The crossover from strong to weak chaos for nonlinear waves in disordered systems

TL;DR

This paper investigates the transition from strong to weak chaos in disordered nonlinear wave systems, revealing a new regime of faster wave spreading and analyzing the crossover dynamics through extensive simulations.

Contribution

It identifies and characterizes a new strong chaos regime with faster spreading, and introduces a novel technique for visualizing slow dynamical crossovers.

Findings

Strong chaos exhibits wave spreading as t^{1/2}

Weak chaos shows spreading as t^{1/3}

A crossover from strong to weak chaos occurs at larger times

Abstract

We observe a crossover from strong to weak chaos in the spatiotemporal evolution of multiple site excitations within disordered chains with cubic nonlinearity. Recent studies have shown that Anderson localization is destroyed, and the wave packet spreading is characterized by an asymptotic divergence of the second moment $m_2$ in time (as $t^{1/3}$), due to weak chaos. In the present paper, we observe the existence of a qualitatively new dynamical regime of strong chaos, in which the second moment spreads even faster (as $t^{1/2}$), with a crossover to the asymptotic law of weak chaos at larger times. We analyze the pecularities of these spreading regimes and perform extensive numerical simulations over large times with ensemble averaging. A technique of local derivatives on logarithmic scales is developed in order to quantitatively visualize the slow crossover processes.