Advertisement

Few-Body Systems

, 58:1 | Cite as

Quantum Effects on an Atom with a Magnetic Quadrupole Moment in a Region with a Time-Dependent Magnetic Field

  • I. C. Fonseca
  • K. Bakke
Article

Abstract

The quantum description of an atom with a magnetic quadrupole moment in the presence of a time-dependent magnetic field is analysed. It is shown that the time-dependent magnetic field induces an electric field that interacts with the magnetic quadrupole moment of the atom and gives rise to a Landau-type quantization. It is also shown that a time-independent Schrödinger equation can be obtained, i.e., without existing the interaction between the magnetic quadrupole moment of the atom and the time-dependent magnetic field, therefore, the Schrödinger equation can be solved exactly. It is also analysed this system subject to scalar potentials.

References

  1. 1.
    Y. Aharonov, A. Casher, Phys. Rev. Lett. 53, 319 (1984)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    M. Ericsson, E. Sjöqvist, Phys. Rev. A 65, 013607 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    H. Wei, R. Han, X. Wei, Phys. Rev. Lett. 75, 2071 (1995)ADSCrossRefGoogle Scholar
  4. 4.
    C. Furtado, J.R. Nascimento, L.R. Ribeiro, Phys. Lett. A 358, 336 (2006)ADSCrossRefGoogle Scholar
  5. 5.
    X.-G. He, B. h. J. McKellar, J. McKellar Phys. Rev. A 47, 3424 (1983)Google Scholar
  6. 6.
    M. Wilkens, Phys. Rev. Lett. 72, 5 (1994)ADSCrossRefGoogle Scholar
  7. 7.
    K. Bakke, H. Belich, Spontaneous Lorentz Symmetry Violation and Low Energy Scenarios (LAMBERT Academic Publishing, Saarbrücken, 2015)zbMATHGoogle Scholar
  8. 8.
    L.R. Ribeiro, E. Passos, C. Furtado, J. Phys. G: Nucl. Part. Phys. 39, 105004 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    M.A. Ajaib, Int. J. Mod. Phys. A 27, 1250139 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    P.M. Parker, J. Chem. Phys. 24, 1096 (1956)ADSCrossRefGoogle Scholar
  11. 11.
    A.D. Buckingham, R.L. Disch, D.A. Dunmur, J. Am. Chem. Soc. 90, 3104 (1968)CrossRefGoogle Scholar
  12. 12.
    J.H. Williams, Acc. Chem. Res. 26, 593 (1993)CrossRefGoogle Scholar
  13. 13.
    G. Karl, J.D. Poll, J. Chem. Phys. 46, 2944 (1967)ADSCrossRefGoogle Scholar
  14. 14.
    P. Piecuch, V. Špirko, J. Paldus, J. Chem. Phys. 105, 11068 (1996)ADSCrossRefGoogle Scholar
  15. 15.
    N. Chetty, V.W. Couling, J. Chem. Phys. 134, 144307 (2011)ADSCrossRefGoogle Scholar
  16. 16.
    J.R.P. Angel, P.G.H. Sandars, G.K. Woodgate, J. Chem. Phys. 47, 1552 (1967)ADSCrossRefGoogle Scholar
  17. 17.
    J.-H. Choi, J.R. Guest, A.P. Povilus, E. Hansist, G. Raithel, Phys. Rev Lett. 95, 243001 (2005)ADSCrossRefGoogle Scholar
  18. 18.
    V.S. Athalye, A. Kumar, J. Chem. Phys. 122, 174302 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    C.-C. Chen, Phys. Rev. A 51, 2611 (1995)ADSCrossRefGoogle Scholar
  20. 20.
    I.C. Fonseca, K. Bakke, Ann. Phys (NY) 363, 253 (2015)ADSCrossRefGoogle Scholar
  21. 21.
