Localization of electrons in infinitely long random systems - diagrammatic approach

  • W. Weller
V. Localisation
Part of the Lecture Notes in Physics book series (LNP, volume 206)


We describe the diagram analysis for the one-dimensional localization problem developed by Berezinskii in a simplified and modified form. Then we discuss the generalization to N coupled chains (a disordered wire). It is shown that all eigenstates are localized and that the localization length is approximately equal to NI2 (I2 scattering length for backward scattering at one chain).


Green Function Combinatorial Factor Localization Length Initial Vertex Diagram Analysis 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. /1/.
    N.F. Mott, and D.W. Twose, Adv.Phys.10,107 (1961).CrossRefADSGoogle Scholar
  2. /2/.
    V.L. Berezinskii,Zh.eksper.teor.Fiz.65,1251 (1973).Google Scholar
  3. /3/.
    D.J. Thouless, Phys.Rev. Letters 39,1167 (1977).CrossRefADSGoogle Scholar
  4. /4/.
    P.W. Anderson, D.J. Thouless, E. Abrahams, and D.S. Fisher, Phys.Rev.B22,3519 (1980).ADSMathSciNetGoogle Scholar
  5. /4a/.
    P.W. Anderson, Phys.Rev.B23,4828 (1981).ADSGoogle Scholar
  6. /5/.
    M.Ya. Azbel, Phys.Rev. Letters46,675 (1981).CrossRefADSGoogle Scholar
  7. /6/.
    W. Weller, V.N. Prigodin, and Yu.A. Firsov, phys.stat.sol.(b)110,143 (1982).CrossRefADSGoogle Scholar
  8. /7/.
    W. Weller, Yu.A. Firsov, and V.N. Prigodin, Proceedings of the International Seminar on “Localization in Disordered Systems”, Johnsbach 1983, ed. by W. Weller and P. Ziesche, B.G. Teubner Leipzig 1984.Google Scholar
  9. /8/.
    O.N. Dorokhov, Solid state Commun.44,915 (1982).CrossRefADSGoogle Scholar
  10. /9/.
    O.N. Dorokhov, Zh.eksper.teor.Fiz.85,1040 (1983).Google Scholar
  11. /10/.
    K.B. Efetov, and A.I. Larkin, ZH.eksper.teor.Fiz.85,764 (1983). K.B. Efetov, Adv.Phys.32,53(1983).Google Scholar
  12. /11/.
    A. MacKinnon, and B. Kramer, Phys. Rev. Letters 47, 1546 (1981).CrossRefADSGoogle Scholar
  13. /12/.
    P.W. Anderson, Phys. Rev.109,1942 (1958).Google Scholar
  14. /13/.
    E.N. Economou, and M.H. Cohen, Phys. Rev.B5,2931 (1972).ADSGoogle Scholar
  15. /14/.
    W. Weller, and M. Kasner, Contribution to MECO-Seminar 1984.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • W. Weller
    • 1
  1. 1.Sektion PhysikKarl-Marx-UniversitätLeipzig

Personalised recommendations