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Absence of wave packet diffusion in disordered nonlinear systems.

G Kopidakis1, S Komineas, S Flach

  • 1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.

Physical Review Letters
|March 21, 2008
PubMed
Summary
This summary is machine-generated.

In disordered nonlinear chains, wave packet spreading does not lead to simultaneous divergence of participation numbers. This finding rules out slow energy diffusion, suggesting a transition to quasiperiodic dynamics.

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Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Wave propagation

Background:

  • Disordered nonlinear chains exhibit complex wave packet spreading.
  • Previous research indicated potential divergence in energy and norm distributions over time.

Purpose of the Study:

  • Investigate the behavior of wave packet participation numbers in disordered nonlinear chains.
  • Determine if wave packet spreading leads to simultaneous divergence of norm and energy density distributions.
  • Analyze the long-time dynamics and energy diffusion in these systems.

Main Methods:

  • Analytical proof for norm-conserving models with strong nonlinearity.
  • Numerical simulations of wave packet dynamics in discrete nonlinear Schrödinger and quartic Klein-Gordon chains.
  • Analysis of participation number, Fourier spectrum, and energy diffusion.

Main Results:

  • The participation number of a wave packet does not diverge simultaneously with norm and energy density.
  • Long-time dynamics reveal a distribution of nondecaying, interacting normal modes.
  • The Fourier spectrum exhibits quasiperiodic dynamics, indicating a lack of slow energy diffusion.

Conclusions:

  • The study analytically proves that participation numbers do not diverge simultaneously under specific conditions.
  • Results suggest that wave packet spreading in these disordered systems does not result in slow energy diffusion.
  • The system's dynamical state may approach a quasiperiodic solution (Kolmogorov-Arnold-Moser torus) in the long-time limit.