Quantum Percolation

  • Yigal Meir
  • Amnon Aharony
  • A. Brooks Harris


Most of the lectures in these proceedings discuss the conductivity of classical resistor networks, in which basic resistors are present (with concentration p) or absent (with concentration 1-p)). The conductivity becomes finite above the geometrical percolation threshold, pc, as soon as there exists an infinite cluster, and its properties are uniquely determined by the geometry of the backbone of this cluster. Both of these aspects change when one considers a quantum particle, whose wave function obeys the Schrodinger equation. Since the wave function may vanish on many sites on the infinite cluster, due to interference effects, the quantum threshold pq turns out to be higher than pc. Quantum conductance also depends drastically on dangling (“dead end”) bonds: a wave may be totally reflected by such bonds, yielding no conductance between the two ends of the sample. Quantitatively, these effects imply localization of all the electronic wave functions up to pq.


Wave Function Quantum Particle Schrodinger Equation Quantum Hall Effect Basic Resistor 
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.
    P.W. Anderson, Phys. Rev. 109: 1492 (1958).CrossRefGoogle Scholar
  2. 2.
    Y. Shapir, A. Aharony and A.B. Harris, Phys. Rev. Lett. 49:486 (1982) and references therein.Google Scholar
  3. 3.
    F.J. Wegner, Z. Phys. B36:209 (1980) and references.Google Scholar
  4. 4.
    M.E. Fisher, in Statistical Mechanics and Statistical Methods in Theory and Applications, edited by U. Landman ( Plenum, N.Y. 1977 ).Google Scholar
  5. 5.
    Details will be published elsewhere.Google Scholar
  6. 6.
    E. Abrahams, P.W. Anderson, D.C. Liciardello and T.V. Ramakrishnan, Phys. Rev. Lett. 42: 673 (1979).CrossRefGoogle Scholar
  7. 7.
    A.B. Harris, Phys. Rev. Lett. 49:296 (1982); Phys. Rev. B29: 2519 (1984).CrossRefGoogle Scholar
  8. 8.
    Y. Gefen, Y. Imry and M. Ya. Azbel’, J. Phys. C15: L655 (1982).Google Scholar
  9. 9.
    D. Hofstadter, Phys. Rev. B14: 2239 (1976).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Yigal Meir
    • 1
  • Amnon Aharony
    • 1
  • A. Brooks Harris
    • 2
  1. 1.School of Physics and AstronomyTel-Aviv UniversityTel-AvivIsrael
  2. 2.Department of PhysicsUniversity of PennsylvaniaPhiladelphiaUSA

Personalised recommendations