From power law to Anderson localization in nonlinear Schr\"odinger equation with nonlinear randomness

TL;DR

This paper investigates wave propagation in nonlinear random potentials, revealing regimes of self-organized criticality with power-law decay and Anderson localization with exponential decay, advancing understanding of nonlinear disordered systems.

Contribution

It introduces a framework to distinguish between self-organized criticality and Anderson localization in nonlinear Schrödinger equations with nonlinear randomness.

Findings

Identification of regimes with power-law decay of transport.

Observation of exponential decay indicating Anderson localization.

Demonstration of the transition between different dynamical regimes.

Abstract

We study the propagation of coherent waves in a nonlinearly-induced random potential, and find regimes of self-organized criticality and other regimes where the nonlinear equivalent of Anderson localization prevails. The regime of self-organized criticality leads to power-law decay of transport [Phys. Rev. Lett. 121, 233901 (2018)], whereas the second regime exhibits exponential decay.