Advertisement

International Journal of Theoretical Physics

, Volume 52, Issue 10, pp 3662–3675 | Cite as

Exact Spin Coherent State Path Integral for a Damped Two-Level Atom in an Electromagnetic Wave

  • Farida Halimi
  • Mekki Aouachria
Article

Abstract

The spin coherent state path integral describing the dynamics of a two-level system interacting with electromagnetic wave of circular polarization is considered. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar and azimuthal directions. Then it is determined exactly using a simple transformations. Thus, the exact energy spectra with corresponding wave functions are deduced.

Keywords

Path integral Propagator Spin coherent state Two level system 

Notes

Acknowledgements

This work was supported by PNR research project 8/u05/4094 N0 31/13.

References

  1. 1.
    Grosche, C., Steiner, F.: Handbook of Feynman Path Integrals. Springer, Berlin (1998) MATHGoogle Scholar
  2. 2.
    Rabi, I.I.: Phys. Rev. 51, 652 (1936) ADSCrossRefGoogle Scholar
  3. 3.
    Tahmasebi, M.J., Sobouti, Y.: Mod. Phys. Lett. B 5, 1919–1925 (1991) MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Tahmasebi, M.J., Sobouti, Y.: Mod. Phys. Lett. B 6, 1255 (1991) MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    Lämmerzahl, C., Bordé, C.J.: Phys. Lett. A 203, 59 (1995) ADSCrossRefGoogle Scholar
  6. 6.
    Qiong-Gui, L.: Phys. Lett. A 342, 67 (2005) ADSCrossRefGoogle Scholar
  7. 7.
    Calvo, M., Codriansky, S.: J. Math. Phys. 24, 553 (1983) MathSciNetADSCrossRefMATHGoogle Scholar
  8. 8.
    Barut, A.O., Beker, H.: Europhys. Lett. 14, 197 (1991) MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    Mijatović, M., Ivanovski, C., Veljanoski, B., Trenčevski, K.: Z. Phys. A 345, 65 (1993) ADSCrossRefGoogle Scholar
  10. 10.
    Codriansky, S., Cordero, P., Salamo, S.: Z. Phys. A 353, 341 (1995) ADSCrossRefGoogle Scholar
  11. 11.
    Boudjedaa, T., Bounames, A., Nouicer, Kh., Chetouani, L., Hammann, T.F.: J. Math. Phys. 36, 1602 (1995) MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Boudjedaa, T., Bounames, A., Nouicer, Kh., Chetouani, L., Hammann, T.F.: Phys. Scr. 54, 225 (1996) MathSciNetADSCrossRefMATHGoogle Scholar
  13. 13.
    Boudjedaa, T., Bounames, A., Nouicer, Kh., Chetouani, L., Hammann, T.F.: Phys. Scr. 56, 545 (1998) ADSCrossRefGoogle Scholar
  14. 14.
    Merdaci, A., Boudjedaa, T., Chetouani, L.: Phys. Scr. 64, 15 (2001) ADSCrossRefMATHGoogle Scholar
  15. 15.
    Merdaci, A., Boudjedaa, T., Chetouani, L.: Czechoslov. J. Phys. 51, 865 (2001) MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Merdaci, A., Boudjedaa, T., Chetouani, L.: Eur. Phys. J. C 22, 585 (2001) ADSCrossRefMATHGoogle Scholar
  17. 17.
    Nouicer, Kh., Chetouani, L.: Phys. Lett. A 281, 218 (2001) MathSciNetADSCrossRefMATHGoogle Scholar
  18. 18.
    Aouachria, M., Chetouani, L.: Can. J. Phys. 87, 389 (2009) ADSGoogle Scholar
  19. 19.
    Alscher, A., Grabert, H.: J. Phys. A 32, 4907 (1999) MathSciNetADSCrossRefMATHGoogle Scholar
  20. 20.
    Alscher, A., Grabert, H.: Eur. Phys. J. D 14, 127 (2001) ADSCrossRefGoogle Scholar
  21. 21.
    Aouachria, M.: Can. J. Phys. 89, 1141 (2011) ADSGoogle Scholar
  22. 22.
    Aouachria, M.: J. Korean Phys. Soc. 58, 689 (2011) CrossRefGoogle Scholar
  23. 23.
    Aouachria, M.: Chin. J. Phys. 49, 689 (2011) Google Scholar
  24. 24.
    Aouachria, M., Rekik, R.: AIP Conf. Proc. 1444, 265 (2012) ADSCrossRefGoogle Scholar
  25. 25.
    Zeng, G.J., Zhou, S.L., Ao, S.M., Zeng, Z.Y.: Phys. Rev. A 55, 2945 (1997) ADSCrossRefGoogle Scholar
  26. 26.
    Zeng, Z.Y., Zeng, G.J., Kuang, L.M., Zhang, L.D.: Phys. Lett. A 261, 316 (1999) ADSCrossRefGoogle Scholar
  27. 27.
    Aouachria, M., Chetouani, L.: Eur. Phys. J. C 25, 333 (2002) ADSCrossRefMATHGoogle Scholar
  28. 28.
    Aouachria, M., Chetouani, L.: Chin. J. Phys. 40, 496 (2002) Google Scholar
  29. 29.
    Klauder, J.R.: Ann. Phys. 11, 123 (1960) MathSciNetADSCrossRefMATHGoogle Scholar
  30. 30.
    Klauder, J.R., Skagerstam, B.S.: Coherent States Application in Physics and Mathematical Physics. World Scientific, Singapore (1985) CrossRefGoogle Scholar
  31. 31.
    Ohnuki, Y., Kashiwa, T.: Prog. Theor. Phys. 60, 548 (1978) MathSciNetADSCrossRefMATHGoogle Scholar
  32. 32.
    Perelomov, A.M.: Commun. Math. Phys. 26, 22 (1972) MathSciNetCrossRefGoogle Scholar
  33. 33.
    Aouachria, M., Halimi, F.: J. Phys. Conf. Ser. 435, 012025 (2013) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Laboratoire de Physique Energétique Appliquée (LPEA), Département des Sciences de la Matière, Faculté des SciencesUniversité Hadj LakhdarBatnaAlgeria

Personalised recommendations