Field distributions and effective-medium approximation for weakly nonlinear media

Details Field distributions and effective-medium approximation for weakly nonlinear media Field distributions and effective-medium approximation for weakly nonlinear media

2000-01-17

arxiv.org/abs/cond-mat/0001228v1

Physical Review B 61, 9365 (2000)

Physics

Condensed Matter

Materials Science

12 pages, 6 eps figures

Scientific paper

10.1103/PhysRevB.61.9365

An effective-medium theory is proposed for random weakly nonlinear dielectric media. It is based on a new gaussian approximation for the probability distributions of the electric field in each component of a multi-phase composite. These distributions are computed to linear order from a Bruggeman-like self-consistent formula. The resulting effective-medium formula for the nonlinear medium reduces to Bruggeman's in the linear case. It is exact up to second order in a weak-disorder expansion, and close to the exact result in the dilute limit (in particular, it is exact for d=1 and d=infinity. In a high contrast situation, the noise exponents are kappa=kappa'=0 near the percolation threshold. Numerical results are provided for different weak nonlinearities.

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