2025/11/30 by Ponno, Antonio, Gradenigo, Giacomo, Baldovin, Marco +1
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2512.00929
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 H of the system with N degrees of freedom, we introduce a mean-field Hamiltonian H such that the difference hN=(H-H)/N, considered as a random variable with respect to the Gibbs measure, tends to zero as N→∞, in probabilistic sense. The dynamics of the mean-field Hamiltonian H consists of N independent oscillation modes with renormalized frequencies Ωk = ωk√(1+γ(ε)), ωk being the frequency of the k-th normal mode of the linearized system, whereas γ(ε) is an explicit function of the specific energy ε of the system. Analytical predictions drawn from the effective Langevin equations ruling the dynamics of such oscillation modes are successfully compared with the numerical data from the original Hamiltonian dynamics. Such a simple decomposition of the true dynamics into N effective normal modes holds at all energy scales, i.e. from the quasi-integrable regime to the strongly chaotic one.