Semiclassical Analysis of the Interaction of the Magnetic Quadrupole Moment of a Neutral Particle with Axial Electric Fields in a Uniformly Rotating Frame

Abstract

By exploring the hypothesis of magnetic monopoles, we consider the existence of electric fields produced by magnetic current densities. Then, we consider a uniformly rotating frame with the purpose of searching for effects of rotation on the interaction of axial electric fields with the magnetic quadrupole moment of a neutral particle. Our analysis is made through the WKB (Wentzel, Kramers and Brillouin) approximation. Therefore, by applying the WKB approximation, we search for bound state solutions to the Schrödinger equation in two particular cases.

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References

  1. 1.

    Castelnovo, C., Moessner, R., Sondhi, S.L.: Magnetic monopoles in spin ice. Nature 451, 42–45 (2008)

    ADS  Article  Google Scholar 

  2. 2.

    Kadowaki, H., et al.: Observation of magnetic monopoles in spin ice. J. Phys. Soc. Jpn. 78, 103706 (2009)

    ADS  Article  Google Scholar 

  3. 3.

    Qi, X.-L., Li, R., Zang, J., Zhang, S.-C.: Inducing a magnetic monopole with topological surface states. Science 323, 1184–1187 (2009)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  4. 4.

    Cabrera, B.: First results from a superconductive detector for moving magnetic monopoles. Phys. Rev. Lett. 48, 1378–1381 (1982)

    ADS  Article  Google Scholar 

  5. 5.

    Tkachuk, V.M.: Quantum topological phase of an electric dipole circulating around a ferromagnetic wire. Phys. Rev. A 62, 052112 (2000)

    ADS  Article  Google Scholar 

  6. 6.

    Mól, L., et al.: Magnetic monopole and string excitations in two-dimensional spin ice. J. Appl. Phys. 106, 063913 (2009)

    ADS  Article  Google Scholar 

  7. 7.

    Mól, L., et al.: Conditions for free magnetic monopoles in nanoscale square arrays of dipolar spin ice. Phys. Rev. B 82, 054434 (2010)

    ADS  Article  Google Scholar 

  8. 8.

    Qi, X.-L., et al.: Seeing the magnetic monopole through the mirror of topological surface states. Science 323, 1184–1187 (2009)

    ADS  MathSciNet  Article  Google Scholar 

  9. 9.

    Ray, M.W., Ruokokoski, E., Kandel, S., Möttönen, M., Hall, D.S.: Observation of Dirac monopoles in a synthetic magnetic field. Nature 505, 657–660 (2014)

    ADS  Article  Google Scholar 

  10. 10.

    Dirac, P.A.M.: Quantised singularities in the electromagnetic field. Proc. R. Soc. A 133, 60–72 (1931)

    ADS  MATH  Google Scholar 

  11. 11.

    Hsu, J.P.: Exact magnetic monopole solutions in Yang–Mills and unified gauge theories. Found. Phys. 7, 801–812 (1977)

    ADS  MathSciNet  Article  Google Scholar 

  12. 12.

    ’t Hooft, G.: Magnetic monopoles in unified gauge theories. Nucl. Phys. B 79, 276–284 (1974)

    ADS  MathSciNet  Article  Google Scholar 

  13. 13.

    Polyakov, A.M.: Particle spectrum in quantum field theory. JETP Lett. 20, 194–195 (1974)

    ADS  Google Scholar 

  14. 14.

    Scott, D.M.: Monopoles in a grand unified theory based on SU(5). Nucl. Phys. B 171, 95–108 (1980)

    ADS  Article  Google Scholar 

  15. 15.

    Preskill, J.: Magnetic monopoles. Annu. Rev. Nucl. Part. Sci. 34, 461–530 (1984)

    ADS  Article  Google Scholar 

  16. 16.

    Dowling, J.P., Williams, C., Franson, J.D.: Maxwell duality, Lorentz invariance, and topological phase. Phys. Rev. Lett. 83, 2486–2489 (1999)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  17. 17.

    Furtado, C., Duarte, G.: Dual Aharonov–Bohm Effect. Phys. Scrip. 71, 7–11 (2005)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  18. 18.

    Griffiths, D.J.: Introduction to Electrodynamics, 3rd edn. Prentice Hall, Upper Saddle River (1999)

    Google Scholar 

  19. 19.

    Barraz Junior, N.M., et al.: Dirac-like monopoles in a Lorentz-and CPT-violating electrodynamics. Phys. Rev. D 76, 027701 (2007)

    ADS  Article  Google Scholar 

  20. 20.

