Thermalization in the discrete nonlinear Klein-Gordon chain in the wave-turbulence framework

Abstract

We study the time of equipartition, Teq, of energy in the one-dimensional Discrete Nonlinear Klein-Gordon (DNKG) equation in the framework of the Wave Turbulence (WT) theory. We discuss the applicability of the WT theory and show how this approach can explain qualitatively the route to thermalization and the scaling of the equipartition time as a function of the nonlinear parameter ϵ, defined as the ratio between the nonlinear and linear part of the Hamiltonian. Two scaling laws, and , for different degrees of nonlinearity are explained in terms of four-wave or six-wave processes in the WT theory. The predictions are verified with extensive numerical simulations varying the system size and the degree of nonlinearity.