Current Relaxation in Nonlinear Random Media

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)~1/t^α. For intermediate times t<t*, the exponent α satisfies a scaling law α=f(Λ=χ/l_∞), where χ is the nonlinearity strength and l_∞ is the localization length of the corresponding random system with χ=0. For tt* and χ>χcr we find a universal decay with α=2/3 which is a signature of the nonlinearity-induced delocalization. Experimental evidence should be observable in coupled nonlinear optical waveguides.