    He, X.-G., McKellar, B.H.J.: Topological phase due to electric dipole moment and magnetic monopole interaction. Phys. Rev. A 47, 3424–3425 (1983)

    ADS  Article  Google Scholar 

  21. 21.

    Wilkens, M.: Quantum phaseof a moving dipole. Phys. Rev. Lett. 72, 5 (1994)

    ADS  Article  Google Scholar 

  22. 22.

    Fonseca, I.C., Bakke, K.: Aharonov–Anandan quantum phases and Landau quantization associated with a magnetic quadrupole moment. Ann. Phys. (NY) 363, 253–261 (2015)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  23. 23.

    De Roeck, A., et al.: Sensitivity of LHC experiments to exotic highly ionising particles. Eur. Phys. J. C 72, 1985 (2012)

    ADS  Article  Google Scholar 

  24. 24.

    MoEDAL Collaboration: The physics programme of the MoEDAL experiment at the LHC. Int. J. Mod. Phys. A 29, 1430050 (2014)

  25. 25.

    Aad, G., et al.: (ATLAS Collaboration), Search for magnetic monopoles in \(\sqrt{s}=7\) TeV \(pp\) collisions with the ATLAS detector. Phys. Rev. Lett. 109, 261803 (2012)

    ADS  Article  Google Scholar 

  26. 26.

    Aad, G., et al.: (ATLAS Collaboration), Search for magnetic monopoles and stable particles with high electric charges in 8 TeV \(pp\) collisions with the ATLAS detector. Phys. Rev. D 93, 052009 (2016)

    ADS  Article  Google Scholar 

  27. 27.

    Acharya, B., et al. (MoEDAL Collaboration), J. High Energy Phys. 2016, 67 (2016)

  28. 28.

    Acharya, B., et al.: (MoEDAL Collaboration), Search for magnetic monopoles with the MoEDAL forward trapping detector in \(2.11\,\text{ fb }^{-1}\) of 13 TeV proton-proton collisions at the LHC. Phys. Lett. B 782, 510–516 (2018)

    ADS  Article  Google Scholar 

  29. 29.

    Acharya, B., et al.: (MoEDAL Collaboration), Magnetic monopole search with the full MoEDAL trapping detector in 13 TeV \(\bar{pp}\) collisions interpreted in photon-fusion and Drell–Yan production. Phys. Rev. Lett. 123, 021802 (2019)

  30. 30.

    Cabrera, B., Trower, W.P.: Magnetic monopoles: evidence since the Dirac conjectur. Found. Phys. 13, 195–215 (1983)

    ADS  Article  Google Scholar 

  31. 31.

    Chen, C.-C.: Topological quantum phase and multipole moment of neutral particles. Phys. Rev. A 51, 2611 (1995)

    ADS  MathSciNet  Article  Google Scholar 

  32. 32.

    Vieira, S.L.R., Bakke, K.: Maxwell duality and semiclassical analysis of the interaction of the magnetic quadrupole moment of a neutral particle with external fields. J. Math. Phys. 60, 102104 (2019)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  33. 33.

    Griffiths, D.J.: Introduction to Quantum Mechanics, 2nd edn. Prentice Hall, Boca Raton (2004)

    Google Scholar 

  34. 34.

    Williams, J.H.: The molecular electric quadrupole moment and solid-state architecture. Acc. Chem. Res. 26, 593–598 (1993)

    Article  Google Scholar 

  35. 35.

    Piecuch, P., \(\check{\text{ S }}\)pirko, V., Paldus, J.: Molecular quadrupole moment function of ammonia, J. Chem. Phys. 105, 11068 (1996)

  36. 36.

    Chetty, N., Couling, V.W.: Measurement of the electric quadrupole moment of N2O. J. Chem. Phys. 134, 144307 (2011)

    ADS  Article  Google Scholar 

  37. 37.

    Angel, J.R.P., Sandars, P.G.H., Woodgate, G.K.: Direct measurement of an atomic quadrupole moment. J. Chem. Phys. 47, 1552 (1967)

    ADS  Article  Google Scholar 

  38. 38.

    Choi, J.-H., Guest, J.R., Povilus, A.P., Hansist, E., Raithel, G.: Magnetic trapping of long-lived cold Rydberg atoms. Phys. Rev. Lett. 95, 243001 (2005)

    ADS  Article  Google Scholar 

  39. 39.

