A mean-field theory of effective normal modes in the Fermi–Pasta–Ulam–Tsingou model (opens in new tab)

We present a non-perturbative, mean-field theory for the Fermi–Pasta–Ulam–Tsingou model with quartic interaction, capturing the quasiperiodic features shown by the system at all energies in the thermodynamic limit. Starting from the true Hamiltonian of the system with degrees of freedom, we introduce a mean-field Hamiltonian such that the difference , considered as a random variable with respect to the Gibbs measure, tends to zero as , in probabilistic sense. The dynamics of the mean-field Ha...