Thermalization of one-dimensional ϕ^{4} lattices: Chirikov overlap criterion and discrete breathers.

Abstract

We investigate the thermalization behavior of one-dimensional ϕ^{4} lattices with the help of the self-consistent phonon theory. As the energy density increases, we observe the double-scaling behavior of the thermalization time as a function of the energy density in the weakly nonlinear regime. This behavior suggests a transition from the Kolmogorov-Arnold-Moser-Nekhoroshev regime to the weak turbulence regime, which can be quantified by the optimized Chirikov overlap criterion. With increasing the energy density, systems exhibit a counterintuitive slowdown of thermalization in the strongly nonlinear regime, indicating the presence of underlying suppressive mechanisms. We demonstrate that these suppressions can be attributed to the formation of discrete breathers.