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).

References in corpus (2)

• Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
• Expansion of a Bose-Einstein Condensate in the Presence of Disorder

Cited by in corpus (11)

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• Anderson localization of a weakly interacting one dimensional Bose gas
• Transmission thresholds in time-periodically driven nonlinear disordered systems
• Role of pinning potentials in heat transport through disordered harmonic chain
• Nonlinear delocalization on disordered Stark ladder
• Density Correlations in Cold Atomic Gases: Atomic Speckles in the Presence of Disorder
• Control of wavepacket spreading in nonlinear finite disordered lattices