Path Integral Approach to Strongly Nonlinear Composite

Abstract

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.

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

References in corpus (3)

• Field distributions and effective-medium approximation for weakly nonlinear media
• Self-Consistent Effective-Medium Approximations with Path Integrals
• A Path Integral Approach to Effective Non-Linear Medium