1988) ADSCrossRefMATHGoogle Scholar
  3. 3.
    R. Balian, M. Vénéroni, Ann. Phys. 195, 324 (1989) ADSCrossRefMATHGoogle Scholar
  4. 4.
    E.P. Gross, Nuovo Cimento 20, 454 (1961) CrossRefMATHGoogle Scholar
  5. 5.
    L. Pitaevskii, Sov. Phys. J. Exp. Theor. Phys. 13, 451 (1961) MathSciNetGoogle Scholar
  6. 6.
    A. Boudjemâa, M. Benarous, Eur. Phys. J. D 59, 427 (2010) ADSCrossRefGoogle Scholar
  7. 7.
    A. Boudjemâa, M. Benarous, Phys. Rev. A 84, 043633 (2011) ADSCrossRefGoogle Scholar
  8. 8.
    V. Chernyak, S. Choi, S. Mukamel, Phys. Rev. A 67, 053604 (2003) ADSCrossRefGoogle Scholar
  9. 9.
    S.A. Morgan, J. Phys. B 33, 3847 (2000) ADSCrossRefGoogle Scholar
  10. 10.
    D.A.W. Hutchinson, R.J. Dodd, K. Burnett, Phys. Rev. Lett. 81, 2298 (1998) ADSCrossRefGoogle Scholar
  11. 11.
    D.A.W. Hutchinson, R.J. Dodd, K. Burnett, S.A. Morgan, M. Rusch, E. Zaremba, N.P. Proukakis, M. Edwards, C.W. Clark, J. Phys. B 33, 3825 (2000) ADSCrossRefGoogle Scholar
  12. 12.
    T. Kita, J. Phys. Soc. Jpn 75, 044603 (2006) ADSCrossRefGoogle Scholar
  13. 13.
    V.I. Yukalov, H. Kleinert, Phys. Rev. A 75, 063612 (2006) ADSCrossRefGoogle Scholar
  14. 14.
    D.S. Jin, M.R. Matthews, J.R. Ensher, C.E. Wieman, E.A. Cornell, Phys. Rev. Lett. 78, 764 (1997) ADSCrossRefGoogle Scholar
  15. 15.
    L. Pricoupenko, Phys. Rev. A 84, 053602 (2011) ADSCrossRefGoogle Scholar
  16. 16.
    L. Pricoupenko, Phys. Rev. A 70, 013601 (2004) ADSCrossRefGoogle Scholar
  17. 17.
    M. Olshanii, L. Pricoupenko, Phys. Rev. Lett. 88, 010402 (2002) ADSCrossRefGoogle Scholar
  18. 18.
    E. Timmermans, P. Tommasini, K. Huang, Phys. Rev. A 55, 3645 (1997) ADSCrossRefMathSciNetGoogle Scholar
  19. 19.
    P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New York, 1980) Google Scholar
  20. 20.
    P. Schuck, X. Vinas, Phys. Rev. A 61, 43603 (2000) ADSCrossRefGoogle Scholar
  21. 21.
    A. Griffin, Phys. Rev. B 53, 9341 (1996) ADSCrossRefGoogle Scholar
  22. 22.
    N.P. Proukakis, K. Burnett, J. Res. Natl. Stand. Technol. 101, 457 (1996) CrossRefGoogle Scholar
  23. 23.
    V.I. Yukalov, Phys. Rev. E 72, 066119 (2005) ADSCrossRefGoogle Scholar
  24. 24.
    V.I. Yukalov, Ann. Phys. 323, 461 (2008) ADSCrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    V.I. Yukalov, Phys. Lett. A 359, 712 (2006) ADSCrossRefGoogle Scholar
  26. 26.
    V.I. Yukalov, Laser Phys. Lett. 3, 406 (2006) ADSCrossRefGoogle Scholar
  27. 27.
    V.I. Yukalov, E.P. Yukalova, Laser Phys. Lett. 2, 506 (2005) ADSCrossRefGoogle Scholar
  28. 28.
    T. Kohler, K. Burnett, Phys. Rev. A 65, 033601 (2002) ADSCrossRefGoogle Scholar
  29. 29.
    M. Benarous, H. Flocard, Ann. Phys. 273, 242 (1999) ADSCrossRefMATHMathSciNetGoogle Scholar
  30. 30.
    C. Gies, M.D. Lee, D.A.W. Hutchinson, J. Phys. B 38, 1797 (2005) ADSCrossRefGoogle Scholar
  31. 31.
    S. Kouidri, M. Benarous, J. Phys. B 44, 205301 (2011) ADSCrossRefGoogle Scholar
  32. 32.
    G. Bruun, Y. Castin, R. Dum, K. Burnett, Eur. Phys. J. D 7, 433 (1999) ADSCrossRefGoogle Scholar
  33. 33.
    K. Huang, Statistical Mechanics (Wiley, New York, 1987) Google Scholar
  34. 34.
    A. Bulgac, Y. Yu, Phys. Rev. Lett. 88, 042504 (2002) ADSCrossRefGoogle Scholar
  35. 35.
    N.M. Hugenholtz, D. Pines, Phys. Rev. 116, 489 (1959) ADSCrossRefMATHMathSciNetGoogle Scholar
  36. 36.
    A. Griffin, H. Shi, Phys. Rep. 304, 1 (1998) ADSCrossRefGoogle Scholar
  37. 37.
    D.M. Gangardt, G.V. Shlyapnikov, Phys. Rev. Lett. 90, 010401 (2003) ADSCrossRefGoogle Scholar
  38. 38.
    D.M. Gangardt, G.V. Shlyapnikov, New J. Phys. 5, 79 (2003) ADSCrossRefGoogle Scholar
  39. 39.
    G.V. Shlyapnikov, private communication Google Scholar
  40. 40.
    J. Kneur, A. Neveu, M.B. Pinto, Phys. Rev. A 69, 053624 (2004) ADSCrossRefGoogle Scholar
  41. 41.
    M. Benarous, Ann. Phys. 269, 107 (1998) ADSCrossRefMATHMathSciNetGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Laboratory for Theoretical Physics and Material Physics, Faculty of Sciences, Hassiba Benbouali University of ChlefChlefAlgeria

Personalised recommendations