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 $t<t^{\ast }$, 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 $t\gg t^{\ast }$ and $\chi >{\chi }_{\mathrm{cr}}$ 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.

revised version, PRL in press, 4 pages, 4 figs (fig 3 with reduced quality)