Statistics of wave interactions in nonlinear disordered systems

TL;DR

This paper investigates the statistical properties of wave interactions in nonlinear disordered one-dimensional systems, focusing on localization, interaction strength, eigenvalue spacing, and resonance probabilities, with implications for wave packet spreading and quantum many-body problems.

Contribution

It provides a detailed statistical analysis of mode interactions, linking localization, overlap integrals, eigenvalue spacing, and resonance probabilities in nonlinear disordered systems.

Findings

Localization volume determines the number of interacting modes.

Overlap integrals quantify interaction strength.

Resonance probabilities influence wave packet spreading.

Abstract

We study the properties of mode-mode interactions for waves propagating in nonlinear disordered one-dimensional systems. We focus on i) the localization volume of a mode which defines the number of interacting partner modes, ii) the overlap integrals which determine the interaction strength, iii) the average spacing between eigenvalues of interacting modes, which sets a scale for the nonlinearity strength, and iv) resonance probabilities of interacting modes. Our results are discussed in the light of recent studies on spreading of wave packets in disordered nonlinear systems, and are related to the quantum many body problem in a random chain.