    Takács, E., et al.: Polarization measurements on a magnetic quadrupole line in Ne-like barium. Phys. Rev. A 54, 1342 (1996)

    ADS  Article  Google Scholar 

  40. 40.

    Majumder, S., Das, B.P.: Relativistic magnetic quadrupole transitions in Be-like ions. Phys. Rev. A 62, 042508 (2000)

    ADS  Article  Google Scholar 

  41. 41.

    Safronova, U.I., et al.: Electric-dipole, electric-quadrupole, magnetic-dipole, and magnetic-quadrupole transitions in the neon isoelectronic sequence. Phys. Rev. A 64, 012507 (2001)

    ADS  Article  Google Scholar 

  42. 42.

    Flambaum, V.V., Khriplovich, I.B., Sushkov, O.P.: Possibility of investigating \(P\)- and \(T\)-odd nuclear forces in atomic and molecular experiments. Sov. Phys. JETP 60, 873 (1984)

    Google Scholar 

  43. 43.

    Flambaum, V.V., Khriplovich, I.B., Sushkov, O.P.: Possibility of investigating \(P\)- and \(T\)-odd nuclear forces in atomic and molecular experiments. Zh. Eksp. Teor. Fiz. 87, 1521 (1984)

    Google Scholar 

  44. 44.

    Nizamidin, H., Anwar, A., Dulat, S., Li, K.: Quantum phase for an electric quadrupole moment in noncommutative quantum mechanics. Front. Phys. 9, 446–450 (2014)

    ADS  Article  Google Scholar 

  45. 45.

    Kharzeev, D.E., Yee, H.-U., Zahed, I.: Anomaly-induced quadrupole moment of the neutron in magnetic field. Phys. Rev. D. 84, 037503 (2011)

    ADS  Article  Google Scholar 

  46. 46.

    Khriplovich, I.B.: Parity Nonconseroation in Atomic Phenomena. Gordon and Breach, London (1991)

    Google Scholar 

  47. 47.

    Flambaum, V.V.: Spin hedgehog and collective magnetic quadrupole moments induced by parity and time invariance violating interaction. Phys. Lett. B 320, 211–215 (1994)

    ADS  Article  Google Scholar 

  48. 48.

    Flambaum, V.V., DeMille, D., Kozlov, M.G.: Time-reversal symmetry violation in molecules induced by nuclear magnetic quadrupole moments. Phys. Rev. Lett. 113, 103003 (2014)

    ADS  Article  Google Scholar 

  49. 49.

    Dmitriev, V.F., Khriplovich, I.B., Telitsin, V.B.: Nuclear magnetic quadrupole moments in the single-particle approximation. Phys. Rev. C 50, 2358 (1994)

    ADS  Article  Google Scholar 

  50. 50.

    Radt, H.S., Hurst, R.P.: Magnetic quadrupole polarizability of closed-shell atoms. Phys. Rev. A 2, 696 (1970)

    ADS  Article  Google Scholar 

  51. 51.

    Fonseca, I.C., Bakke, K.: Quantum aspects of a moving magnetic quadrupole moment interacting with an electric field. J. Math. Phys. 56, 062107 (2014)

    ADS  MATH  Article  Google Scholar 

  52. 52.

    Mashhoon, B.: Neutron interferometry in a rotating frame of reference. Phys. Rev. Lett. 61, 2639 (1988)

    ADS  Article  Google Scholar 

  53. 53.

    Aharonov, Y., Carmi, G.: Quantum aspects of the equivalence principle. Found. Phys. 3, 493–498 (1973)

    ADS  Article  Google Scholar 

  54. 54.

    Page, L.A.: Effect of Earth’s rotation in neutron interferometry. Phys. Rev. Lett. 35, 543 (1975)

    ADS  Article  Google Scholar 

  55. 55.

    Werner, S.A., Staudenmann, J.-L., Colella, R.: Effect of Earth’s rotation on the quantum mechanical phase of the neutron. Phys. Rev. Lett. 42, 1103 (1979)

    ADS  Article  Google Scholar 

  56. 56.

    Hehl, F.W., Ni, W.-T.: Inertial effects of a Dirac particle. Phys. Rev. D 42, 2045 (1990)

    ADS  Article  Google Scholar 

  57. 57.

    Lu, L.-H., Li, Y.-Q.: Effects of an optically induced non-Abelian gauge field in cold atoms. Phys. Rev. A 76, 023410 (2007)

    ADS  Article  Google Scholar 

  58. 58.

