Universal scaling of the FPUT equipartition time
In plain words
Recent work claims that the time to reach equal sharing of energy grows as the inverse square of the nonlinearity strength in large lattices. Whether this law is universal, and from which system size it applies, needs independent confirmation.
Precise statement
For alpha- and beta-FPUT chains with $N$ particles at energy density $\epsilon$ and effective nonlinearity g (g ~ alpha^2 epsilon or beta epsilon), determine whether the equipartition time obeys $T_{\mathrm{eq}} \sim g^{-2}$ for $N > N*(g)$ in the thermodynamic limit, as wave-turbulence theory of resonant wave interactions predicts, and determine $N*(g)$ and the small-N regime where exact resonances are absent and the exponent differs. An answer is the exponent with its range of validity.
What would settle it
Simulations at increasing N and decreasing g showing convergence of the exponent, matched by a kinetic-equation derivation of the prefactor.
Status in the literature
Unverified note
A 2026 review argues $T_{\mathrm{eq}} \sim g^{-2}$ holds generically for lattices with extended normal modes (arXiv:2603.23347); independent tests of the asymptotic regime are limited.
See also
- Related Role of Toda integrals in the FPUT metastable state
- Related Does the relaxation rate scale as $g^{2}$ in the thermodynamic limit
- Related Are Kerr-AdS black holes nonlinearly stable with reflecting boundary conditions?
- Related Fourier's law of heat conduction for a deterministic anharmonic lattice
- Related Endless spreading of wave packets in disordered nonlinear lattices