Control of wavepacket spreading in nonlinear finite disordered lattices

TL;DR

This paper investigates how gradually increasing nonlinearity affects wavepacket spreading in disordered lattices, revealing a critical ramping speed that determines whether the wave remains localized or becomes delocalized.

Contribution

It introduces a model for linearly ramping nonlinearity in finite disordered lattices and identifies a critical ramping speed dependent on disorder strength and system size.

Findings

A critical ramping speed separates localized and delocalized states.

Wavepacket spreading depends on the relation between localization length and system size.

Self-trapping occurs when nonlinearity-induced frequency shifts dominate.

Abstract

In the absence of nonlinearity all normal modes (NMs) of a chain with disorder are spatially localized (Anderson localization). We study the action of nonlinearity, whose strength is ramped linearly in time. It leads to a spreading of a wavepacket due to interaction with and population of distant NMs. Eventually the nonlinearity induced frequency shifts take over, and the wavepacket becomes selftrapped. On finite chains a critical ramping speed is obtained, which separates delocalized final states from localized ones. The critical value depends on the strength of disorder and is largest when the localization length matches the system size.