    H. Nizamidin, A. Anwar, S. Dulat, K. Li, Front. Phys. 9, 446 (2014)CrossRefGoogle Scholar
  22. 22.
    E. Takács et al., Phys. Rev. A 54, 1342 (1996)ADSCrossRefGoogle Scholar
  23. 23.
    S. Majumder, B.P. Das, Phys. Rev. A 62, 042508 (2000)ADSCrossRefGoogle Scholar
  24. 24.
    U.I. Safronova et al., Phys. Rev. A 64, 012507 (2001)ADSCrossRefGoogle Scholar
  25. 25.
    V.V. Flambaum, I.B. Khriplovich, O.P. Sushkov, Sov. Phys. JETP 60, 873 (1984) [Zh. Eksp. Teor. Fiz. 87, 1521 (1984)]Google Scholar
  26. 26.
    D.E. Kharzeev, H.-U. Yee, I. Zahed, Phys. Rev. D. 84, 037503 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    I.C. Fonseca, K. Bakke, J. Chem. Phys. 144, 014308 (2016)ADSCrossRefGoogle Scholar
  28. 28.
    I.C. Fonseca, K. Bakke, Ann. Phys. (Berlin) 527, 820 (2015)ADSCrossRefGoogle Scholar
  29. 29.
    V.F. Dmitriev, I.B. Khriplovich, V.B. Telitsin, Phys. Rev. C 50, 2358 (1994)ADSCrossRefGoogle Scholar
  30. 30.
    H.S. Radt, R.P. Hurst, Phys. Rev. A 2, 696 (1970)ADSCrossRefGoogle Scholar
  31. 31.
    I.B. Khriplovich, Zh. Eksp. Teor. Fiz. 71, 51 (1976) [Sov. Phys. JETP 44, 25 (1976)]Google Scholar
  32. 32.
    O.P. Sushkov, V.V. Flambaum, I.B. Khriplovich, Zh. Eksp. Teor. Fiz. 87, 1521 (1984) [Sov. Phys. JETP 60, 873 (1984)]Google Scholar
  33. 33.
    V.F. Dmitriev, V.B. Telitsin, V.V. Flambaum, V.A. Dzuba, Phys. Rev. C 54, 3305 (1996)ADSCrossRefGoogle Scholar
  34. 34.
    I.C. Fonseca, K. Bakke, J. Math. Phys. 56, 062107 (2014)ADSCrossRefGoogle Scholar
  35. 35.
    I.C. Fonseca, K. Bakke, Proc. R. Soc. A 471, 20150362 (2015)ADSCrossRefGoogle Scholar
  36. 36.
    J. Griffiths, Introduction to Electrodynamics, 3rd edn. (Prentice Hall, New Jersey, 1999)Google Scholar
  37. 37.
    L.D. Landau, E.M. Lifshitz, Quantum Mechanics, the Nonrelativistic Theory, 3rd edn. (Pergamon, Oxford, 1977)zbMATHGoogle Scholar
  38. 38.
    M. Abramowitz, I.A. Stegum, Handbook of Mathematical Functions (Dover Publications Inc., New York, 1965)Google Scholar
  39. 39.
    L. Solimany, B. Kramer, Solid State Commun. 96, 471 (1995)ADSCrossRefGoogle Scholar
  40. 40.
    R. Rosas, R. Riera, J.L. Marín, J. Phys.: Condens. Matter 12, 6851 (2000)ADSGoogle Scholar
  41. 41.
    E. Tsitsishvili, G.S. Lozano, A.O. Gogolin, Phys. Rev. B 70, 115316 (2004)ADSCrossRefGoogle Scholar
  42. 42.
    N. Aquino, E. Castaño, E. Ley-Koo, Chin. J. Phys. 41, 276 (2003)Google Scholar
  43. 43.
    A.L. Silva Netto, C. Chesman, C. Furtado, Phys. Lett. A 372, 3894 (2008)ADSCrossRefGoogle Scholar
  44. 44.
    C. Furtado, C.A. de Lima Ribeiro, S. Azevedo, Phys. Lett. A 296, 171 (2002)ADSCrossRefGoogle Scholar
  45. 45.
    P. Gribi, E. Sigmund, Phys. Rev. B 44, 3537 (1991)ADSCrossRefGoogle Scholar
  46. 46.
    F. Gesztesy, B. Thallert, J. Phys. A: Math. Gen. 14, 639 (1981)ADSCrossRefGoogle Scholar
  47. 47.
    J.A. Reyes, M. del Castillo-Mussot, J. Phys. A: Math. Gen. 32, 2017 (1999)ADSCrossRefGoogle Scholar
  48. 48.
    Y. Ran, L. Xue, S. Hu, R.-K. Su, J. Phys. A: Math. Gen. 33, 9265 (2000)ADSCrossRefGoogle Scholar