    Fischer, U.R., Schopohl, N.: Hall state quantization in a rotating frame. Europhys. Lett. 54, 502–507 (2001)

    ADS  Article  Google Scholar 

  59. 59.

    Shen, J.Q., He, S.L.: Geometric phases of electrons due to spin-rotation coupling in rotating C60 molecules. Phys. Rev. B 68, 195421 (2003)

    ADS  Article  Google Scholar 

  60. 60.

    Shen, J.Q., He, S., Zhuang, F.: Aharonov–Carmi effect and energy shift of valence electrons in rotating C60 molecules. Eur. Phys. J. D 33, 35–38 (2005)

    ADS  Article  Google Scholar 

  61. 61.

    Merlin, R.: Rotational anomalies of mesoscopic rings. Phys. Lett. A 181, 421–423 (1993)

    ADS  Article  Google Scholar 

  62. 62.

    Vignale, G., Mashhoon, B.: Persistent current in a rotating mesoscopic ring. Phys. Lett. A 197, 444–448 (1995)

    ADS  Article  Google Scholar 

  63. 63.

    Dantas, L., Furtado, C., Silva Netto, A.L.: Quantum ring in a rotating frame in the presence of a topological defect. Phys. Lett. A 379, 11–15 (2015)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  64. 64.

    Matsuo, M., Ieda, J., Saitoh, E., Maekawa, S.: Effects of mechanical rotation on spin currents. Phys. Rev. Lett. 106, 076601 (2011)

    ADS  Article  Google Scholar 

  65. 65.

    Chowdhury, D., Basu, B.: Effect of spin rotation coupling on spin transport. Ann. Phys. (NY) 339, 358–370 (2013)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  66. 66.

    Matsuo, M., Ieda, J., Saitoh, E., Maekawa, S.: Spin-dependent inertial force and spin current in accelerating systems. Phys. Rev. B 84, 104410 (2011)

    ADS  Article  Google Scholar 

  67. 67.

    Landau, L.D., Lifshitz, E.M.: Mechanics, 3rd edn. Pergamon Press, Oxford (1980)

    Google Scholar 

  68. 68.

    Landau, L.D., Lifshitz, E.M.: Statistical Physics—Part 1, 3rd edn. Pergamon Press, New York (1980)

    Google Scholar 

  69. 69.

    Tsai, C.-H., Neilson, D.: New quantum interference effect in rotating systems. Phys. Rev. A 37, 619 (1988)

    ADS  Article  Google Scholar 

  70. 70.

    Anandan, J., Suzuki, J.: Quantum mechanics in a rotating frame. arXiv:quant-ph/0305081

  71. 71.

    Fonseca, I.C., Bakke, K.: Rotating effects on the Landau quantization for an atom with a magnetic quadrupole moment. J. Chem. Phys. 144, 014308 (2016)

    ADS  Article  Google Scholar 

  72. 72.

    Fonseca, I.C., Bakke, K.: Some aspects of the interaction of a magnetic quadrupole moment with an electric field in a rotating frame. J. Math. Phys. 58, 102103 (2017)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  73. 73.

    Brack, M., Bhaduri, R.K.: Semiclassical Physics. Addison-Wesley Publishing Company, Boston (1997)

    Google Scholar 

  74. 74.

    Landau, L.D., Lifshitz, E.M.: Quantum Mechanics, the Nonrelativist Theory, 3rd edn. Pergamon, Oxford (1977)

    Google Scholar 

  75. 75.

    Gaudreau, P., Slevinsky, R.M., Safouhi, H.: An asymptotic expansion for energy eigenvalues of anharmonic oscillators. Ann. Phys. (NY) 337, 261–277 (2013)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  76. 76.

    Cornwall, J.M., Tiktopoulos, G.: Semiclassical matrix elements for the quartic oscillator. Ann. Phys. (NY) 228, 365–410 (1993)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  77. 77.

    Adhikari, R., Dutt, R., Varshni, Y.P.: On the averaging of energy eigenvalues in the supersymmetric WKB method. Phys. Lett. A 131, 217–221 (1998)

    ADS  MathSciNet  Article  Google Scholar 

  78. 78.

    Fernández, F.M.: Comment on: Exact solution of the inverse-square-root potential \(V\left(r\right)=-\frac{\alpha }{\sqrt{r}}\). Ann. Phys. (NY) 379, 83–85 (2017)

    ADS  Article  Google Scholar 

  79. 79.

