Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
Abstract
We study the spreading of an initially localized wavepacket in two nonlinear chains (discrete nonlinear Schroedinger and quartic Klein-Gordon) with disorder. Previous studies suggest that there are many initial conditions such that the second moment of the norm and energy density distributions diverge as a function of time. We find that the participation number of a wavepacket does not diverge simultaneously. We prove this result analytically for norm-conserving models and strong enough nonlinearity. After long times the dynamical state consists of a distribution of nondecaying yet interacting normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this result holds for any initially localized wavepacket, a limit profile for the norm/energy distribution with infinite second moment should exist in all cases which rules out the possibility of slow energy diffusion (subdiffusion). This limit profile could be a quasiperiodic solution (KAM torus).
Cite
@article{arxiv.0710.2621,
title = {Absence of Wavepacket Diffusion in Disordered Nonlinear Systems},
author = {G. Kopidakis and S. Komineas and S. Flach and S. Aubry},
journal= {arXiv preprint arXiv:0710.2621},
year = {2009}
}