Spreading of waves in nonlinear disordered media

TL;DR

This paper investigates how wave packets spread in nonlinear disordered media, identifying regimes of strong and weak chaos, and predicting a crossover influenced by nonlinearity and system parameters.

Contribution

It introduces a detailed analysis of wave spreading regimes, resonance probabilities, and a dynamical crossover in nonlinear disordered systems, extending to higher dimensions.

Findings

Identification of strong and weak chaos regimes

Prediction of a dynamical crossover between regimes

Critical values for nonlinearity and dimension effects

Abstract

We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We predict that wave packets can spread in two regimes of strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion equations, and predict a dynamical crossover from strong to weak chaos. The crossover is controlled by the ratio of nonlinear frequency shifts and the average eigenvalue spacing of eigenstates of the linear equations within one localization volume. We consider generalized models in higher lattice dimensions and obtain critical values for the nonlinearity power, the dimension, and norm density, which influence possible dynamical outcomes in a qualitative way.