Scaling of energy spreading in strongly nonlinear disordered lattices

TL;DR

This paper investigates how strong nonlinearity affects energy spreading in disordered lattices, revealing a subdiffusive behavior and establishing a scaling relation that explains the slowing down at low densities.

Contribution

It introduces a phenomenological nonlinear diffusion model and confirms a new scaling law for energy spreading in nonlinear disordered systems.

Findings

Energy spreads nearly subdiffusively due to chaotic interactions.

A one-parameter scaling relation between spreading velocity and density is established.

Spreading slows down at very low densities compared to pure power law.

Abstract

To characterize a destruction of Anderson localization by nonlinearity, we study the spreading behavior of initially localized states in disordered, strongly nonlinear lattices. Due to chaotic nonlinear interaction of localized linear or nonlinear modes, energy spreads nearly subdiffusively. Based on a phenomenological description by virtue of a nonlinear diffusion equation we establish a one-parameter scaling relation between the velocity of spreading and the density, which is confirmed numerically. From this scaling it follows that for very low densities the spreading slows down compared to the pure power law.