• Corpus ID: 121304858

Anomalous correlators, "ghost" waves and nonlinear standing waves in the $\beta$-FPUT system

@article{Zaleski2019AnomalousC,
  title={Anomalous correlators, "ghost" waves and nonlinear standing waves in the \$\beta\$-FPUT system},
  author={Joseph Zaleski and Miguel Onorato and Yuri V. Lvov},
  journal={arXiv: Chaotic Dynamics},
  year={2019}
}
We show that Hamiltonian nonlinear dispersive wave systems with cubic nonlinearity and random initial data develop, during their evolution, anomalous correlators. These are responsible for the appearance of "ghost" excitations, i.e. those characterized by negative frequencies, in addition to the positive ones predicted by the linear dispersion relation. We use generalization of the Wick's decomposition and the wave turbulence theory to explain theoretically the existence of anomalous… 

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References

SHOWING 1-10 OF 21 REFERENCES

Generation of dispersion in nondispersive nonlinear waves in thermal equilibrium

This work demonstrates how nonlinear interactions can indeed give rise to effective dispersive-wave–like characteristics in thermal equilibrium, and derives the form of the corresponding dispersion relation, which describes the effective dispersion structures, using the generalized Langevin equations obtained in the Zwanzig–Mori projection framework.

Incoherent Fermi-Pasta-Ulam recurrences and unconstrained thermalization mediated by strong phase correlations

The long-standing and controversial Fermi-Pasta-Ulam problem addresses fundamental issues of statistical physics, and the attempt to resolve the mystery of the recurrences has led to many great

REVIEWS OF TOPICAL PROBLEMS: Spin-wave turbulence beyond the parametric excitation threshold

The nonlinear stage of the parametric excitation of spin waves in ferromagnetic dielectrics is reviewed. The main nonlinear mechanism which limits the amplitude of the exponentially growing waves is

Nonlinear interactions of random waves in a dispersive medium

  • D. J. BenneyP. Saffman
  • Mathematics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1966
A study is made of the way that the spectrum function of random, spatially homogeneous, dispersive waves varies slowly with time owing to weak nonlinear interactions between the waves. A continuous

Thermalization in the discrete nonlinear Klein-Gordon chain in the wave-turbulence framework

We study the time of equipartition, Teq, of energy in the one-dimensional Discrete Nonlinear Klein-Gordon (DNKG) equation in the framework of the Wave Turbulence (WT) theory. We discuss the

Route to thermalization in the α-Fermi–Pasta–Ulam system

This article theoretically investigates the original α-Fermi–Pasta–Ulam (FPU) system by applying the wave–wave interaction theory and finds that the first nontrivial resonances correspond to six-wave interactions, responsible for the thermalization of the energy in the spectrum.

Double Scaling in the Relaxation Time in the β-Fermi-Pasta-Ulam-Tsingou Model.

This work derives a simple formula for the nonlinear frequency broadening and shows that when the phenomenon of overlap of frequencies takes place, a different scaling for the thermalization time scale is observed, which supports the idea that the Chirikov overlap criterion identifies a transition region between two different relaxation time scalings.

Wave Turbulence

In this article, we state and review the premises on which a successful asymptotic closure of the moment equations of wave turbulence is based, describe how and why this closure obtains, and examine

Anomalous probability of large amplitudes in wave turbulence