Skip to main content

The Tunneling Time Problem Revisited

  • Chapter
Nanoelectrodynamics

Part of the book series: NanoScience and Technology ((NANO))

  • 221 Accesses

Abstract

Tunneling is undoubtedly the most important quantum phenomena with a wide range of applications. Like other physical phenomena, it should be possible to understand tunneling phenomena from a spatial and also from a temporal point of view (see Fig. 6.1). Of interest from a spatial point of view is the question as to how many particles initially on one side of the barrier will finally be found on the other side of the barrier at sufficiently later times. We are thus led to the concept of tunneling probability. Of interest from a temporal point of view would be the tunneling time, that is, the time a particle ‘spends’ in the barrier region. From a spacetime point of view, it seems natural to characterize tunneling phenomena according to the two quantities tunneling probability and tunneling time.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Landauer and T. Martin: Rev. Mod. Phys. 66, 217 (1994)

    Article  Google Scholar 

  2. E.H. Hauge and J.A. Stovneng: Rev. Mod. Phys. 61, 917 (1989)

    Article  Google Scholar 

  3. V.S. Olkhovsky and E. Recami: Phys. Rep. 214, 339 (1992)

    Article  Google Scholar 

  4. M. Büttiker: In: Electronic Properties of Multilayers and low Dimensional Semiconductors, ed. by J.M. Chamberlain, L. Eaves, and J.C. Portal, ( Plenum, New York 1990 ) p. 297

    Google Scholar 

  5. C.R. Leavens and G.C. Aers: In: Scanning Tunneling Microscopy and Related Methods, ed. by R.J. Behm, N. Garcia and H. Rohrer ( Kluwer, Dordrecht 1990 ) p. 59

    Google Scholar 

  6. M. Jonson: In: Quantum Transport in Semiconductors, ed. by D.K. Ferry and C. Jacoboni ( Plenum, New York 1991 ) p. 193

    Google Scholar 

  7. A.P. Jauho: In: Hot Carriers in Semiconductor Nanostructures: Physics and Applications, ed. by J. Shah ( Academic, Boston 1992 ) p. 121

    Google Scholar 

  8. Proceedings of the Adriatico Research Conference on Tunneling and its Implications,ed. by D. Mugnai, A. Ranfagni, L.S. Schulman (World Scientific, Singapore 1997)

    Google Scholar 

  9. N. Yamada: Phys. Rev. Lett. 83, 3350 (1999)

    Article  CAS  Google Scholar 

  10. R.B. Griffiths: J. Stat. Phys. 36, 219 (1984)

    Article  Google Scholar 

  11. R. Omnès: J. Stat. Phys. 53, 893 (1988)

    Article  Google Scholar 

  12. R. Omnès: The Interpretation of Quantum Mechanics ( Princeton University Press, Princeton, NJ 1994 )

    Google Scholar 

  13. M. Gell-Mann and J.B. Hartle: In: Proceedings of the 3rd International Symposium on the Foundations of Quantum Mechanics in the Light of New Technology, ed. by S. Kobayashi, H. Ezawa, Y. Murayama, and S. Nomura ( Physical Society of Japan, Tokyo 1990 )

    Google Scholar 

  14. J.B. Hartle: Phys. Rev. D 44, 3173 (1991)

    Article  Google Scholar 

  15. N. Yamada and S. Takagi: Prog. Theor. Phys. 85, 985 (1991)

    Article  Google Scholar 

  16. N. Yamada and S. Takagi: Prog. Theor. Phys. 86, 599 (1991)

    Article  Google Scholar 

  17. J.A. Stovneng: Can One Speak about Tunneling Times in Polite Society in [2], pp. 1–17 (see Sect, 4.3)

    Google Scholar 

  18. K.W.H. Stevens: J. Phys. C: Solid State Phys. 16, 3649 (1983)

    Article  CAS  Google Scholar 

  19. N. Teranishi, A.M. Kriman, and D.K. Ferry: Superlatt. Microstruc. 3, 509 (1987)

    Google Scholar 

  20. A.P. Jauho and M. Jonson: Superlatt. Microstruc. 6, 303 (1989)

    Article  Google Scholar 

  21. A. Ranfagni, D. Mugnai, and A. Agresti: Phys. Lett. A 158, 161 (1991)

    Article  Google Scholar 

  22. P. Moretti: Phys. Rev. A 46, 1233 (1992)

    Article  Google Scholar 

  23. J.G. Muga, S. Brouard, V. Delgado, and J.P. Palao: Characteristic Times in One-Dimensional Tunneling. In: Proceedings of the Adriatico Research Conference on Tunneling and its Implications, ed. by D. Mugnai, A. Ranfagni, L.S. Schulman ( World Scientific, Singapore, 1997 ) pp. 34–49

