Subdiffusion of nonlinear waves in quasiperiodic potentials

TL;DR

This paper investigates how nonlinearity affects wave packet spreading in quasiperiodic lattices, revealing subdiffusive behavior with distinct temporal regimes and the influence of fractal spectral structures.

Contribution

It extends the analysis of nonlinear wave dynamics in quasiperiodic potentials to large scales, identifying specific subdiffusive laws and the role of spectral fractality.

Findings

Asymptotic $m_2 \,\sim\, t^{1/3}$ law observed

Intermediate $m_2 \,\sim\, t^{1/2}$ regime identified

Fractal gap structure influences self-trapping events

Abstract

We study the spatio-temporal evolution of wave packets in one-dimensional quasiperiodic lattices which localize linear waves. Nonlinearity (related to two-body interactions) has destructive effect on localization, as recently observed for interacting atomic condensates [Phys. Rev. Lett. 106, 230403 (2011)]. We extend the analysis of the characteristics of the subdiffusive dynamics to large temporal and spatial scales. Our results for the second moment $m_2$ consistently reveal an asymptotic $m_2 \sim t^{1/3}$ and intermediate $m_2 \sim t^{1/2}$ laws. At variance to purely random systems [Europhys. Lett. 91, 30001 (2010)] the fractal gap structure of the linear wave spectrum strongly favors intermediate self-trapping events. Our findings give a new dimension to the theory of wave packet spreading in localizing environments.