Delocalization of wave packets in disordered nonlinear chains

TL;DR

This paper studies how wave packets in disordered nonlinear chains spread over time, showing that nonlinearity destroys Anderson localization and causes subdiffusive delocalization through mode resonances.

Contribution

It provides a detailed analysis of wave packet spreading, mode resonances, and the statistical properties of detrapping times in disordered nonlinear systems.

Findings

Nonlinearity destroys Anderson localization leading to subdiffusive spreading.

Mode-mode resonances facilitate incoherent delocalization.

Wave packets exhibit subdiffusive spreading without limits.

Abstract

We consider the spatiotemporal evolution of a wave packet in disordered nonlinear Schr\"odinger and anharmonic oscillator chains. In the absence of nonlinearity all eigenstates are spatially localized with an upper bound on the localization length (Anderson localization). Nonlinear terms in the equations of motion destroy Anderson localization due to nonintegrability and deterministic chaos. At least a finite part of an initially localized wave packet will subdiffusively spread without limits. We analyze the details of this spreading process. We compare the evolution of single site, single mode and general finite size excitations, and study the statistics of detrapping times. We investigate the properties of mode-mode resonances, which are responsible for the incoherent delocalization process.