    Google Scholar 

  24. S. Brouard and J.G. Muga: Phys. Rev. A 54, 3055 (1996)

    Article  CAS  Google Scholar 

  25. G. Garcia-Calderon: Tunneling dynamics of the Plane Wave Shutter. In: Proceedings of the Adriatico Research Conference on Tunneling and its Implications, ed. by D. Mugnai, A. Ranfagni, L.S. Schulman ( World Scientific, Singapore, 1997 ) pp. 176–190

    Google Scholar 

  26. G. García-Calderón and A. Rubio: Phys. Rev. A 55, 3361 (1997)

    Article  Google Scholar 

  27. A. Goldberg, H.M. Schey, and J.L. Schwartz: Am. J. Phys. 35, 117 (1967)

    Article  Google Scholar 

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

    Article  Google Scholar 

  29. A.I. Baz’: Yad. Fiz. 4, 252 (1966) [Soy. J. Nucl. Phys. 4, 182 (1967)]

    Google Scholar 

  30. V.F. Rybachenko: Yad. Fiz. 5, 895 (1966) [Sov. J. Nucl. Phys. 5, 635 (1967)]

    Google Scholar 

  31. C.R. Leavens and G.C. Aers: Solid State Commun. 63, 1101 (1987)

    Article  Google Scholar 

  32. C.R. Leavens and G.C. Aers: Solid State Commun. 67, 1135 (1988)

    Article  Google Scholar 

  33. M. Hino, N. Achiwa, S. Tasaki, T. Ebisawa, T. Kawai, T. Akiyoshi, and D. Yamazaki: Phys. Rev. A 59, 2261 (1999)

    Article  CAS  Google Scholar 

  34. M. Büttiker and R. Landauer: Phys. Rev. Lett. 49, 1739 (1982)

    Article  Google Scholar 

  35. M. Büttiker and R. Landauer: Phys. Scr. 32, 429 (1985)

    Article  Google Scholar 

  36. S. Takagi: Tunneling Through a Squeezing Barrier: A Comment on the Barrier Traversal Time. In: Proceedings of the 4th International Symposium on the Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, August 24–27, 1992, ed. by M. Tsukada et al. ( JJAP, Tokyo 1993 ) pp. 82–85

    Google Scholar 

  37. W.S. Truscott: Phys. Rev. A 70, 1900 (1993)

    Google Scholar 

  38. A.P. Jauho and M. Jonson: J. Phys. Condens. Matter 1, 9027 (1989)

    Article  Google Scholar 

  39. H. De Raedt, N. Garcia, and J. Huyghebaert: Solid State Commun. 76, 847 (1990)

    Article  Google Scholar 

  40. C.R. Leavens and G.C. Aers: Solid State Commun. 78, 1015 (1991)

    Article  Google Scholar 

  41. F.T. Smith: Phys. Rev. 118, 349 (1960)

    Article  Google Scholar 

  42. C.R. Leavens and G.C. Aers: Phys. Rev. B 39, 1202 (1989)

    Article  Google Scholar 

  43. E.H. Hauge, J.P. Falck, and T.A. Fjeldly: Phy. Rev. B 36, 4203 (1987)

    Article  Google Scholar 

  44. L.M. Baskin and D.G. Sokolovski: Soy. Phys. J. 30, 204 (1987)

    Article  Google Scholar 

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

    Article  Google Scholar 

  46. C.R. Leavens and G.C. Aers: Bohm Trajectories and the Tunneling Time Problem. In: Scanning Tunneling Microscopy III, ed. by R. Wiesendanger and H.-J. Güntherodt ( Springer, Berlin, Heidelberg, New York 1993 ) pp. 105–140

    Chapter  Google Scholar 

  47. W. Jaworski and D. Wardlaw: Phys. Rev. A 37 2843 (1988)

    Article  Google Scholar 

  48. W. Jaworski and D. Wardlaw: Phys. Rev. A 40 6210 (1989)

    Article  Google Scholar 

  49. H. Yamamoto, Y. Senshu, K. Miyamoto, and S. Tanaka: Physics. Status Solidi B 206, 601 (1998)

    Article  CAS  Google Scholar 

  50. G. Iannaccone and B. Pellegrini: Phys. Rev. B 49, 16548 (1994)

    Article  CAS  Google Scholar 

  51. T. Martin: Int. J. Mod. Phys. B 10, 3747 (1996)

    Article  CAS  Google Scholar 

  52. L.S. Schulman and R..W. Ziolkowski: In: Proceedings of Third International Conference on Path Integrals from meV to MeV,ed. by V. Sa-yakanit et al. (World Scientific, Singapore 1989)

