Advertisement

Zeitschrift für Physik B Condensed Matter

, Volume 42, Issue 4, pp 297–304 | Cite as

Stochastic properties of the resistivity in a one-dimensional disordered conductor

  • Reiner Kree
  • Albert Schmid
Article

Abstract

We investigate the stochastic properties of the resistanceR and its logarithm lnR for a one-dimensional disordered conductor of finite length and at zero temperature. In the model which we consider, the non-interacting electrons are scattered by a Gaussian random potential of vanishing correlation length. It is shown that for long samples, lnR is distributed according to a Gaussian law and the parameters of this distribution are calculated explicitly. For weak disorder potentials, we recover known relations between <lnR>, ln<R>, and ln<R−1>, whereas for strong disorder new results are derived.

Keywords

Spectroscopy Neural Network State Physics Complex System Nonlinear Dynamics 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1a.
    Mott, N.F., Twose, W.D.: Adv. Phys.10, 107 (1961)Google Scholar
  2. 1b.
    Borland, R.E.: Proc. Phys. Soc. London78, 926 (1961)Google Scholar
  3. 2.
    This is at least true if the Coulomb interaction is absent. This interaction may change the picture qualitatively [3]Google Scholar
  4. 3.
    Apel, W.: Conductivity of a 1-D System of Interacting Fermions in a Random Potential. Preprint 1981, Universität HannoverGoogle Scholar
  5. 4.
    Ishii, K.: Prog. Theor., Phys. Suppl.53, 77 (1973)Google Scholar
  6. 5.
    Anderson, P.W., Thouless, D.J., Abrahams, E., Fisher, D.S.: Phys. Rev. B22 (8), 3519 (1980)Google Scholar
  7. 6.
    Kramer, B.: PTB Mitteilungen1/1981Google Scholar
  8. 7a.
    Andereck, B., Abrahams, E.: J. Phys. C13, L 383 (1980)Google Scholar
  9. 7b.
    Abrahams, E., Stephen, M.J.: J. Phys. C13, L 377 (1980)Google Scholar
  10. 8.
    Halperin, B.I.: Phys. Rev.139, 104 (1965)Google Scholar
  11. 9.
    Stratonovich, R.L.: Topics in the Theory of Random Noise. New York: Gordon and Breach 1963Google Scholar
  12. 9b.
    Arnold, L.: Stochastische Differentialgleichungen. München-Wien: R. Oldenbourg Verlag 1973Google Scholar
  13. 10.
    Landauer, R.: Philos Mag.21, 104 (1970)Google Scholar
  14. 11.
    In general, we should introduce an additional label in order to distinguish between left-handed and right-handed eigen-functions. In the present context, no confusion arises if we omit this extra labelGoogle Scholar
  15. 12.
    The distribution (2.16) should not be used for an estimate of this small fractionGoogle Scholar
  16. 13.
    Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions. New York: Dover Publ. Inc. 1965Google Scholar
  17. 14.
    Note thatw st (q) andw st (s) are normalized each in its own way. Therefore,w st(q)=ε−1 w st(s)Google Scholar
  18. 15.
    E.g.: Smirnow, W.I.: Lehrgang der höheren Mathematik; Teil III/2. VEB Deutscher Verlag der Wissenschaften, Berlin 1974Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Reiner Kree
    • 1
  • Albert Schmid
    • 1
  1. 1.Institut für Theorie der Kondensierten MaterieUniversität KarlsruheKarlsruheGermany

Personalised recommendations