    Trost, J., Friedrich, H.: WKE3 and exact wave functions for inverse power-law potentials. Phys. Lett. A 228, 127–133 (1997)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  80. 80.

    Friedrich, H., Trost, J.: Accurate WKB wave functions for weakly attractive inverse-square potentials. Phys. Rev. A 59, 1683 (1999)

    ADS  MathSciNet  Article  Google Scholar 

  81. 81.

    Frisk, H., Guhr, T.: Spin–orbit coupling in semiclassical approximation. Ann. Phys. (NY) 221, 229–257 (1993)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  82. 82.

    Nanayakkara, A., Dasanayake, I.: Analytic semiclassical energy expansions of general polynomial potentials. Phys. Lett. A 294, 158–162 (2002)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  83. 83.

    Das, A., Frenkel, J., Pereira, S.H., Taylor, J.C.: Quantum behavior of a charged particle in an axial magnetic field. Phys. Rev. A 70, 053408 (2004)

    ADS  Article  Google Scholar 

  84. 84.

    Yi, H.S., Lee, H.R., Sohn, K.S.: Semiclassical quantum theory and its applications in two dimensions by conformal mapping. Phys. Rev. A 49, 3277 (1994)

    ADS  MathSciNet  Article  Google Scholar 

  85. 85.

    Bender, C.M., et al.: Complex WKB analysis of energy-level degeneracies of non-Hermitian Hamiltonians. J. Phys. A: Math. Gen. 34, L31 (2001)

    MathSciNet  MATH  Article  Google Scholar 

  86. 86.

    Dorey, P., et al.: Beyond the WKB approximation in PT-symmetric quantum mechanics. J. Phys. A: Math. Gen. 38, 1305 (2005)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  87. 87.

    Bender, C.M., Jones, H.F.: Semiclassical calculation of the \(C\) operator in PT-symmetric quantum mechanic. Phys. Lett. A 328, 102–109 (2004)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  88. 88.

    Delplace, P., Montambaux, G.: WKB analysis of edge states in graphene in a strong magnetic field. Phys. Rev. B 82, 205412 (2010)

    ADS  Article  Google Scholar 

  89. 89.

    Zhang, Y., Barlas, Y., Yang, K.: Coulomb impurity under magnetic field in graphene: a semiclassical approach. Phys. Rev. B 85, 165423 (2012)

    ADS  Article  Google Scholar 

  90. 90.

    Bakke, K., Furtado, C.: Analysis of the interaction of an electron with radial electric fields in the presence of a disclination. Int. J. Geom. Methods Mod. Phys. 16, 1950172 (2019)

    MathSciNet  Article  Google Scholar 

  91. 91.

    Langer, R.E.: On the connection formulas and the solutions of the wave equation. Phys. Rev. 51, 669 (1937)

    ADS  MATH  Article  Google Scholar 

  92. 92.

    Berry, M.V., Mount, K.E.: Semiclassical approximations in wave mechanics. Rep. Prog. Phys. 35, 315–397 (1972)

    ADS  Article  Google Scholar 

  93. 93.

    Berry, M.V., Ozorio de Almeida, A.M.: Semiclassical approximation of the radial equation with two-dimensional potentials. J. Phys. A: Math. Nucl. Gen. 6, 1451 (1973)

    ADS  Article  Google Scholar 

  94. 94.

    Morehead, J.J.: Asymptotics of radial wave equations. J. Math. Phys. 36, 5431 (1995)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  95. 95.

    Ou, Y., Cao, Z., Shen, Q.: Exact energy eigenvalues for spherically symmetrical three-dimensional potential. Phys. Lett. A 318, 36–39 (2013)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  96. 96.

    Hainz, J., Grabert, H.: Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen. Phys. Rev. A 60, 1698 (1999)

    ADS  Article  Google Scholar 

  97. 97.

    Aharonov, Y., Bohm, D.: Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485 (1959)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  98. 98.

    Peshkin, M., Tonomura, A.: The Aharonov–Bohm effect. In: Lecture Notes in Physics, Vol. 340, Springer, Berlin, (1989)

  99. 99.

    Katanaev, M.O., Volovich, I.V.: Theory of defects in solids and three-dimensional gravity. Ann. Phys. (NY) 216, 1–28 (1992)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  100. 100.

    Valanise, K.C., Panoskaltsis, V.P.: Material metric, connectivity and dislocations in continua. Acta Mech. 175, 77–103 (2005)

    MATH  Article  Google Scholar 

  101. 101.

