The European Physical Journal C

, Volume 55, Issue 1, pp 125–132 | Cite as

Delay time computation for relativistic tunneling particles

Regular Article - Theoretical Physics

Abstract

We study the tunneling zone solutions of a one-dimensional electrostatic potential for the relativistic (Dirac to Klein–Gordon) wave equation when the incoming wave packet exhibits the possibility of being almost totally transmitted through the barrier. The transmission probabilities, the phase times and the dwell times for the proposed relativistic dynamics are obtained and the conditions for the occurrence of accelerated tunneling transmission are all quantified. We show that, in some limiting cases, the analytical difficulties that arise when the stationary phase method is employed for obtaining phase (traversal) tunneling times are all overcome. Lessons concerning the phenomenology of the relativistic tunneling suggest revealing insights into condensed-matter experiments using electrostatic barriers for which the accelerated tunneling effect can be observed.

Keywords

Dwell Time Wave Packet Phase Time Tunneling Time Schroedinger Equation 

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References

  1. 1.
    M. Büttiker, S. Washburn, Nature 422, 271 (2003)CrossRefADSGoogle Scholar
  2. 2.
    H.G. Winful, Nature 424, 638 (2003)CrossRefADSGoogle Scholar
  3. 3.
    H.G. Winful, Phys. Rev. Lett. 91, 260401 (2003)CrossRefADSGoogle Scholar
  4. 4.
    V.S. Olkhovsky, E. Recami, J. Jakiel, Phys. Rep. 398, 133 (2004)CrossRefADSGoogle Scholar
  5. 5.
    A. Enders, G. Nimtz, J. Phys. I France 2, 1693 (1992)CrossRefGoogle Scholar
  6. 6.
    A.M. Steinberg, P.G. Kwiat, R.Y. Chiao, Phys. Rev. Lett. 71, 708 (1993)CrossRefADSGoogle Scholar
  7. 7.
    C. Spielmann, R. Szipöcs, A. Stingl, F. Krausz, Phys. Rev. Lett. 73, 2308 (1994)CrossRefADSGoogle Scholar
  8. 8.
    G. Nimtz, A. Enders, H. Spieker, J. Phys. I France 4, 1 (1994)Google Scholar
  9. 9.
    A. Haybel, G. Nimtz, Ann. Phys. (Leipzig) 10, 707 (2001)CrossRefADSGoogle Scholar
  10. 10.
    E.H. Hauge, J.A. Stovneng, Rev. Mod. Phys. 61, 917 (1989)CrossRefADSGoogle Scholar
  11. 11.
    D. Sokolorski, L.M. Baskin, Phys. Rev. A 36, 4604 (1987)CrossRefADSGoogle Scholar
  12. 12.
    K. Imafuku, I. Ohba, Y. Yamanaka, Phys. Rev. A 56, 1142 (1997)CrossRefADSGoogle Scholar
  13. 13.
    M. Abolhasani, M. Golshani, Phys. Rev. A 62, 012106 (2000)CrossRefADSGoogle Scholar
  14. 14.
    S. Brouard, R. Sala, J.G. Muga, Phys. Rev. A 49, 4312 (1994)CrossRefADSGoogle Scholar
  15. 15.
    M. Büttiker, Phys. Rev. B 27, 6178 (1983)CrossRefADSGoogle Scholar
  16. 16.
    M. Büttiker, R. Landauer, Phys. Rev. Lett. 49, 1739 (1982)CrossRefADSGoogle Scholar
  17. 17.
    E.P. Wigner, Phys. Rev. 98, 145 (1955)CrossRefADSMathSciNetMATHGoogle Scholar
  18. 18.
    R. Landauer, T. Martin, Rev. Mod. Phys. 66, 217 (1994)CrossRefADSGoogle Scholar
  19. 19.
    V.S. Olkhovsky, E. Recami, Phys. Rep. 214, 339 (1992)CrossRefADSGoogle Scholar
  20. 20.
    V.S. Olkhovsky, E. Recami, F. Raciti, A.K. Zaichenko, J. Phys. I France 5, 1351 (1995)CrossRefGoogle Scholar
