Path Integral Approach to Strongly Nonlinear Composite

Details Path Integral Approach to Strongly Nonlinear Composite Path Integral Approach to Strongly Nonlinear Composite

2000-05-29

arxiv.org/abs/cond-mat/0005504v1

Phys. Rev. B 62 (2000) 8576.

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 1 figure, to appear in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.62.8576

We study strongly nonlinear disordered media using a functional method. We solve exactly the problem of a nonlinear impurity in a linear host and we obtain a Bruggeman-like formula for the effective nonlinear susceptibility. This formula reduces to the usual Bruggeman effective medium approximation in the linear case and has the following features: (i) It reproduces the weak contrast expansion to the second order and (ii) the effective medium exponent near the percolation threshold are $s=1$, $t=1+\kappa$, where $\kappa$ is the nonlinearity exponent. Finally, we give analytical expressions for previously numerically calculated quantities.

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