Conductivity of a “colored” plane

  • V. G. Marikhin
Condensed Matter


The conductivity of a “colored” plane, i.e., a plane divided into domains differing in conductivity, is calculated. The exact relation between the effective conductivities of the cited and dual (with inverse conductivities) systems is derived for the isotropic case (i.e., the effective conductivity tensor is proportional to the unit matrix). The conductivity of two-colored systems such as a “chessboard” or triangular lattice is exactly calculated to give σ=(σ1σ2)1/2. The particular case of a “hexagon, ” as well as the duality relations for anisotropic systems and for a system in a magnetic field are discussed.

PACS numbers

73.50.Bk 75.70.Ak 


  1. 1.
    A. M. Dykhne, Zh. Éksp. Teor. Fiz. 59, 110 (1970) [Sov. Phys. JETP 32, 63 (1971)].Google Scholar
  2. 2.
    A. M. Dyugaev and Yu. N. Ovchinnikov, Zh. Éksp. Teor. Fiz. 117 (2000) (in press).Google Scholar
  3. 3.
    A. Yu. Kamenshchik and I. M. Khalatnikov, private communication.Google Scholar
  4. 4.
    Yu. N. Ovchinnikov, submitted for publication in Zh. Éksp. Teor. Fiz.Google Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2000

Authors and Affiliations

  • V. G. Marikhin
    • 1
  1. 1.Landau Institute of Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia

Personalised recommendations