International Journal of Theoretical Physics

, Volume 54, Issue 11, pp 4054–4067 | Cite as

Supersymmetric Model of a Bose-Einstein Condensate in a 𝓟𝓣-Symmetric Double-delta Trap

Article

Abstract

The most important properties of a Bose-Einstein condensate subject to balanced gain and loss can be modelled by a Gross-Pitaevskii equation with an external 𝓟𝓣-symmetric double-delta potential. We study its linear variant with a supersymmetric extension. It is shown that both in the 𝓟𝓣-symmetric as well as in the 𝓟𝓣-broken phase arbitrary stationary states can be removed in a supersymmetric partner potential without changing the energy eigenvalues of the other state. The characteristic structure of the singular delta potential in the supersymmetry formalism is discussed, and the applicability of the formalism to the nonlinear Gross-Pitaevskii equation is analysed. In the latter case the formalism could be used to remove 𝓟𝓣-broken states introducing an instability to the stationary 𝓟𝓣-symmetric states.

Keywords

𝓟𝓣 symmetry Supersymmetry Double-delta potential Stationary states 

References

  1. 1.
    Klaiman, S., Günther, U., Moiseyev, N.: Phys. Rev. Lett. 101, 080402 (2008)MathSciNetCrossRefADSGoogle Scholar
  2. 2.
    Dast, D., Haag, D., Cartarius, H., Wunner, G., Eichler, R., Main, J.: Fortschr. Phys. 61, 124 (2013)CrossRefGoogle Scholar
  3. 3.
    Graefe, E.M., Korsch, H.J., Niederle, A.E.: Phys. Rev. Lett. 101, 150408 (2008)CrossRefADSGoogle Scholar
  4. 4.
    Bender, C.M., Boettcher, S.: Phys. Rev. Lett. 80, 5243 (1998)MATHMathSciNetCrossRefADSGoogle Scholar
  5. 5.
    Dast, D., Haag, D., Cartarius, H., Main, J., Wunner, G.: J. Phys. A 46, 375301 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ramezani, H., Kottos, T., El-Ganainy, R., Christodoulides, D.N.: Phys. Rev. A 82, 043803 (2010)CrossRefADSGoogle Scholar
  7. 7.
    Musslimani, Z., Makris, K.G., El-Ganainy, R., Christodoulides, D.N.: Phys. Rev. Lett. 100, 30402 (2008)CrossRefADSGoogle Scholar
  8. 8.
    Driben, R., Malomed, B.A.: Opt. Lett. 36, 4323 (2011)CrossRefADSGoogle Scholar
  9. 9.
    Bludov, Y.V., Konotop, V.V., Malomed, B.A.: Phys. Rev. A 87, 013816 (2013)CrossRefADSGoogle Scholar
  10. 10.
    Haag, D., Dast, D., Löhle, A., Cartarius, H., Main, J., Wunner, G.: Phys. Rev. A 89, 023601 (2014)CrossRefADSGoogle Scholar
  11. 11.
    Löhle, A., Cartarius, H., Haag, D., Dast, D., Main, J., Wunner, G.: Acta Polytechnica 54, 133 (2014)CrossRefGoogle Scholar
  12. 12.
    Gelfand, Y.A., Likhtman, E.P.: JETP Lett. 13, 323 (1971)ADSGoogle Scholar
  13. 13.
    Neveu, A., Schwarz, J.H.: Nucl. Phys. B 31, 86 (1971)CrossRefADSGoogle Scholar
  14. 14.
    Ramond, P.: Phys. Rev. D 3, 2415 (1971)MathSciNetCrossRefADSGoogle Scholar
  15. 15.
    Nicolai, H.: J. Phys. A 9, 1497 (1976)MathSciNetCrossRefADSGoogle Scholar
  16. 16.
    Witten, E.: Nucl. Phys. B 188, 513 (1981)MATHCrossRefADSGoogle Scholar
  17. 17.
    Witten, E.: Nucl. Phys. B. 202, 253 (1982)CrossRefADSGoogle Scholar
  18. 18.
    Znojil, M., Cannata, F., Bagchi, B., Roychoudhury, R.: Phys. Lett. B 483, 284 (2000)MATHMathSciNetCrossRefADSGoogle Scholar
  19. 19.
    Znojil, M.: J. Phys. A 35, 2341 (2002)MATHMathSciNetCrossRefADSGoogle Scholar
  20. 20.
    Lévai, G., Znojil, M.: J. Phys. A 35, 8793 (2002)MATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Bazeia, D., Das, A., Greenwood, L., Losano, L.: Phys. Lett. B 673, 283 (2009)MathSciNetCrossRefADSGoogle Scholar
  22. 22.
    Abhinav, K., Panigrahi, P.K.: Ann. Phys. 325, 1198 (2010)MATHMathSciNetCrossRefADSGoogle Scholar
  23. 23.
    Lévai, G.: J. Phys. A 37, 10179 (2004)MATHMathSciNetCrossRefGoogle Scholar
  24. 24.
    Bagchi, B., Roychoudhury, R.: J. Phys. A 33, L1 (2000)MATHMathSciNetCrossRefADSGoogle Scholar
  25. 25.
    Midya, B.: Phys. Rev. A. 89, 032116 (2014)CrossRefADSGoogle Scholar
  26. 26.
    Miri, M.A., Heinrich, M., El-Ganainy, R., Christodoulides, D.N.: Phys. Rev. Lett. 110, 233902 (2013)CrossRefADSGoogle Scholar
  27. 27.
    Miri, M.A., Heinrich, M., Christodoulides, D.N.: Phys. Rev. A 87, 043819 (2013)CrossRefADSGoogle Scholar
  28. 28.
    Cartarius, H., Wunner, G.: Phys. Rev. A 86, 013612 (2012)CrossRefADSGoogle Scholar
  29. 29.
    Cartarius, H., Haag, D., Dast, D., Wunner, G.: J. Phys. A 45, 444008 (2012)MathSciNetCrossRefADSGoogle Scholar
  30. 30.
    Jakubský, V., Znojil, M.: Czech. J. Phys. 55, 1113 (2005)CrossRefADSGoogle Scholar
  31. 31.
    Mehri-Dehnavi, H., Mostafazadeh, A., Batal, A.: J. Phys. A 145301, 43 (2010)MathSciNetGoogle Scholar
  32. 32.
    Jones, H.F.: Phys. Rev. D. 78, 065032 (2008)CrossRefADSGoogle Scholar
  33. 33.
    Mayteevarunyoo, T., Malomed, B.A., Dong, G.: Phys. Rev. A 053601, 78 (2008)Google Scholar
  34. 34.
    Rapedius, K., Korsch, H.J.: J. Phys. B 42, 044005 (2009)MathSciNetCrossRefADSGoogle Scholar
  35. 35.
    Fassari, S., Rinaldi, F.: Rep. Math. Phys. 69, 353 (2012)MATHMathSciNetCrossRefADSGoogle Scholar
  36. 36.
    Uchino, T., Tsutsui, I.: Nucl. Phys. B 662, 447 (2003)MATHMathSciNetCrossRefADSGoogle Scholar
  37. 37.
    Correa, F., Nieto, L.M., Plyushchay, M.S.: Phys. Lett. B 659, 746 (2008)MATHMathSciNetCrossRefADSGoogle Scholar
  38. 38.
    Fernández, D.J., Gadella, C.M., Nieto, L.M.: SIGMA 7, 29 (2011)Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institut für Theoretische Physik 1Universität StuttgartStuttgartGermany

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