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Area of Science:

  • Nonlinear physics
  • Wave dynamics
  • Statistical mechanics

Background:

  • Non-phase-invariant Hamiltonian models describe complex wave behaviors.
  • Understanding phase correlations is crucial for nonlinear wave dynamics.

Purpose of the Study:

  • Investigate the emergence of phase correlations in nonlinear dispersive waves.
  • Analyze the formation of anomalous correlators and negative frequencies.
  • Determine the timescale of anomalous correlator development.

Main Methods:

  • Theoretical analysis of a generic non-phase-invariant Hamiltonian model.
  • Derivation of anomalous correlators using analytical techniques.
  • Validation through direct numerical simulations of the deterministic system.

Main Results:

  • Initial random phases evolve into phase correlations between positive and negative wave numbers.
  • Emergence of nonzero anomalous correlators and negative frequencies.
  • Anomalous correlators develop on a timescale of O(1/ε), faster than the kinetic timescale.

Conclusions:

  • Nonlinear dispersive wave dynamics can spontaneously generate order from random initial conditions.
  • Anomalous correlations play a significant role in the early evolution of these systems.
  • The findings are robust, supported by both theoretical predictions and numerical simulations.