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Electron Localization in Disordered Systems

  • K. B. Efetov
Part of the NATO ASI Series book series (NSSB, volume 218)

Abstract

These lectures contain a review of results obtained by the supersymmetry method in the theory of disordered metals. It is shown, how such problems as level statistics in a limited volume, localization in wires, films and granulated materials, Anderson transition, can be reduced to the study of supermatrix σ-models in spaces of different dimensionality. The solution of the σ-models in these cases is presented. The group of the symmetry of Q-matrices entering the σ- model under consideration is noncompact. The role of the noncompactness is discussed. The phenomenon of localization is a formal consequence of this property. The noncompactness results in a very unusual critical behavior near the Anderson transition which is inconsistent with the hypothesis of one parameter scaling.

Keywords

Correlation Function Schrodinger Equation Localization Length Previous Chapter Bethe Lattice 
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.

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References

  1. 1.
    P.W. Anderson, Phys. Rev. 109, 1492, 1958ADSCrossRefGoogle Scholar
  2. 2.
    N.F. Mott, W.D. Twose, Adv. Phys. 10, 107, 1961; V.L. Berenzinsky, Zh. eksp. teor. Fiz. 65, 1251, 1973 (Sov. Phys. JETP, 38, 620, 1974)ADSCrossRefGoogle Scholar
  3. 3.
    D.J. Thouless, J. Phys. C 8, 1803, 1975; Phys. Rev. Lett. 39, 1167, 1977ADSCrossRefGoogle Scholar
  4. 4.
    E. Abrahams, P.W. Anderson, D.C. Licciardello, T.V. Ramakrishnan, Phys. Rev. Lett. 42, 673, 1979ADSCrossRefGoogle Scholar
  5. 5.
    E.P. Wigner, Ann. Math. 53 36, 1951MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    A.A. Abrikosov, L.P. Gor’kov, I.E. Dzyaloshinsky: Methods of Quantum Field Theory in Statistical Physics (New York: Prentice Hall).Google Scholar
  7. 7.
    L.P. Gor’kov, A.I. Larkin, D.E. Khmel’nitsky, Pis’ma Zh. eksp. theor. Fiz. 30, 248, 1979 (Sov. JETP Lett. 30, 228, 1979)Google Scholar
  8. 8.
    F.A. Berezin, Dokl. Akad. Nauk SSSR, 137, 31, 1961; Method vtorichnogo Kvantovaniya ”Nauka”, 1965 (The Method of Second Quantization). (English translation published by Academic Press, N.Y: Math. Z. 1, 3, 1967MathSciNetGoogle Scholar
  9. 9.
    K.B. Efetov, Adv. in Physics 32, 53, 1983MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    A.J. McKane, Phys. Lett. A 76, 33, 1980.MathSciNetCrossRefGoogle Scholar
  11. 11.
    F.J. Dyson, J. Math. Phys. 3, 140,157,166, 1962; M.L. Mehta, F.J. Dyson, J. Math. Phys. 4, 713, 1963MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    J.J.M. Verbaarschot, H.A. Weidenmüller, M. R. Zirnbauer, Phys. Rep. 129, 367, 1985MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    L.P. Gor’kov, G.M. Eliashberg, Zh. eksp. teor. Fiz. 48, 1407, 1965 (Soviet Phys. JETP, 21, 940)Google Scholar
  14. 14.
    P.W. Anderson, D.J. Thouless, E. Abrahams, D.S. Fisher, Phys. Rev. B22, 3519, 1980MathSciNetADSGoogle Scholar
  15. 15.
    A.M. Polyakov, Phys. Lett. B59, 79, 1975MathSciNetADSGoogle Scholar
  16. 16.
    E. Brezin, J. Zinn-Justin, Phys. Rev. B14, 3110, 1976ADSGoogle Scholar
  17. E. Brezin, J. Zinn-Justin, J.C. Le Guillou, Phys. Rev. D14, 2615, 1976ADSGoogle Scholar
  18. E. Brezin, S. Hikami, J. Zinn-Justin, Nucl. Phys. B165, 528, 1980ADSCrossRefGoogle Scholar
  19. 17.
    L. Schäfer, F. Wegner, Z. Phys. B38, 113, 1980ADSCrossRefGoogle Scholar
  20. K.B. Efetov, A.I. Larkin, D.E. Khmel’nitskii, Zh. eksp. teor. Fiz. 79, 1120, 1980 (Sov. Phys. JETP, 52, 568, 1980)MathSciNetGoogle Scholar
  21. 18.
    F. Wegner, Z. Phys. B44, 9, 1976MathSciNetADSGoogle Scholar
  22. 19.
    F. Wegner, Nucl. Phys. B, 316, 663, 1989MathSciNetADSCrossRefGoogle Scholar
  23. 20.
    S. Hikami, A.I. Larkin, Y. Nagaoka, Progr. Theor. Phys. 62, 707, 1980ADSCrossRefGoogle Scholar
  24. 21.
    F. Wegner, Z. Phys. 25, 327, 1976Google Scholar
  25. 22.
    W. Götze, Sol. St. Commun. 27, 1393, 1978; Phil. Mag.B43, 219, 1981; J. Phys. C12, 1279, 1979ADSCrossRefGoogle Scholar
  26. 23.
    P. Wölfle, D. Vollhardt, Phys. Rev. Lett. 45, 842, 1980; Phys. Rev. B22, 4666, 1980ADSCrossRefGoogle Scholar
  27. 24.
    V.G. Vaks, A.I. Larkin, S.A. Pikin, Zh. eksp. teor. Fiz. 52, 1089, 1967Google Scholar
  28. 25.
    K.B. Efetov, Pis’ma v Zh. eksp. teor. Fiz. 40, 17, 1984 (Sov. Phys. JETP Lett. 40, 738, 1984); Zh. eksp. teor. Fiz. 88, 1032, 1984 (Sov. Phys. JETP 61, 606, 1984), Zh. eksp. teor. Fiz. 92, 638, 1987 (Sov. Phys. JETP 65, 360, 1987); Zh. eksp. teor. Fiz. 93, 1125, 1987 (Sov. Phys. JETP 66, 634, 1987); M.R. Zirnbauer, Nucl. Phys. B, 265, 375, 1986; Phys. Rev. 34, 6394, 1986Google Scholar
  29. 26.
    K.B. Efetov, Zh. eksp. teor. Fiz. 94, 357, 1988 (Sov. Phys. JETP, 67, 199, 1988)Google Scholar
  30. 27.
    S. Kirkpatrick, Rev. Mod. Phys. 45, 574, 1973ADSCrossRefGoogle Scholar
  31. 28.
    B.L. Altshuler, Pis’ma Zh. eksp. teor. Fiz. 41, 530, 1985 (Sov. Phys. JETP Lett. 41, 648,1985); P.A. Lee, A.D. Stone, Phys. Rev. Lett. 55, 1622, (1985)Google Scholar
  32. 29.
    B. Shapiro, Phys. Rev. B34, 4394, 1986ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • K. B. Efetov
    • 1
  1. 1.Max-Planck-Institut für FestkörperforschungStuttgart 80Federal Republic of Germany

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