    Google Scholar 

  53. A.B. Nassar: Phys. Rev. A 38, 683 (1988)

    Article  Google Scholar 

  54. M.-Q. Chen and M.S. Wang: Phys. Lett. A 149, 441 (1990)

    Article  CAS  Google Scholar 

  55. K. Imafuku, I. Ohba, Y. Yamanaka: Phys. Lett. A 204, 329 (1995)

    Article  CAS  Google Scholar 

  56. K.L. Jensen and F.A. Buot: Appl. Phys. Lett. 55, 669 (1989)

    Article  Google Scholar 

  57. J.G. Muga, S. Brouard, and R. Sala: Phys. Lett. A 167, 24 (1992)

    Article  Google Scholar 

  58. T.P. Spiller, T.D. Clark, R.J. Prance, and H. Prance: Europhys. Lett. 12, 1 (1990)

    Article  Google Scholar 

  59. E. Pollak and W.H. Miller: Phys. Rev. Lett 53, 115 (1984)

    Article  CAS  Google Scholar 

  60. T. Martin and R. Landauer: Phys. Rev. A 47, 2023 (1993)

    Article  Google Scholar 

  61. C.R. Leavens: Superlattices and Microstructures 23, 795 (1998)

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  63. C.R. Leavens and G.C. Aers: J. Vac. Sci. Technol. A 6, 305 (1988)

    Article  CAS  Google Scholar 

  64. D. Sokolovski and J.N.L. Connor: Phys. Rev. A 44, 1500 (1991)

    Article  Google Scholar 

  65. D. Sokolovski and J.N.L. Connor: Solid State Commun. 89, 475 (1994)

    Article  CAS  Google Scholar 

  66. D. Sokolovski: Phys. Rev. A 52, R5 (1995)

    Google Scholar 

  67. D. Sokolovski: Phys. Rev. Lett. 79, 4946 (1997)

    Article  CAS  Google Scholar 

  68. D. Sokolovski: Phys. Rev. A 57, R1469 (1998)

    Article  CAS  Google Scholar 

  69. C.R. Leavens: Found. Phys. 25, 229 (1995)

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  71. J.G. Muga, S. Brouard, and R. Sala: J. Phys. Condens. Matter 4, L579 (1992)

    Article  Google Scholar 

  72. S. Brouard, R. Sala, and J.G. Muga: Europhys. Lett. 22, 159 (1993)

    Article  Google Scholar 

  73. B.A. van Tiggelen, A. Tip, and A. Lagendijk: J. Phys. A 26, 1731 (1993)

    Article  Google Scholar 

  74. C.R. Leavens: Bohmian Mechanics and the Tunneling Time Problem for Electrons. In: Proceedings of the Adriatico Research Conference on Tunneling and its Implications, ed. by D. Mugnai, A. Ranfagni, L.S. Schulman ( World Scientific, Singapore 1997 ) pp. 100–120

    Google Scholar 

  75. A.M. Steinberg: Phys. Rev. Lett. 74, 2405 (1995)

    Article  Google Scholar 

  76. A.M. Steinberg: Phys. Rev. A 52, 32 (1995)

    Article  CAS  Google Scholar 

  77. G. Iannaccone: Weak Measurement and the Traversal Time Problem. In: Proceedings of the Adriatico Research Conference on Tunneling and its Implications, ed. by D. Mugnai, A. Ranfagni, L.S. Schulman ( World Scientific, Singapore 1997 ) pp. 292–309

    Google Scholar 

  78. Y. Aharonov, D.Z. Albert, and L. Vaidman: Phys. Rev. Lett. 60, 1351 (1988)

    Article  Google Scholar 

  79. Y. Aharonov and L. Vaidman: Phys. Rev. A 41, 11 (1990)

    Article  CAS  Google Scholar 

  80. C.R. Leavens: Solid State Commun. 74, 923 (1990)

    Article  Google Scholar 

  81. C.R. Leavens: Solid State Commun. 76, 253 (1990)

    Article  CAS  Google Scholar 

  82. N. Yamada: Phys. Rev. A 54, 182, (1996)

    Article  CAS  Google Scholar 

  83. M. Gell-Mann and J.B. Hartle: In: Proceedings of the 25th International Conference on High Energy Physics, ed. by K.K. Phua and Y. Yamaguchi ( World Scientific, Singapore 1991 )

    Google Scholar 

  84. D. Sokolovski and J.N.L. Connor: Phys. Rev. A 47, 4677 (1993)

    Article  Google Scholar 

  85. D. Sokolovski, S. Brouard, and J.N.L. Connor: Phys. Rev. A 50, 1240 (1994)

    Article  CAS  Google Scholar 

  86. H.A. Fertig: Phys. Rev. Lett. 65, 2321 (1990)

    Article  Google Scholar 

  87. H.A. Fertig: Phys. Rev. B 47, 1346 (1993)

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Yamada, N. (2003). The Tunneling Time Problem Revisited. In: Nejo, H. (eds) Nanoelectrodynamics. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05084-2_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-05084-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07679-4

  • Online ISBN: 978-3-662-05084-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics