Current relaxation in nonlinear random media

Abstract

We study the current relaxation of a wave packet in a nonlinear random sample coupled to the continuum and show that the survival probability decays as $P(t) \sim 1/t^{\alpha}$. For intermediate times $t<t^*$, the exponent $\alpha$ satisfies a scaling law $\alpha =f(\Lambda=\chi/l_{\infty})$ where $\chi$ is the nonlinearity strength and $l_{\infty}$ is the localization length of the corresponding random system with $\chi=0$. For $t\gg t^*$ and $\chi>\chi_{\rm cr}$ we find a universal decay with $\alpha=2/3$ which is a signature of the {\it nonlinearity-induced delocalization}. Experimental evidence should be observable in coupled nonlinear optical waveguides.