  21. 21.
    J. Jakiel, V.S. Olkhovsky, E. Recami, Phys. Lett. A 248, 156 (1998)CrossRefADSGoogle Scholar
  22. 22.
    V.S. Olkhovsky, E. Recami, G. Salesi, Europhys. Lett. 57, 879 (2002)CrossRefADSGoogle Scholar
  23. 23.
    C.G.B. Garret, D.E. McCumber, Phys. Rev. A 01, 305 (1970)CrossRefADSGoogle Scholar
  24. 24.
    S. Chu, W. Wong, Phys. Rev. Lett. 48, 738 (1982)CrossRefADSGoogle Scholar
  25. 25.
    B. Segard, B. Macke, Phys. Lett. A 109, 213 (1985)CrossRefADSGoogle Scholar
  26. 26.
    M.W. Mitchell, R.Y. Chiao, Phys. Lett. A 230, 122 (1997)CrossRefGoogle Scholar
  27. 27.
    L.J. Wang, A. Kuzmich, A. Dogariu, Nature 406, 277 (2000)CrossRefADSGoogle Scholar
  28. 28.
    T.E. Hartman, J. Appl. Phys. 33, 3427 (1962)CrossRefADSGoogle Scholar
  29. 29.
    F. Delgado et al., Phys. Rev. A 68, 032101 (2003)CrossRefADSMathSciNetGoogle Scholar
  30. 30.
    A. Calogeracos, N. Dombey, Int. J. Mod. Phys. A 14, 631 (1999)CrossRefADSMathSciNetMATHGoogle Scholar
  31. 31.
    N. Dombey, A. Calogeracos, Phys. Rep. 315, 41 (1999)CrossRefGoogle Scholar
  32. 32.
    C.-F. Li, X. Chen, Ann. Phys. (Leipzig) 12, 916 (2002)ADSGoogle Scholar
  33. 33.
    O. Klein, Z. Phys. 53, 157 (1929)CrossRefADSGoogle Scholar
  34. 34.
    C. Itzykson, J.B. Zuber, Quantum Field Theory (Mc Graw-Hill Inc., New York, 1980)Google Scholar
  35. 35.
    R.K. Su, G. Siu, X. Chou, J. Phys. A 26, 1001 (1993)CrossRefADSGoogle Scholar
  36. 36.
    B.R. Holstein, Am. J. Phys. 66, 507 (1998)CrossRefADSMathSciNetGoogle Scholar
  37. 37.
    H. Nitta, T. Kudo, H. Minowa, Am. J. Phys. 67, 966 (1999)CrossRefADSGoogle Scholar
  38. 38.
    P. Krekora, Q. Su, R. Grobe, Phys. Rev. Lett. 92, 040406 (2004)CrossRefADSGoogle Scholar
  39. 39.
    P. Krekora, Q. Su, R. Grobe, Phys. Rev. A 63, 032107 (2001)CrossRefADSGoogle Scholar
  40. 40.
    V. Petrillo, D. Janner, Phys. Rev. A 67, 012110 (2003)CrossRefADSGoogle Scholar
  41. 41.
    V.L. Telegdi, in Klein’s Paradox Revisited, ed. by U. Lingstrom (World Scientific, Singapore, 1995)Google Scholar
  42. 42.
    A. Hansen, F. Ravndal, Phys. Scripta 23 1036 (1999)Google Scholar
  43. 43.
    R. Landauer, Nature 341, 567 (1989)CrossRefADSGoogle Scholar
  44. 44.
    A.E. Bernardini, Phys. Rev. A 74, 062111 (2006)CrossRefADSGoogle Scholar
  45. 45.
    A.E. Bernardini, S. De Leo, P.P. Rotelli, Mod. Phys. Lett. A 19, 2717 (2004)CrossRefMATHGoogle Scholar
  46. 46.
    B. Gaveau et al., Phys. Rev. Lett. 53, 419 (1984)CrossRefADSMathSciNetGoogle Scholar
  47. 47.
    W. Greiner, B. Mueller, J. Rafelski, Quantum Electrodynamics of Strong Fields (Springer, Berlin, 1985)Google Scholar
  48. 48.
    D.N. Page, New J. Phys. 7, 203 (2005)CrossRefADSMathSciNetGoogle Scholar
  49. 49.
    M.I. Katsnelson, K.S. Novoselov, A.K. Geim, Nature Phys. 02, 620 (2006)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2008

Authors and Affiliations

  1. 1.Instituto de Física Gleb WataghinUNICAMPCampinasBrasil
  2. 2.Departamento de FísicaISTLisboaPortugal

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