Journal of Statistical Physics

, Volume 80, Issue 1, pp 125–146

Effective conductivity and skew Brownian motion

  • Reinhard Lang
Articles

DOI: 10.1007/BF02178356

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

Abstract

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 conductivityGreen-Kubo formuladiscontinuous random mediaskew Brownian motionreversible diffusionsDirichlet forms

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

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