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Effects on the non-relativistic dynamics of a charged particle interacting with a Chern-Simons potential

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Abstract

The hydrogen atom in two dimensions, described by a Schrödinger equation with a Chern-Simons potential, is numerically solved. Both its wavefunctions and eigenvalues were determined for small values of the principal quantum number n. The only possible states correspond to l = 0. How the result depends on the topological mass of the photon is also discussed. In the case n = 1, the energy of the fundamental state, corresponding to different choice for the photon mass scale, are found to be comprehended in the interval −3.5 × 10-3 eV ≤ E ≤ −9.0 × 10−2 eV, corresponding to a mean radius of the electron in the range (5.637 ± 0.005) × 10−8 cm ≤ ⟨r⟩ ≤ (48.87 ± 0.03) × 10-8 cm. In any case, the planar atom is found to be very weekly bounded showing some features similar to the Rydberg atoms in three dimensions with a Coulombian interaction.

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References

  1. J.G. Berdnoz, K.A. Müller, Z. Phys. B 64, 189 (1986)

    Article  ADS  Google Scholar 

  2. P.W. Anderson, Science 235, 1196 (1987)

    Article  ADS  Google Scholar 

  3. P.W. Anderson, The Theory of Superconductivity in the High- T c Cuprates(University Princeton Press, Princeton, 1997)

  4. K. von Klitzing, G. Dorda, M. Pepper, Phys. Rev. Lett. 45, 494 (1980)

    Article  ADS  Google Scholar 

  5. R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983)

    Article  ADS  Google Scholar 

  6. H.L. Stormer, Rev. Mod. Phys. 71, 875 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. R.E. Prange, S.M. Girvin, The Quantum Hall Effect, 2nd edn. (Springer-Verlag, New York, 1990)

  8. S. Tomonaga, Prog. Theor. Phys. 5, 544 (1950)

    Article  MathSciNet  ADS  Google Scholar 

  9. J.M. Luttinger, J. Math. Phys. 4, 1154 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  10. F.D.M. Haldane, J. Phys. C 14, 2585 (1981)

    Article  ADS  Google Scholar 

  11. P.A. Marchetti, Z.B. Su, L. Yu, Phys. Rev. B 58, 5808 (1998)

    Article  ADS  Google Scholar 

  12. A.M. Tsvelik, Quantum Field Theory in Condensed Matter Physics, 2nd edn. (Cambridge University Press, Cambridge, 2003)

  13. A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)

    Article  ADS  Google Scholar 

  14. A.K. Geim, Science 324, 1530 (2009)

    Article  ADS  Google Scholar 

  15. L. Fu, C.L. Kane, Phys. Rev. B 76, 045302 (2007)

    Article  ADS  Google Scholar 

  16. H. Zhang et al., Nat. Phys. 5, 438 (2009)

    Article  Google Scholar 

  17. D. Hsieh et al., Nature 452, 970 (2008)

    Article  ADS  Google Scholar 

  18. Y.L. Chen et al., Science 325, 178 (2009)

    Article  ADS  Google Scholar 

  19. X.-L. Qi, S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)

    Article  ADS  Google Scholar 

  20. N. Read, D. Green, Phys. Rev. B 61, 10267 (2000)

    Article  ADS  Google Scholar 

  21. X.-L. Qi, T.L. Hughes, S. Raghu, S.-C. Zhang, Phys. Rev. Lett. 102, 187001 (2009)

    Article  ADS  Google Scholar 

  22. L. Fu, E. Berg, Phys. Rev. Lett. 105, 097001 (2010)

    Article  ADS  Google Scholar 

  23. X.-L. Qi, E. Witten, S.-C. Zhang, Phys. Rev. B 87, 134519 (2013)

    Article  ADS  Google Scholar 

  24. J. Fröhlich, T. Kerler, Nucl. Phys. B 354, 369 (1991)

    Article  ADS  Google Scholar 

  25. S. Deser, R. Jackiw, S. Templeton, Ann. Phys. 140, 372 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  26. S. Deser, R. Jackiw, S. Templeton, Phys. Rev. Lett. 48, 975 (1982)

    Article  ADS  Google Scholar 

  27. J.M. Leinaas, J. Myrheim, Nuovo Cim. B 37, 1 (1977)

    Article  ADS  Google Scholar 

  28. F. Wilczek, Phys. Rev. Lett. 49, 957 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  29. H.R. Christiansen, O.M. Del Cima, M.M. Ferreira, J.A. Helayël-Neto, Int. J. Mod. Phys. A 18, 725 (2003)

