Journal of Statistical Physics

, Volume 80, Issue 1, pp 125–146

Effective conductivity and skew Brownian motion

  • Reinhard Lang

DOI: 10.1007/BF02178356

Cite this article as:
Lang, R. J Stat Phys (1995) 80: 125. doi:10.1007/BF02178356


We consider heat conduction in a periodic body which is composed of finitely many different components. The effective conductivity is represented in terms of skew Brownian motion. The representation formula is a fluctuation-dissipation relation. The dissipation term in this formula is related to the transmission of heat through the surface separating the different components of the body; it is described by the skew reflections of Brownian motion at these surfaces. The problems caused by the discontinuity of the microscopic conductivity are handled in the framework of Dirichlet forms.

Key Words

Effective conductivity Green-Kubo formula discontinuous random media skew Brownian motion reversible diffusions Dirichlet forms 

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Reinhard Lang
    • 1
  1. 1.Institut für Angewandte MathematikHeidelbergGermany

Personalised recommendations