Subdiffusion of nonlinear waves in quasiperiodic potentials

Abstract

We study the time evolution of wave packets in one-dimensional quasiperiodic lattices which localize linear waves. Nonlinearity (related to two-body interactions) has a destructive effect on localization, as observed recently for interacting atomic condensates (Lucioni et al 2011 Phys. Rev. Lett. 106 230403). 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 ∼ t 1/3 and an intermediate m 2 ∼ t 1/2 law. At variance with purely random systems (Laptyeva et al 2010 Europhys. Lett. 91 30001), the fractal gap structure of the linear wave spectrum strongly favours intermediate self-trapping events. Our findings give a new dimension to the theory of wave packet spreading in localizing environments. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.