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Localization and Fluctuations

  • Angus MacKinnon
Part of the NATO ASI Series book series (NSSB, volume 254)

Abstract

The subject of fluctuations in the transport properties of disordered solids is often presented as an effect that was first observed in the mid 80’s. It may well be that such effects were first observed experimentally at that time, but they have been dogging the theory and especially those doing computer simulations from much earlier. In this paper I shall present a personal view of the subject. I offer no apology for the large dose of hindsight which the discussion will contain.

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References

  1. [1]
    V.L. Bonch-Bruevich, Fundamental Physics of Amorphous Semiconductors, F. Yonezawa, ed., p. 145, Springer Verlag, Berlin, Heidelberg (1981)CrossRefGoogle Scholar
  2. [2]
    N.F. Mott and W.D. Twose, Adv. Phys. 10, 107 (1961)ADSCrossRefGoogle Scholar
  3. [3]
    G. Czycholl and B. Kramer, Z. Phys. B 39, 193 (1980)CrossRefMathSciNetGoogle Scholar
  4. [4]
    A. MacKinnon, J. Phys. C: Sol. St. Phys. 13, L1031 (1980)ADSCrossRefGoogle Scholar
  5. [5]
    G. Czycholl, B. Kramer, and A. MacKinnon, Z. Phys. B 43, 5 (1981)CrossRefGoogle Scholar
  6. [6]
    B. Kramer, A. MacKinnon, and D. Weaire, Phys. Rev. B 23, 6357 (1981)ADSCrossRefGoogle Scholar
  7. [7]
    R. Landauer, Phil. Mag. 21, 863 (1970)ADSCrossRefGoogle Scholar
  8. [8]
    E.N. Economou and C. M. Soukoulis, Phys. Rev. Lett. 46, 618 (1981)ADSCrossRefGoogle Scholar
  9. [9]
    D.C. Langreth and E. Abrahams, Phys. Rev. B 31, 2978 (1981)CrossRefGoogle Scholar
  10. [10]
    M.Ya. Azbel, Phys. Rev. B 28, 4106 (1983)ADSCrossRefGoogle Scholar
  11. [11]
    J.B. Pendry, J. Phys. C: Sol. St. Phys. 20, 733 (1987)ADSCrossRefGoogle Scholar
  12. [12]
    P.W. Anderson, Phys. Rev. 109, 1492 (1958)ADSCrossRefGoogle Scholar
  13. [13]
    B. Andereck, E. Abrahams, J. Phys. C: Sol. St. Phys. 13,L383 (1980)ADSGoogle Scholar
  14. [14]
    J. Sak, B. Kramer, Phys. Rev. 24, 1761 (1981)ADSCrossRefGoogle Scholar
  15. [15]
    Y. Kantor, A. Kapitulnik, Sol. St. Commun. 42, 161 (1982)ADSCrossRefGoogle Scholar
  16. [16]
    A.A. Abrikosov, Sol. St. Commun. 37, 997 (1981)ADSCrossRefGoogle Scholar
  17. [17]
    A.J. O’Connor, Commun. Math. Phys. 45, 63 (1975)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  18. [18]
    P.D. Kirkman and J.B. Pendry, J. Phys. C: Sol. St. Phys. 17, 4327 (1984);ADSCrossRefGoogle Scholar
  19. [18a]
    P.D. Kirkman and J.B. Pendry, J. Phys. C: Sol. St. Phys.17, 5707 (1984)ADSCrossRefGoogle Scholar
  20. [19]
    M. Büttiker, Y. Imry, R. Landauer, and S. Pinhas, Phys. Rev. B 31, 6207 (1985)CrossRefGoogle Scholar
  21. [20]
    K.S. Chase, PhD Thesis, University of London (1987)Google Scholar
  22. [21]
    J.B. Pendry, A. MacKinnon, and A.B. Prêtre, Physica A 168, 400 (1990)CrossRefGoogle Scholar
  23. [22]
    R.G. Wheeler, K.K. Choi, A. Goel, R. Wisnieff, and D.E. Prober, Phys. Rev. Lett. 49, 1574 (1982)ADSCrossRefGoogle Scholar
  24. [23]
    S. Washburn and R.A. Webb, Adv. Phys. 35, 375 (1986)ADSCrossRefGoogle Scholar
  25. [24]
    P.A. Lee and A.D. Stone, Phys. Rev. Lett. 55, 1622 (1985)ADSCrossRefGoogle Scholar
  26. [25]
    B.L. Altshuler, JETP Lett. 41, 648 (1985)ADSGoogle Scholar
  27. [26]
    K.S. Chase and A. MacKinnon, J. Phys. C: Sol. St. Phys. 20, 6189 (1987)ADSCrossRefGoogle Scholar
  28. [27]
    H.H. Bethe, Proc. R. Soc. A 216, 45 (1935)Google Scholar
  29. [28]
    A. Cayley, Collected Mathematical Papers, Vol 3 (1889)Google Scholar
  30. [29]
    E. Abrahams, P.W. Anderson, D.C. Licciardello, and T.V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Angus MacKinnon
    • 1
  1. 1.Blackett LaboratoryImperial CollegeLondonUK

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