Anderson localization or nonlinear waves? A matter of probability

TL;DR

This paper investigates how nonlinearity affects Anderson localization in disordered systems, revealing that even small nonlinearities can cause localization to break down with a probability that depends on system parameters.

Contribution

It demonstrates that finite probability exists for the breakdown of Anderson localization due to nonlinearity, with this probability increasing with nonlinearity and applicable across dimensions.

Findings

Finite probability of localization breakdown at small nonlinearities

Probability increases with nonlinearity and reaches unity at a threshold

Results extend to higher-dimensional systems

Abstract

In linear disordered systems Anderson localization makes any wave packet stay localized for all times. Its fate in nonlinear disordered systems is under intense theoretical debate and experimental study. We resolve this dispute showing that at any small but finite nonlinearity (energy) value there is a finite probability for Anderson localization to break up and propagating nonlinear waves to take over. It increases with nonlinearity (energy) and reaches unity at a certain threshold, determined by the initial wave packet size. Moreover, the spreading probability stays finite also in the limit of infinite packet size at fixed total energy. These results are generalized to higher dimensions as well.