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Average transmission times for the tunneling of wave packets

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Journal of Russian Laser Research Aims and scope

Abstract

We consider the average time for a localized wave packet to tunnel through a finite rectangular barrier, as prescribed by the Salecker–Wigner–Peres clock after a post-selection of transmitted final states. We investigate the properties of this time both in the relativistic and nonrelativistic regimes and address the questions of the emergence of the Hartman effect and superluminal tunneling velocities.

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References

  1. A. Peres, Am. J. Phys., 48, 552 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  2. H. G. Winful, Phys. Rep., 436, 1 (2006).

    Article  ADS  Google Scholar 

  3. T. E. Hartman, J. Appl. Phys., 33, 3427 (1962).

    Article  ADS  Google Scholar 

  4. N. G. Kelkar, H. M. Castañeda, and M. Nowakowski, Europhys. Lett., 85, 20006 (2009).

    Article  ADS  Google Scholar 

  5. H. Salecker and E. P. Wigner, Phys. Rev., 109, 571 (1958).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. J. T. Lunardi, L. A. Manzoni, and A. T. Nystrom, Phys. Lett. A, 375, 415 (2011).

    Article  ADS  Google Scholar 

  7. J. P. Falck and E. H. Hauge, Phys. Rev. B, 38, 3287 (1988).

    Article  ADS  Google Scholar 

  8. C. R. Leavens and G. C. Aers, Phys. Rev. B, 40, 5387 (1989).

    Article  ADS  Google Scholar 

  9. M. Calçada, J. T. Lunardi, and L. A. Manzoni, Phys. Rev. A, 79, 012110 (2009).

    Article  ADS  Google Scholar 

  10. C. R. Leavens and W. R. McKinnon, Phys. Lett. A, 194, 12 (1994).

    Article  ADS  Google Scholar 

  11. D. Sokolovski and L. M. Baskin, Phys. Rev. A, 36, 4604 (1987).

    Article  ADS  Google Scholar 

  12. D. Sokolovski and J. N. L. Connor, Phys. Rev. A, 42, 6512 (1990).

    Article  ADS  Google Scholar 

  13. M. Büttiker, Phys. Rev. B, 27, 6178 (1983).

    Article  ADS  Google Scholar 

  14. S. Brouard, R. Sala, and J. G. Muga, Phys. Rev. A, 49, 4312 (1994).

    Article  ADS  Google Scholar 

  15. P. Krekora, Q. Su, and R. Grobe, Phys. Rev. A, 63, 032107 (2001).

    Article  ADS  Google Scholar 

  16. P. Krekora, Q. Su, and R. Grobe, Phys. Rev. A, 64, 022105 (2001).

    Article  ADS  Google Scholar 

  17. V. Petrillo and D. Janner, Phys. Rev. A, 67, 012110 (2003).

    Article  ADS  Google Scholar 

  18. H. G. Winful, M. Ngom, and N. M. Litchinitser, Phys. Rev. A, 70, 052112 (2004).

    Article  ADS  Google Scholar 

  19. S. De Leo and P. P. Rotelli, Phys. Lett. A, 342, 294 (2005).

    Article  ADS  Google Scholar 

  20. J. T. Lunardi and L. A. Manzoni, Phys. Rev. A, 76, 042111 (2007).

    Article  ADS  Google Scholar 

  21. J. Zhao and C.-y. Long, Phys. Rev. A, 76, 012105 (2007).

    Article  MathSciNet  ADS  Google Scholar 

  22. A. E. Bernardini, Ann. Phys., 324, 1303 (2009).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. S. De Leo and V. Leonardi, Phys. Rev. A, 83, 022111 (2011).

    Article  ADS  Google Scholar 

  24. O. del Barco and V. Gasparian, J. Phys. A: Math. Theor., 44, 015303 (2011).

    Article  ADS  Google Scholar 

  25. J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics, McGraw-Hill, New York (1964).

    Google Scholar 

  26. W. Greiner, Relativistic Quantum Mechanics–Wave Equations, Springer, New York (2000).

    MATH  Google Scholar 

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Correspondence to L. A. Manzoni.

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Lunardi, J.T., Manzoni, L.A., Nystrom, A.T. et al. Average transmission times for the tunneling of wave packets. J Russ Laser Res 32, 431–438 (2011). https://doi.org/10.1007/s10946-011-9232-0

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  • DOI: https://doi.org/10.1007/s10946-011-9232-0

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