Advertisement

Russian Physics Journal

, Volume 49, Issue 3, pp 314–325 | Cite as

New approach to the quantum tunneling process: Characteristic times for transmission and reflection

  • N. L. Chuprikov
Open Access
Elementary Particle Physics and Field Theory

Abstract

In [1] we have demonstrated that scattering of a quantum particle on a one-dimensional potential barrier should be considered as a combined process involving two alternative elementary transmission and reflection processes. For symmetric potential barriers, we have found solutions of the Schrödinger equation which describe the transmission and reflection processes in all stages of scattering. The present work studies time aspects of both processes. The local and asymptotic group tunneling times, dwell time, and Larmor tunneling time are determined for each process. Among these time characteristics, the group tunneling times should be considered as auxiliary. As to the dwell and Larmor tunneling times, they are the best estimates (of the expected values) of times the quantum particle in stationary and localized nonstationary states dwells in the barrier region. Moreover, the Larmor time is simply the dwell time averaged over the corresponding ensemble of particles. This characteristic can be measured experimentally and hence the suggested model of scattering can be verified.

Keywords

Dwell Time Wave Packet Barrier Region Tunneling Time Rectangular Barrier 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    N. L. Chuprikov, Russ. Phys. J., 49, No. 2, 119–126 (2006).CrossRefGoogle Scholar
  2. 2.
    L. A. MacColl, Phys. Rev., 40, 621 (1932).MATHCrossRefADSGoogle Scholar
  3. 3.
    E. H. Hauge and J. A. Støvneng, Rev. Mod. Phys., 61, 917 (1989).CrossRefADSGoogle Scholar
  4. 4.
    R. Landauer and Th. Martin, Rev. Mod. Phys., 66, 217 (1994).CrossRefADSGoogle Scholar
  5. 5.
    V. S. Olkhovsky and E. Recami, Phys. Rep., 214, 339 (1992).CrossRefADSGoogle Scholar
  6. 6.
    A. M. Steinberg, Phys. Rev. Lett., 74, 2405 (1995).CrossRefADSGoogle Scholar
  7. 7.
    J. G. Muga and C. R. Leavens, Phys. Rep., 338, 353 (2000).MathSciNetCrossRefADSGoogle Scholar
  8. 8.
    C. A. A. de Carvalho and H. M. Nussenzveig, Phys. Rep., 364, 83 (2002).MATHMathSciNetCrossRefADSGoogle Scholar
  9. 9.
    M. Buttiker and R. Landauer, Phys. Rev. Lett., 49, 1739 (1982).CrossRefADSGoogle Scholar
  10. 10.
    T. E. Hartman, J. Appl. Phys., 33, 3427 (1962).CrossRefGoogle Scholar
  11. 11.
    J. G. Muga, I. L. Egusquiza, J. A. Damborenea, and F. Delgado, Phys. Rev., A66, 042115 (2002).Google Scholar
  12. 12.
    H. G. Winful, Phys. Rev. Lett., 91, 260401 (2003).Google Scholar
  13. 13.
    V. S. Olkhovsky, V. Petrillo, and A. K. Zaichenko, Phys. Rev., A70, 034103 (2004).Google Scholar
  14. 14.
    D. Sokolovski, A. Z. Msezane, and V. R. Shaginyan, Phys. Rev., A71, 064103 (2005).Google Scholar
  15. 15.
    M. Buttiker, Phys. Rev., B27, 6178 (1983).ADSGoogle Scholar
  16. 16.
    Li Zhi-Jian, J. Q. Liang, and D. H. Kobe, Phys. Rev., A64, 043112 (2001).Google Scholar
  17. 17.
    C. R. Leavens and G. C. Aers, Phys. Rev., B40, 5387 (1989).ADSGoogle Scholar
  18. 18.
    N. L. Chuprikov, Fiz. Tekh. Poluprovodn., 26, 2040 (1992).Google Scholar
  19. 19.
    E. Merzbacher, Quantum Mechanics, New York (1970).Google Scholar
  20. 20.
    J. R. Taylor, Scattering Theory: The Quantum Theory of Nonrelativistic Collisions, New York-London-Sydney (1972).Google Scholar
  21. 21.
    A. I. Baz’, Yad. Fiz., 4, 252 (1966).Google Scholar
  22. 22.
    V. F. Rybachenko, Yad. Fiz., 5, 895 (1966).Google Scholar
  23. 23.
    N. L. Chuprikov, Fiz. Tekh. Poluprovodn., 27, 799 (1993).Google Scholar
  24. 24.
    E. H. Hauge, J. P. Falck, and T. A. Fjeldly, Phys. Rev., B36, 4203 (1987).ADSGoogle Scholar
  25. 25.
    W. Jaworski and D. M. Wardlaw, Phys. Rev., A37, 2843 (1988).ADSGoogle Scholar
  26. 26.
    J. G. Muga, S. Brouard, and R. Sala, Phys. Lett., A167, 24 (1992).ADSGoogle Scholar
  27. 27.
    V. G. Bagrov, V. V. Belov, V. N. Zadorozhnyi, and A. Yu. Trifonov, Methods of Mathematical Physics [in Russian], Tomsk (2002).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • N. L. Chuprikov
    • 1
  1. 1.Tomsk State Pedagogical UniversityTomsk

Personalised recommendations