Particle density and transition temperature of weakly interacting quantum gases

Regular Article

Abstract

An expression for single particle density of weakly interacting trapped quantum gases has been obtained for Fermi gas at all temperatures and for Bose gas above the transition temperature (Tc). This expression has been used to study the effect of interaction on density of harmonically trapped Bose gas. It is found that interaction has a large effect on the density at centre of the trap as observed experimentally. The same expression for density is also used to obtain the transition temperature of homogeneous Bose gas. Experimental results for Tc has been re-analysed on the basis of perturbative and non-perturbative theories. It is found that both the theories fit experimental data equally well in low-density regimes.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    A.S. Parkins, D.F. Walls, Phys. Rep. 303, 1 (1998)ADSCrossRefGoogle Scholar
  2. 2.
    C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2002) Google Scholar
  3. 3.
    L. Pitaevskii, S. Stringari, Bose-Einstein Condensation (Clarendon Press, Oxford, 2003)Google Scholar
  4. 4.
    M. Greiner, C.A. Regal, J.T. Stewart, Phys. Rev. Lett. 94, 110401 (2005) ADSCrossRefGoogle Scholar
  5. 5.
    X.Z. Wang, Eur. Phys. J. B 48, 385 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    H.T.C. Stoof, Phys. Rev. A 45, 8398 (1992) ADSCrossRefGoogle Scholar
  7. 7.
    M. Bijlsma, H.T.C. Stoof, Phys. Rev. A 54, 5085 (1996) ADSCrossRefGoogle Scholar
  8. 8.
    G. Baym, J.P. Blaizot, M. Holzman, F. Laloe, D. Vautherin, Phys. Rev. Lett. 83, 1703 (1999) ADSCrossRefGoogle Scholar
  9. 9.
    M. Holzmann, P. Gruter, F. Laloe, Eur. Phys. J. B 10, 739 (1999)ADSCrossRefGoogle Scholar
  10. 10.
    K. Huang, Phys. Rev. Lett. 83, 19 (1999)ADSCrossRefGoogle Scholar
  11. 11.
    X.Z. Wang, Physica A 341, 433 (2004) ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    P. Arnold, G. Moore, Phys. Rev. Lett. 87, 12 (2001)CrossRefGoogle Scholar
  13. 13.
    M. Holzmann, W. Krauth, Phys. Rev. Lett. 83, 2687 (1999) ADSCrossRefGoogle Scholar
  14. 14.
    K. Morawetz, M. Mannel, M. Schreiber, Phys. Rev. B 76, 075116 (2007) ADSCrossRefGoogle Scholar
  15. 15.
    J.D. Reppy, B.C Crooker, B. Hebral, A.D. Corwin, J. He, G.M. Zassenhaus, Phys. Rev. Lett. 84, 2060 (2000) ADSCrossRefGoogle Scholar
  16. 16.
    P. Arnold, B. Tomasik, Phys. Rev. A 62, 063604 (2000) ADSCrossRefGoogle Scholar
  17. 17.
    P. Gruter, D. Ceperley, F. Laloe, Phys. Rev. Lett. 79, 3549 (1997) ADSCrossRefGoogle Scholar
  18. 18.
    A.M.J. Schakel, Int. J. Mod. Phys. B 8, 2021 (1994)ADSCrossRefGoogle Scholar
  19. 19.
    D.N. Zubarev, Soviet Phys. Uspekhi 3, 3 (1960)MathSciNetCrossRefGoogle Scholar
  20. 20.
    J. Bosse, K.N. Pathak, A. Pelster (unpublished) Google Scholar
  21. 21.
    K. Huang, C.N. Yang, J.M. Luttinger, Phys. Rev. 105, 776 (1957) ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    T.D. Lee, C.N. Yang, Phys. Rev. 116, 25 (1959)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    L.P. Kadanoff, G. Baym, in Quantum statistical mechanics (W.A. Benjamin, New York, 1962), p. 83Google Scholar
  24. 24.
    R.K. Pathria, P.D. Beale, Statistical Mechanics, 3rd edn. (Elsevier, 2011)Google Scholar
  25. 25.
  26. 26.
    K. Huang, AAPPS Bulletin 18, 4 (2008)Google Scholar
  27. 27.
    A.L. Gaunt, T.F. Schmidutz, I. Gotlibovych, R.P. Smith, Z. Hadzibabic, Phys. Rev. Lett. 110, 200406 (2013) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Renu Bala
    • 1
  • Sunita Srivastava
    • 2
  • Kare Narain Pathak
    • 2
  1. 1.Department of PhysicsDAV UniversityJalandharIndia
  2. 2.Centre for Advanced Study in Physics, Panjab UniversityChandigarhIndia

Personalised recommendations