  49. 49.
    Y. Chargui, A. Dhahbi, A. Trabelsi, Phys. Scr. 90, 015201 (2015)ADSCrossRefGoogle Scholar
  50. 50.
    S.M. Ikhdair, B.J. Falaye, M. Hamzavi, Ann. Phys. (NY) 353, 282 (2015)ADSCrossRefGoogle Scholar
  51. 51.
    I.I. Guseinov, B.A. Mamedov, J. Chem. Phys. 121, 1649 (2004)ADSCrossRefGoogle Scholar
  52. 52.
    I.I. Guseinov, J. Chem. Phys. 120, 9454 (2004)ADSCrossRefGoogle Scholar
  53. 53.
    S.M. Ikhdair, M. Hamzavi, Phys. B 407, 419 (2012)Google Scholar
  54. 54.
    S.M. Ikhdair, M. Hamzavi, Phys. B 407, 4797 (2012)ADSCrossRefGoogle Scholar
  55. 55.
    A.D. Alhaidari, Phys. Rev. A 66, 042116 (2002)ADSCrossRefGoogle Scholar
  56. 56.
    A.D. Alhaidari, Phys. Lett. A 322, 72 (2004)ADSMathSciNetCrossRefGoogle Scholar
  57. 57.
    J. Yu, S.-H. Dong, Phys. Lett. A 325, 194 (2004)ADSMathSciNetCrossRefGoogle Scholar
  58. 58.
    A. Kratzer, Z. Phys. 3, 289 (1920)ADSCrossRefGoogle Scholar
  59. 59.
    M.R. Setare, E. Karimi, Phys. Scr. 75, 90 (2007)ADSMathSciNetCrossRefGoogle Scholar
  60. 60.
    G. de A. Marques, V.B. Bezerra, Class. Quantum Grav. 19, 985 (2002)ADSCrossRefGoogle Scholar
  61. 61.
    H. Asada, T. Futamase, Phys. Rev. D 56, R6062 (1997)ADSCrossRefGoogle Scholar
  62. 62.
    C.L. Chrichfield, J. Math. Phys. 17, 261 (1976)ADSCrossRefGoogle Scholar
  63. 63.
    A. Verćin, Phys. Lett. B 260, 120 (1991)ADSMathSciNetCrossRefGoogle Scholar
  64. 64.
    J. Myrhein, E. Halvorsen, A. Verćin, Phys. Lett. B 278, 171 (1992)ADSCrossRefGoogle Scholar
  65. 65.
    E.R. Figueiredo Medeiros, E.R. Bezerra de Mello, Eur. Phys. J. C 72, 2051 (2012)ADSCrossRefGoogle Scholar
  66. 66.
    V.R. Khalilov, Phys. Rev. A 71, 012105 (2005)ADSCrossRefGoogle Scholar
  67. 67.
    H.W. Crater, J.-H. Yoon, C.-Y. Wong, Phys. Rev. D 79, 034011 (2009)ADSCrossRefGoogle Scholar
  68. 68.
    A. Ronveaux, Heun’s Differential Equations (Oxford University Press, Oxford, 1995)zbMATHGoogle Scholar
  69. 69.
    G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists, 6th edn. (Elsevier Academic Press, New York, 2005)zbMATHGoogle Scholar
  70. 70.
    D.J. Griffiths, Introduction to Quantum Mechanics, Second Edition edn. (Prentice Hall, New Jersey, 2004)Google Scholar
  71. 71.
    E.J. Austin, Mol. Phys. 40, 893 (1980)ADSCrossRefGoogle Scholar
  72. 72.
    E.R. Vrscay, Phys. Rev. A 31, 2054 (1985)ADSMathSciNetCrossRefGoogle Scholar
  73. 73.
    K. Killingbeck, Rep. Prog. Phys. 40, 963 (1977)ADSCrossRefGoogle Scholar
  74. 74.
    K. Killingbeck, Phys. Lett. A 65, 87 (1978)ADSMathSciNetCrossRefGoogle Scholar
  75. 75.
    R.P. Saxena, V.S. Varma, J. Phys. A: Math. Gen. 15, L149 (1982)ADSCrossRefGoogle Scholar
  76. 76.
    E. Castro, P. Martín, J. Phys. A: Math. Gen. 33, 5321 (2000)ADSCrossRefGoogle Scholar
  77. 77.
    M.K. Bahar, F. Yasuk, Adv. High Energy Phys. 2013, 814985 (2013)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidade Federal da ParaíbaJoão PessoaBrazil

Personalised recommendations