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Mesoscopic Physics and Electronics pp 109–119Cite as

Crossover from Quantum to Classical Regime

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

Abstract

The quantum Hall effect is a manifestation of quantum effects in macroscopic transport phenomena. In particular, the integer quantum Hall effect has provided various fundamental problems in solid state physics such as localization in high magnetic fields, a topological winding number, edge channels, etc. It has been used also as a resistance standard and has opened up a way to examine the validity of quantum electrodynamics through comparison of the fine structure constant.

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References

  1. T. Ando, Prog. Theor. Phys. Suppl. 84, 69 (1985)

    Article  CAS  Google Scholar 

  2. The Quantum Hall Effect,edited by R.E. Prange and S.M. Girvin (Springer, New York, 1987)

    Google Scholar 

  3. H. Aoki, Rev. Progr. Phys. 50, 655 (1987)

    Article  Google Scholar 

  4. R.B. Laughlin, Phys. Rev. B 23, 5632 (1981)

    Article  Google Scholar 

  5. D.J. Thouless, M. Kohmoto, M.P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982)

    Article  CAS  Google Scholar 

  6. J. Avron, R. Seiler, and B. Simon, Phys. Rev. Lett. 51, 51 (1983)

    Article  Google Scholar 

  7. B. Simon, Phys. Rev. Lett. 51, 2167 (1983)

    Article  Google Scholar 

  8. Q. Niu, D.J. Thouless, and Y.-S. Wu, Phys. Rev. B 31, 3372 (1985)

    Article  Google Scholar 

  9. H. Aoki and T. Ando, Phys. Rev. Lett. 57, 3093 (1986)

    Article  Google Scholar 

  10. R. Landauer, IBM J. Res. Dev. 1, 223 (1957); Phil. Mag. 21, 863 (1970)

    Google Scholar 

  11. M. Büttiker, Phys. Rev. Lett. 57, 1761 (1986)

    Article  Google Scholar 

  12. E.N. Economou and C.M. Soukoulis, Phys. Rev. Lett. 46, 618 (1981)

    Article  CAS  Google Scholar 

  13. D.S. Fisher and P.A. Lee, Phys. Rev. B 23, 6851 (1981)

    Article  CAS  Google Scholar 

  14. D.C. Langreth and E. Abrahams, Phys. Rev. B 24, 2978 (1981)

    Article  CAS  Google Scholar 

  15. D.J. Thouless, Phys. Rev. Lett. 47, 972 (1981)

    Article  CAS  Google Scholar 

  16. T. Ando and H. Aoki, Physica B 184, 365 (1983)

    Article  Google Scholar 

  17. J. Hajdu, M. Janßen, and O. Viehweger, Z. Phys. B 66, 433 (1987)

    Article  Google Scholar 

  18. T. Ohtsuki and Y. Ono, Solid State Commun. 68, 787 (1988)

    Article  CAS  Google Scholar 

  19. A.H. MacDonald, T.M. Rice, and W.F. Brinkman, Phys. Rev. B 28, 3648 (1983)

    Article  Google Scholar 

  20. J. Riess, J. Phys. C 17, L847 (1984)

    Article  Google Scholar 

  21. D.J. Thouless, J. Phys. C 18, 6211 (1985)

    Article  Google Scholar 

  22. O. Heinonen and P.L. Taylor, Phys. Rev. B 32, 633 (1985)

    Article  CAS  Google Scholar 

  23. D. Pfannkuche and J. Hajdu, Phys. Rev. B 46, 7032 (1992)

    Article  Google Scholar 

  24. D.J. Thouless, Phys. Rev. Lett. 71, 1879 (1993)

    Article  CAS  Google Scholar 

  25. C. Wexler and D.J. Thouless, Phys. Rev. B 49, 4815 (1994)

    Article  Google Scholar 

  26. H. Hirai and S. Komiyama, Phys. Rev. B 49, 14012 (1994)

    Article  CAS  Google Scholar 

  27. See, for example, S. Komiyama and H. Nii, Physica B 184, 7 (1993) and references cited therein

    Google Scholar 

  28. S. Kawaji, K. Hirakawa, and M. Nagata, Physica B 184, 17 (1993)

    Article  Google Scholar 

  29. T. Ando, Phys. Rev. B 44, 8017 (1991)

    Article  Google Scholar 

  30. T. Ando, J. Phys. Soc. Jpn. 35, 3199 (1986)

    Article  Google Scholar 

  31. S. Koch, R.J. Haug, K. von Klitzing, and K. Ploog, Phys. Rev. Lett. 67, 883 (1991)

    Article  CAS  Google Scholar 

  32. T. Ando and H. Aoki, J. Phys. Soc. Jpn. 54, 2238 (1985)

    Article  CAS  Google Scholar 

  33. M. Büttiker, Phys. Rev. B 32, 1846 (1985)

    Article  Google Scholar 

  34. M. Büttiker, Phys. Rev. B 33, 3020 (1986)

    Article  Google Scholar 

  35. M. Büttiker, IBM J. Res. Develop. 32, 63 (1988)

    Article  Google Scholar 

  36. J.L. D’Amato and H.M. Pastawski, Phys. Rev. B 41, 7411 (1990)

    Article  Google Scholar 

  37. T. Ando, Surf. Sci. 361 /362, 270 (1996)

    Article  Google Scholar 

  38. T. Ando, J. Phys. Soc. Jpn. 52, 1893 (1983); 53, 310 (1983); 53, 3126 (1983); Phys. Rev. B 40, 9965 (1989)

    Google Scholar 

  39. B. Huckestein and B. Kramer, Phys. Rev. Lett. 64, 1437 (1990); Solid State Commun 71, 445 (1989)

    Google Scholar 

  40. T. Ando, Phys. Rev. B 49, 4679 (1994)

    Article  Google Scholar 

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Authors
  1. T. Ando
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Editor information

Editors and Affiliations

  1. Institute for Solid State Physics, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106, Japan

    T. Ando

  2. Institute of Industrial Science, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106, Japan

    Y. Arakawa

  3. Department of Electrical and Electronic Engineering, Tokyo Institute of Technology, 2-1-12 O-okayama, Meguro-ku, Tokyo 152, Japan

    K. Furuya

  4. Department of Basic Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153, Japan

    S. Komiyama

  5. Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567, Japan

    H. Nakashima

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© 1998 Springer-Verlag Berlin Heidelberg

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Ando, T. (1998). Crossover from Quantum to Classical Regime. In: Ando, T., Arakawa, Y., Furuya, K., Komiyama, S., Nakashima, H. (eds) Mesoscopic Physics and Electronics. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71976-9_15

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  • DOI: https://doi.org/10.1007/978-3-642-71976-9_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-71978-3

  • Online ISBN: 978-3-642-71976-9

  • eBook Packages: Springer Book Archive

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