Transitions and time scales to equipartition in oscillator chains: low-frequency initial conditions

We study the times to equipartition T(eq) in an oscillator chain, which is the discretized Klein-Gordon equation with a quartic nonlinearity (phi(4) system). The numerical results are compared to the Fermi-Pasta-Ulam (FPU) oscillator chain with quartic nonlinearity (FPU-beta system). For both chains we consider initial energies in low-frequency modes, of the linear systems. The methods previously developed to estimate the equipartition times for the FPU-beta chain are applied to the more complicated phi(4) chain. The results indicate that the methods are still applicable, but do not give as accurate predictions of the equipartition time or the transitions between power-law and exponential behavior.