    Article  ADS  MATH  Google Scholar 

  30. N. Dorey, N.E. Mavromatos, Phys. Lett. B 266, 163 (1991)

    Article  ADS  Google Scholar 

  31. N. Dorey, N.E. Mavromatos, Nucl. Phys. B 386, 614 (1992)

    Article  ADS  Google Scholar 

  32. H. Belich Jr., O.M. Del Cima, M.M. Ferreira Jr., J.A. Helayël-Neto, J. Phys. G 29, 1431 (2003)

    Article  ADS  Google Scholar 

  33. H. Belich Jr., O.M. Del Cima, M.M. Ferreira Jr., J.A. Helayël-Neto, Eur. Phys. J. B 32, 145 (2003)

    Article  ADS  Google Scholar 

  34. H. Belich Jr., O.M. Del Cima, M.M. Ferreira Jr., J.A. Helayël-Neto, J. Phys. G 29, 1431 (2003)

    Article  ADS  Google Scholar 

  35. H. Belich Jr., T. Costa-Soares, M.M. Ferreira Jr., J.A. Helayël-Neto, Eur. Phys. J. C 42, 127 (2005)

    Article  ADS  Google Scholar 

  36. J.M. Fonseca, W.A. Moura-Melo, A.R. Pereira, arXiv:1210.3100 (2012)

    Google Scholar 

  37. H. Belich Jr., O.M. Del Cima, M.M. Ferreira Jr., J.A. Helayël-Neto, Int. J. Mod. Phys. A 16, 4939 (2001)

    Article  ADS  MATH  Google Scholar 

  38. G.V. Dunne, R. Jackiw, C.A. Trugenberger, Phys. Rev. D 41, 661 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  39. T.P. Orlando, K.A. Delin, Foundations of Applied Superconductivity (Addison-Wesley, Reading, Massachusetts, 1991)

  40. O. Atabek, C. Deutsch, M. Lavaud, Phys. Rev. A 9, 2617 (1974)

    Article  ADS  Google Scholar 

  41. B.V. Numerov, Month. Notices R. Astron. Soc. 84, 592 (1924)

    ADS  Google Scholar 

  42. B.V. Numerov, Astronomische Nachrichten 230, 359 (1927)

    Article  ADS  MATH  Google Scholar 

  43. J.M. Blatt, J. Comput. Phys. 1, 382 (1967)

    Article  ADS  MATH  Google Scholar 

  44. F. Caruso, J. Martins, V. Oguri, Phys. Lett. A 377, 694 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  45. G. Cowan, Statistical Data Analysis (Clarendon Press, Oxford, 1998)

  46. F. James, Rep. Prog. Phys. 43, 1145 (1980)

    Article  ADS  Google Scholar 

  47. Particle Data Group, Phys. Rev. D 86, 010001 (2012)

    Article  Google Scholar 

  48. C. Baxter, Phys. Rev. Lett. 74, 514 (1995)

    Article  ADS  Google Scholar 

  49. T.F. Gallagher, Rep. Prog. Phys. 51, 143 (1988)

    Article  ADS  Google Scholar 

  50. T.F. Gallagher, Rydberg Atoms (University Press, Cambridge, 2005)

  51. J.-Z. Zhang, Phys. Rev. Lett. 77, 44 (1996)

    Article  ADS  Google Scholar 

  52. J.-Z. Zhang, Phys. Rev. Lett. 93, 043002 (2004)

    Article  ADS  Google Scholar 

  53. V. Bendkowsky, B. Butscher, J. Nipper, J.P. Shaffer, R. Löw, T. Pfau, Nature 458, 1005 (2009)

    Article  ADS  Google Scholar 

  54. S.M. Farooqi et al., Phys. Rev. Lett. 91, 183002 (2003)

    Article  ADS  Google Scholar 

  55. C. Boisseau, I. Simbotin, E. Côté, Phys. Rev. Lett. 88, 133004 (2002)

    Article  ADS  Google Scholar 

  56. S.K. Paul, A. Khare, Phys. Lett. B193, 253, erratum (1987)

  57. S.K. Paul, A. Khare, Phys. Lett. B196, 571 (1987)

    Google Scholar 

  58. F.A.S. Nobre, C.A.S. Almeida, Phys. Lett. B455, 213 (1999)

    ADS  Google Scholar 

  59. R.C. Paschoal, J.A. Helayël-Neto, Phys. Lett. A313, 412 (2003)

    ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, 22290-180, Urca, Rio de Janeiro, Brazil

    F. Caruso & J. A. Helayël-Neto

  2. Instituto de Física Armando Dias Tavares, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier, 524, 20550-900, Maracanã, Rio de Janeiro, Brazil

    F. Caruso, J. Martins & V. Oguri

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  1. F. Caruso
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  2. J. A. Helayël-Neto
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  3. J. Martins
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  4. V. Oguri
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Correspondence to F. Caruso.

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Caruso, F., Helayël-Neto, J.A., Martins, J. et al. Effects on the non-relativistic dynamics of a charged particle interacting with a Chern-Simons potential. Eur. Phys. J. B 86, 324 (2013). https://doi.org/10.1140/epjb/e2013-40282-1

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