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arXiv · 0710.2621

Absence of Wavepacket Diffusion in Disordered Nonlinear Systems

G. Kopidakis·S. Komineas·S. Flach·S. Aubry
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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).

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G. Kopidakis, S. Komineas, S. Flach, S. Aubry. 2007-10-13. Absence of Wavepacket Diffusion in Disordered Nonlinear Systems. https://doi.org/10.1103/physrevlett.100.084103

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