Current relaxation in nonlinear random media

TL;DR

This paper investigates how wave packets relax in nonlinear random media, revealing a power-law decay of survival probability influenced by nonlinearity and localization, with universal behavior indicating nonlinearity-induced delocalization.

Contribution

It introduces a scaling law for the decay exponent in nonlinear random media and identifies a universal decay regime linked to delocalization effects.

Findings

Survival probability decays as $1/t^{ ext{alpha}}$

Scaling law for alpha depending on nonlinearity and localization length

Universal decay with alpha=2/3 indicating delocalization

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.