    Bezerra, V.B., et al.: Some remarks on topological defects and their gravitational consequences. Int. J. Mod. Phys. A 17, 4365–4374 (2002)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  102. 102.

    de Carvalho, A.M., et al.: The self-energy of a charged particle in the presence of a topological defect distribution. Int. J. Mod. Phys. A 19, 2113–2122 (2004)

    ADS  Article  Google Scholar 

  103. 103.

    Guimarães, M.E.X., Oliveira, A.L.N.: Quantum effects in the spacetime of a magnetic flux cosmic string. Int. J. Mod. Phys. A 18, 2093–2098 (2003)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  104. 104.

    de Marques, A.G., et al.: Quantum effects due to a magnetic flux associated to a topological defect. Int. J. Mod. Phys. A 20, 6051–6064 (2005)

    ADS  MATH  Article  Google Scholar 

  105. 105.

    de Montigny, M., et al.: The spin-zero Duffin–Kemmer–Petiau equation in a cosmic-string space-time with the Cornell interaction. Int. J. Mod. Phys. A 31, 1650191 (2016)

    MATH  Article  Google Scholar 

  106. 106.

    Duan, Y.S., Zhao, L.: Topological structure and evolution of space-time dislocations and disclinations. Int. J. Mod. Phys. A 22, 1335–1351 (2007)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  107. 107.

    Bennett, D.L., et al.: The relation between the model of a crystal with defects and Plebanski’s theory of gravity. Int. J. Mod. Phys. A 28, 1350044 (2013)

    ADS  MathSciNet  Article  Google Scholar 

  108. 108.

    Tartaglia, A.: Space time defects as a source of curvature and torsion. Int. J. Mod. Phys. A 20, 2336–2340 (2005)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  109. 109.

    Wang, Z., et al.: Geometric phase for a two-level atom immersed in a thermal bath in the global monopole space-time. Int. J. Mod. Phys. A 34, 1950023 (2019)

    ADS  MATH  Article  Google Scholar 

  110. 110.

    Rahaman, F., et al.: Multidimensional global monopole in presence of electromagnetic field. Int. J. Mod. Phys. A 20, 993–999 (2005)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  111. 111.

    Wang, B.-Q., et al.: The study of a half-spin relativistic particle in the rotating cosmic string space-time. Int. J. Mod. Phys. A 33, 1850158 (2018)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  112. 112.

    Cavalcanti de Oliveira, A.L., Bezerra de Mello, E.R.: Nonrelativistic charged particle-magnetic monopole scattering in the global monopole background. Int. J. Mod. Phys. A 18, 3175–3187 (2003)

    ADS  MATH  Article  Google Scholar 

  113. 113.

    Hun, M.A., Candemir, N.: Relativistic quantum motion of the scalar bosons in the background space-time around a chiral cosmic string. Int. J. Mod. Phys. A 34, 1950056 (2019)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  114. 114.

    Bezerra, V.B., de Marques, A.G.: On a result concerning the behavior of a relativistic quantum system in the cosmic string spacetime. Int. J. Mod. Phys. A 24, 1549–1556 (2009)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  115. 115.

    Bakke, K., et al.: Holonomic quantum computation associated with a defect structure of conical graphene. EPL 87, 30002 (2009)

    ADS  Article  Google Scholar 

  116. 116.

    Bueno, M.J., et al.: Landau levels in graphene layers with topological defects. Eur. Phys. J. B 85, 53 (2012)

    ADS  Article  Google Scholar 

  117. 117.

    Bueno, M.J., et al.: Quantum dot in a graphene layer with topological defects. Eur. Phys. J. Plus 129, 201 (2014)

    Article  Google Scholar 

  118. 118.

    Amaro Neto, J., et al.: Quantum ring in gapped graphene layer with wedge disclination in the presence of a uniform magnetic field. Eur. Phys. J. Plus 133, 185 (2018)

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank the Brazilian agencies CNPq and CAPES for financial support.

Funding

The Funding was provided by CNPq (Grant No. 301385/2016-5).

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Vieira, S.L.R., Bakke, K. Semiclassical Analysis of the Interaction of the Magnetic Quadrupole Moment of a Neutral Particle with Axial Electric Fields in a Uniformly Rotating Frame. Found Phys 50, 735–748 (2020). https://doi.org/10.1007/s10701-020-00348-2

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Keywords

  • WKB approximation
  • Semiclassical approximation
  • Magnetic quadrupole moment
  • Neutral particles
  • Rotating reference frame
  • Magnetic monopole