Advertisement

Algebraic solution and coherent states for the Dirac oscillator interacting with a topological defect

  • M. Salazar-RamírezEmail author
  • D. Ojeda-Guillén
  • A. Morales-González
  • V. H. García-Ortega
Regular Article
  • 47 Downloads

Abstract.

In this work we study and exactly solve the Dirac oscillator interacting with three different topological defects, namely the cosmic string spacetime (\(\Lambda_{\mp}\)), the magnetic cosmic string spacetime (\( \Theta_{\mp}\)) and the cosmic dislocation spacetime (\( \Pi_{\mp}\)). Moreover, we show that the radial part of this problem possesses an SU(1, 1) symmetry. Then, we obtain the wave functions and their respective energy spectrum by means of the Schrödinger factorization. Finally, we compute the radial coherent states and their time evolution in a general form for each topological defect.

References

  1. 1.
    E. Copeland, D. Haws, S. Holbraad, R. Rivers, Nucl. Phys. B 319, 687 (1989)ADSCrossRefGoogle Scholar
  2. 2.
    A. Vilenkin, E.P.S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, 2000)Google Scholar
  3. 3.
    A.C. Davis, R. Brandenberger, Formation and Interaction of Topological Defects, in NATO Advanced Study of Institute, Series B: Physics, Vol. 349 (Plenum, New York, 1995)Google Scholar
  4. 4.
    D. Ito, K. Mori, E. Carrieri, Nuovo Cimento A 51, 1119 (1967)ADSCrossRefGoogle Scholar
  5. 5.
    P.A. Cook, Lett. Nuovo Cimento 1, 419 (1971)CrossRefGoogle Scholar
  6. 6.
    M. Moshinsky, A. Szczepaniak, J. Phys. A 22, L817 (1989)ADSCrossRefGoogle Scholar
  7. 7.
    C. Quesne, M. Moshinsky, J. Phys. A 23, 2263 (1990)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    J. Carvalho, C. Furtado, F. Moraes, Phys. Rev. A 84, 032109 (2011)ADSCrossRefGoogle Scholar
  9. 9.
    K. Bakke, Eur. Phys. J. Plus 127, 82 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    K. Bakke, C. Furtado, Ann. Phys. (NY) 336, 489 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    K. Bakke, Gen. Relativ. Gravit. 45, 1847 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    F.M. Andrade, E.O. Silva, Eur. Phys. J. C 74, 3187 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    O. Yeşiltaş, Eur. Phys. J. Plus 130, 128 (2015)CrossRefGoogle Scholar
  14. 14.
    M. Salazar-Ramírez, D. Ojeda-Guillén, R.D. Mota, Ann. Phys. 372, 283 (2016)ADSCrossRefGoogle Scholar
  15. 15.
    J. Carvalho, A.M. de M. Carvalho, E. Cavalcante, C. Furtado, Eur. Phys. J. C 76, 365 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    J.A. Neto, M.J. Bueno, C. Furtado, Ann. Phys. 373, 273 (2016)ADSCrossRefGoogle Scholar
  17. 17.
    J.A. Neto, J.R. de S. Oliveira, C. Furtado, S. Sergeenkov, Eur. Phys. J. Plus 133, 185 (2018)CrossRefGoogle Scholar
  18. 18.
    L. Infeld, Phys. Rev. 59, 737 (1941)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    L. Infeld, T.E. Hull, Rev. Mod. Phys. 23, 21 (1951)ADSCrossRefGoogle Scholar
  20. 20.
    A. Andrianov, N. Borisov, M. Ioffe, Phys. Lett. A 105, 19 (1984)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    V. Spiridonov, L. Vinet, A. Zhedanov, Lett. Math. Phys. 29, 63 (1993)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    M. Salazar-Ramírez, D. Martínez, R.D. Mota, V.D. Granados, EPL 95, 60002 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    M. Salazar-Ramírez, D. Ojeda-Guillén, R.D. Mota, V.D. Granados, Eur. Phys. J. Plus 132, 39 (2017)CrossRefGoogle Scholar
  24. 24.
    E. Schrödinger, Naturwissenschaften 14, 664 (1926)ADSCrossRefGoogle Scholar
  25. 25.
    R.J. Glauber, Phys. Rev. 130, 2529 (1963)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    J.R. Klauder, Ann. Phys. 11, 123 (1960)ADSCrossRefGoogle Scholar
  27. 27.
    J.R. Klauder, J. Math. Phys. 4, 1055 (1963)ADSCrossRefGoogle Scholar
  28. 28.
    E.C.G. Sudarshan, Phys. Rev. Lett. 10, 227 (1963)ADSCrossRefGoogle Scholar
  29. 29.
    N.N. Lebedev, Special Functions and their Applications (Dover Publications, New York, 1972)Google Scholar
  30. 30.
    A.M. Perelomov, Generalized Coherent States and Their Applications (Springer-Verlag, Berlin, 1986)Google Scholar
  31. 31.
    C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics (Wiley-VCH, Berlin, 1977)Google Scholar
  32. 32.
    Y. Gur, A. Mann, Phys. At. Nucl. 68, 1700 (2005)CrossRefGoogle Scholar
  33. 33.
    C.C. Gerry, J. Kiefer, Phys. Rev. A 37, 665 (1988)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    M. Salazar-Ramírez, D. Ojeda-Guillén, R.D. Mota, J. Math. Phys. 57, 021704 (2016)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    D.V. Gal'tsov, P.S. Letelier, Phys. Rev. D 47, 4273 (1993)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    D. Ojeda-Guillén, R.D. Mota, V.D. Granados, J. Math. Phys. 57, 062104 (2016)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    E. Choreño, D. Ojeda-Guillén, M. Salazar-Ramírez, V.D. Granados, Ann. Phys. 387, 121 (2017)ADSCrossRefGoogle Scholar
  38. 38.
    D. Loss, D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998)ADSCrossRefGoogle Scholar
  39. 39.
    H. Jeong, M.S. Kim, Phys. Rev. A 65, 042305 (2002)ADSCrossRefGoogle Scholar
  40. 40.
    T.C. Ralph, A. Gilchrist, G.J. Milburn, W.J. Munro, S. Glancy, Phys. Rev. A 68, 042319 (2003)ADSCrossRefGoogle Scholar
  41. 41.
    A. Vourdas, Phys Rev. A 41, 1653 (1990)ADSCrossRefGoogle Scholar
  42. 42.
    B.G. Adams, Algebraic Approach to Simple Quantum Systems (Springer, Berlin, 1994)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • M. Salazar-Ramírez
    • 1
    Email author
  • D. Ojeda-Guillén
    • 1
  • A. Morales-González
    • 1
  • V. H. García-Ortega
    • 1
  1. 1.Escuela Superior de Cómputo, Instituto Politécnico NacionalAv. Juan de Dios Bátiz esq. Av. Miguel Othón de Mendizábal, Col. Lindavista, Delegación Gustavo A. MaderoCiudad de MéxicoMexico

Personalised recommendations