Expansion of a wave-packet in lattices with disorder and nonlinearity

TL;DR

This paper demonstrates that increasing disorder can enhance wave-packet spreading in lattices, and nonlinearity further promotes expansion, revealing a transition from diffusion to localization.

Contribution

It provides both theoretical and experimental evidence that disorder and nonlinearity influence wave-packet dynamics in lattices, highlighting a transition between spreading and localization regimes.

Findings

Disorder can enhance wave spreading in lattices.

Nonlinearity facilitates wave-packet expansion.

A diffusion peak indicates the transition between spreading and localization.

Abstract

We show, theoretically and experimentally, the counterintuitive result that an increase of disorder can result in an enhanced spreading of an initially localized excitation. Moreover, we find that adding a focusing nonlinearity facilitates the expansion of the wave-packet even further by increasing its effective size. We find a clear transition between between the regions of enhanced spreading (weak disorder) and localization (strong localization) described by a "diffusion peak".