Nonlinearity accelerates the thermalization of the quartic FPU model with stochastic baths

Abstract

We investigate the equilibration process of the strongly coupled quartic Fermi-Pasta-Ulam (FPU) model by adding Langevin baths to the ends of the chain. The time evolution of the system is investigated by means of extensive numerical simulations and shown to match the results expected from equilibrium statistical mechanics in the time-asymptotic limit. Upon increasing the nonlinear coupling, the thermalization of the energy spectrum displays an increasing asymmetry in favour of short-scale, high-frequency modes, which relax significantly faster than the large-scale, short-frequency ones. The global equilibration time is found to scale linearly with system size and shown to exhibit a power-law decrease with the strength of the nonlinearity. Nonlinear interaction adds to energy distribution among modes, thus speeding up the thermalization process.