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Phase transitions for an ideal Bose condensate trapped in a quartic potential

  • J.H. WangEmail author
  • J.Z. He
Cold Matter and Quantum Gases Regular Article

Abstract.

Based on the classification scheme of phase transitions, we study the phase transitions for an ideal Bose gas with a finite number of particles confined in a three-dimensional quartic trap. We show that the phase transition of an ideal Bose gas in the three-dimensional quartic trap is of third order for finite particle numbers, quite different from the fact that the phase transition is of first order in the thermodynamic limit. We discuss the effects of finite particle numbers on the nature of the phase transitions, and determine the dependence of transition temperature on particle number.

Keywords

Partition Function Particle Number Thermodynamic Limit Harmonic Trap Potential Trap 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell, Science 269, 198 (1995)ADSCrossRefGoogle Scholar
  2. 2.
    C.C. Bradley, C.A. Sackett, J.J. Tollett, R.G. Hulet, Phys. Rev. Lett. 75, 1687 (1995)ADSCrossRefGoogle Scholar
  3. 3.
    D.M. Stamper-Kurn, M.R. Andrews, A.P. Chikkatur, S. Inouye, H.J. Miesner, J. Stenger, W. Ketterle, Phys. Rev. Lett. 80, 2027 (1998)ADSCrossRefGoogle Scholar
  4. 4.
    A. Melzer, M. Klindworth, A. Piel, Phys. Rev. Lett. 87, 115002 (2001)ADSCrossRefGoogle Scholar
  5. 5.
    M. Klindworth, A. Melzer, A. Piel, V.A. Schweigert, Phys. Rev. B 61, 8404 (2000)ADSCrossRefGoogle Scholar
  6. 6.
    M. Schmidt, T. Hippler, J. Donges, W. Kronmüller, B. von Issendorff, H. Haberland, P. Labastie, Phys. Rev. Lett. 87, 203402 (2001)ADSCrossRefGoogle Scholar
  7. 7.
    C.N. Yang, D.T. Lee, Phys. Rev. 87, 404 (1952)MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. 8.
    D.T. Lee, C.N. Yang, Phys. Rev. 87, 410 (1952)MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. 9.
    S. Grossmann, W. Rosenhauer, Z. Phys. 207, 138 (1967)ADSCrossRefGoogle Scholar
  10. 10.
    S. Grossmann, W. Rosenhauer, Z. Phys. 218, 437 (1969)ADSCrossRefGoogle Scholar
  11. 11.
    S. Grossmann, V. Lehmann, Z. Phys. 218, 449 (1969)ADSCrossRefGoogle Scholar
  12. 12.
    P. Borrmann, O. Mülken, J. Harting, Phys. Rev. Lett. 84, 3511 (2000)ADSCrossRefGoogle Scholar
  13. 13.
    O. Mülken, P. Borrmann, J. Harting, H. Stamerjohanns, Phys. Rev. A 64, 013611 (2001)ADSCrossRefGoogle Scholar
  14. 14.
    D.J. Dean, T. Papenbrock, Phys. Rev. A 65, 043603 (2002)ADSCrossRefGoogle Scholar
  15. 15.
    J.H. Wang, Y.L. Ma, J. Phys. B At. Mol. Opt. Phys. 42, 245301 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    H. Stamerjohanns, O. Mülken, P. Borrmann, Phys. Rev. Lett. 88, 053401 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    O. Mülken, P. Borrmann, Phys. Rev. C 63, 024306 (2001)ADSCrossRefGoogle Scholar
  18. 18.
    D.H.E. Gross, E.V. Votyakov, Eur. Phys. J. B 15, 115 (2000)ADSGoogle Scholar
  19. 19.
    D.H.E. Gross, Nucl. Phys. A 681, 366 (2001)ADSzbMATHCrossRefGoogle Scholar
  20. 20.
    W. Janke, R. Kenna, J. Stat. Phys. 102, 1211 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    W. Janke, D.A. Johnston, R. Kenna, Nucl. Phys. B 682, 618 (2004)MathSciNetADSzbMATHCrossRefGoogle Scholar
  22. 22.
    V. Bretin, S. Stock, Y. Seurin, J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004)ADSCrossRefGoogle Scholar
  23. 23.
    S. Stock, V. Bretin, F. Chevy, J. Dalibard, Europhys. Lett. 65, 594 (2004)ADSCrossRefGoogle Scholar
  24. 24.
    M. Cozzini, B. Jackson, S. Stringari, Phys. Rev. A 73, 013603 (2006)ADSCrossRefGoogle Scholar
  25. 25.
    S. Bargi, G. M. Kavoulakis, S.M. Reimann, Phys. Rev. A 73, 033613 (2006)ADSCrossRefGoogle Scholar
  26. 26.
    E.Ö. Karabulut, M. Koyuncu, M. Tomak, Physica A 389, 1371 (2010)ADSCrossRefGoogle Scholar
  27. 27.
    S. Gautam, D. Angom, Eur. Phys. J. D 46, 151 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    J. Dunkel, S. Hilbert, Physica A 370, 390 (2006), and refrences thereinADSCrossRefGoogle Scholar
  29. 29.
    H. Schmidt, Am. J. Phys. 57, 1150 (1989)ADSCrossRefGoogle Scholar
  30. 30.
    W.J. Mullin, J.P. Fernandez, Am. J. Phys. 71, 661 (2003)ADSCrossRefGoogle Scholar
  31. 31.
    P.T. Landsberg, Thermodynamics with Quantum Statistical Illustrations (Interscience, New York, 1961)Google Scholar
  32. 32.
    M. Wilkens, C. Weiss, J. Mod. Opt. 44, 1801 (1997)MathSciNetADSzbMATHCrossRefGoogle Scholar
  33. 33.
    C. Weiss, M. Wilkens, Optic. Express 1, 272 (1997)ADSCrossRefGoogle Scholar
  34. 34.
    P. Borrmann, J. Harting, O. Mülken, E.R. Hilf, Phys. Rev. A 60, 1519 (1999)ADSCrossRefGoogle Scholar
  35. 35.
    K. Glaum, H. Kleinert, A. Pelster, Phys. Rev. A 76, 063604 (2007)ADSCrossRefGoogle Scholar
  36. 36.
    P. Navez, D. Bitouk, M. Gajda, Z. Idziaszek, K. Rzazewski, Phys. Rev. Lett. 79, 1789 (1997)ADSCrossRefGoogle Scholar
  37. 37.
    J.H. Wang, Y.L. Ma, Phys. Rev. A 79, 033604 (2009)ADSCrossRefGoogle Scholar
  38. 38.
    J.H. Wang, H.Y. Tang, Y.L. Ma, Ann. Phys. 326, 634 (2011)ADSzbMATHCrossRefGoogle Scholar
  39. 39.
    J.H. Wang, Y.L. Ma, J.Z. He, J. Low. Temp. Phys. 162, 23 (2011)ADSCrossRefGoogle Scholar
  40. 40.
    P.M. Mathews, M. Seetharaman, S. Raghavan, J. Phys. A 15, 103 (1982)MathSciNetADSCrossRefGoogle Scholar
  41. 41.
    G.-X. Hu, X.-X. Dai, J.-X. Dai, W.E. Evenson, J. Low. Temp. Phys. 133, 239 (2003)CrossRefGoogle Scholar
  42. 42.
    V.V. Kocharovsky, VI.V. Kocharovsky, M.O. Scully, Phys. Rev. A 61, 053606 (2000)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of PhysicsNanchang UniversityNanchangP.R. China

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