Rigorous derivation of the 4-wave kinetic equation for the full beta-FPUT system in the joint limit N to infinity and beta to zero under weakly nonlinear scalings, reaching times up to the kinetic timescale to the power 2/3, by directly incorporating non-resonant terms in a diagrammatic expansion.
Rigorous Derivation of the Wave Kinetic Equation for β -FPUT System
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Derives a new kinetic equation for the alpha-FPUT lattice with site-dependent coefficients, revealing a resonant three-wave manifold and faster thermalization plus Bragg scattering.
Survey compiling rigorous results on stability of FPU chains via Toda approximation, continuous KdV limits, and lower bounds on thermalization times from slow autocorrelation decay.
Review summarizing kinetic theory for oscillator chains including wave kinetic equations, hydrodynamic limits, mathematical state of the art, and connections to the FPU paradox and Fourier's law.
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Rigorous Derivation of the Wave Kinetic Equation for full $\beta$-FPUT System
Rigorous derivation of the 4-wave kinetic equation for the full beta-FPUT system in the joint limit N to infinity and beta to zero under weakly nonlinear scalings, reaching times up to the kinetic timescale to the power 2/3, by directly incorporating non-resonant terms in a diagrammatic expansion.
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Resonant interactions in the $\alpha$-FPUT lattice with site-dependent coefficients
Derives a new kinetic equation for the alpha-FPUT lattice with site-dependent coefficients, revealing a resonant three-wave manifold and faster thermalization plus Bragg scattering.
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A survey on rigorous results for the dynamics of periodic FPU chains
Survey compiling rigorous results on stability of FPU chains via Toda approximation, continuous KdV limits, and lower bounds on thermalization times from slow autocorrelation decay.
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A review on the kinetic theory of oscillator chains
Review summarizing kinetic theory for oscillator chains including wave kinetic equations, hydrodynamic limits, mathematical state of the art, and connections to the FPU paradox and Fourier's law.