Behaviors of thermalization for the Fermi-Pasta-Ulam-Tsingou system with small number of particles

We study the behaviors of thermalization in Fermi-Pasta-Ulam-Tsingou (FPUT) system with small number of particles using periodic boundary conditions. The total energy has initially equidistributed among some of the lowest frequency modes. The thermalization time t_eq depending on system's energy density ε scales as t_eq ∝ ε^-4 only within a certain range of nonlinearity. In this range of nonlinearity, energies can interchange between the initial excited modes and other modes continuously with time until reaching the thermalized state. With a further decreasing nonlinearity, a steeper growth than ε^-4 will appear. In the very weakly nonlinear regime, energies on low frequency modes are found to be frozen on large time scales. Redistribution of mode energies happens through the resonances of high frequency modes.