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Numerical Computation of Quantized Vortices in the Bose-Einstein Condensate

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Recent Progress in Computational and Applied PDES

Abstract

The theoretical analysis of many recent experimental work on a single component Bose-Einstein condensate has been based on the mean-field Gross-Pitaevskii equations. We discuss a few algorithms for solving the Gross-Pitaevskii equations and we use them to compute the quantized vortices in Bose-Einstein condensate.

Rearch supported in pan by ihe state major basic research project G19990128 and a grant from FR-HK joint research scheme.

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References

  1. J. Abo-Shaeer, C. Raman, J. Vogels, and W. Ketterle, Science, 292 476 (2001).

    Article  Google Scholar 

  2. A.Aftalion, E.Sandier and S.Serfaty, to appear in J. Math. Pures et Appl. (2000).

    Google Scholar 

  3. A.Aftalion and Q. Du, Phy. Rev. A, December 2001.

    Google Scholar 

  4. A.Aftalion and T.Riviere, cond-mat/0105208.

    Google Scholar 

  5. W. Bao, S. Jin and P. Markowich, J. Comp. Phys., to appear.

    Google Scholar 

  6. T. Bridges and S. Reich, Physics Letters A, 284 184 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  7. D.Butts and D.Rokhsar, Nature 397, 327 (1999).

    Article  Google Scholar 

  8. Y.Castin and R.Dum, Eur. Phys. J. D, 7, 399 (1999).

    Article  Google Scholar 

  9. T. Chan and L. Shen, SIAM J. Numer. Anal., 24 336 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  10. S. Chapman, Q. Du, M. Gunzburger and J. Peterson, Adv. Math.Sci. Appl. 5, 193 (1995).

    MathSciNet  MATH  Google Scholar 

  11. J. Chen, M. Qin and Y. Tang, CCAST-WL reading 6 125 (2001)

    Google Scholar 

  12. F.Dalfovo, S.Giorgini, L.Pitaevskii and S.Stringari, Rev. Mod. Phys. 71,463 (1999).

    Article  Google Scholar 

  13. F.Dalfovo, L.Pitaevskii and S.Stringari, Phys. Rev. A 54,4213 (1996).

    Google Scholar 

  14. J. Deang, Q. Du and M. Gunzburger, Phy. Rev. B, 64, 50256, 2001

    Article  Google Scholar 

  15. Q. Du, Math Comp, 67 965 (1997).

    Article  Google Scholar 

  16. Q. Du, P. Gray, SI AM Appl Math, 56, 1060 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  17. Q. Du, M.D. Gunzburger and J.S. Peterson, SIAM Review, 34, 54 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  18. Q. Du, M.D. Gunzburger and J.S. Peterson, Phys. Rev. B, 46, 9027 (1992);

    Article  Google Scholar 

  19. Q. Du, M.D. Gunzburger and J.S. Peterson, Phys. Rev. B, 51, 16194 (1995).

    Article  Google Scholar 

  20. Q. Du, R. Nicolaides and X. Wu, SIAM Numer Anal, 35, 1049 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  21. D.L.Feder, C.W.Clark and B.I.Schneider, Phys. Rev. A, 61 011601(R) (1999).

    Article  Google Scholar 

  22. D.L.Feder, C.W.Clark and B.I.Schneider, Phys. Rev. Lett., 82, 4956 (1999).

    Article  Google Scholar 

  23. K. Feng, J. Comput. Math, 4, 279 (1986).

    MathSciNet  MATH  Google Scholar 

  24. A.L.Fetter and D.L.Feder, Phys. Rev. A, 58, 3185 (1998).

    Article  Google Scholar 

  25. A.L.Fetter, Phys. Rev A, 148,429 (1965).

    MathSciNet  Google Scholar 

  26. A.L.Fetter and A.A.Svidzinsky, cond-mat/0102003.

    Google Scholar 

  27. J. Hong and M. Qin, CCAST-WL reading 6 1 (2001)

    Google Scholar 

  28. R. Kellog, Math Comp, 23, 23 (1969)

    Article  MathSciNet  Google Scholar 

  29. R. Klein and A.J. Majda, Physica D., 53 267 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  30. F. Lin, Q. Du, SIAM Math Anal, 28, 1265 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  31. [31 ] K.W. Madison, F. Chevy, W. Wohlleben and J. Dalibard, Phys. Rev. Lett., 84, 806 (2000).

    Article  Google Scholar 

  32. K.W. Madison, F. Chevy, W. Wohlleben and J. Dalibard, J.Mod.Opt., 47, 2715 (2000).

    Google Scholar 

  33. J. Marsden G. Patrick and S. Shkoller, Comm. Math Phys 199 351 (1999).

    MathSciNet  Google Scholar 

  34. M.R.Matthews et al. Phys. Rev. Lett., 83, 2498 (1999).

    Article  Google Scholar 

  35. R. Onofrio et al. Phys. Rev. Lett., 85, 2228 (2000).

    Article  Google Scholar 

  36. D. Peaceman and H. Rachford, J. Soc. Ind. Appl. Math., 3, 28 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  37. J.S.Stiessberger and W.Zwerger, PRA 62 061601 (2000).

    Article  Google Scholar 

  38. A.A.Svidzinsky and A.L.Fetter, Phys. Rev. Lett., 84, 5919 (2000).

    Article  Google Scholar 

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Du, Q. (2002). Numerical Computation of Quantized Vortices in the Bose-Einstein Condensate. In: Chan, T.F., Huang, Y., Tang, T., Xu, J., Ying, LA. (eds) Recent Progress in Computational and Applied PDES. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0113-8_11

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  • DOI: https://doi.org/10.1007/978-1-4615-0113-8_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-4929-7

  • Online ISBN: 978-1-4615-0113-8

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