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This study explores wave packet delocalization in nonlinear disordered lattices using numerical simulations. Findings reveal key characteristics of chaos and spreading, offering a new scaling law for predictions.

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Area of Science:

  • Nonlinear Dynamics
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Wave packet dynamics in disordered systems are crucial for understanding energy transport and localization phenomena.
  • Previous theoretical predictions exist for wave packet spreading in chaotic regimes, but experimental verification and detailed characterization are ongoing.
  • Nonlinear disordered lattices present complex behavior, including chaos and thermalization, which require advanced simulation techniques for analysis.

Purpose of the Study:

  • To reveal generic characteristics of wave packet delocalization in two-dimensional nonlinear disordered lattices.
  • To investigate the interplay between chaos and wave packet spreading in different dynamical regimes (weak vs. strong chaos).
  • To propose and validate a dimension-independent scaling law relating wave packet spreading and chaoticity.

Main Methods:

  • Extensive numerical simulations were performed on two fundamental disordered models: the Klein-Gordon system and the discrete nonlinear Schrödinger equation.
  • Analysis involved tracking the wave packet's second moment evolution over time.
  • Finite-time maximum Lyapunov exponent (Λ) was calculated to quantify the strength and decay of chaos.

Main Results:

  • Wave packet delocalization follows power-law scaling (t^{a_{m}}) with exponents a_{m}≈1/5 (weak chaos) and a_{m}≈1/3 (strong chaos), consistent with theory.
  • Chaos persists but weakens over time, with the Lyapunov exponent decaying as Λ∝t^{α_{Λ}}, where α_{Λ}≈-0.37 (weak) and α_{Λ}≈-0.46 (strong).
  • Deviation vector distributions indicate wandering chaotic seeds, leading to wave packet thermalization.

Conclusions:

  • The study confirms theoretical predictions for wave packet spreading exponents in nonlinear disordered lattices.
  • A novel dimension-independent scaling law between wave packet spreading and chaoticity is proposed and validated.
  • The findings provide a deeper understanding of delocalization, chaos decay, and thermalization mechanisms in complex lattice systems.