Chopping Time of the FPU \({\alpha }\)-Model

We study, both numerically and analytically, the time needed to observe the breaking of an FPU \(\alpha \)-chain in two or more pieces, starting from an unbroken configuration at a given temperature. It is found that such a “chopping” time is given by a formula that, at low temperatures, is of the Arrhenius–Kramers form, so that the chain does not break up on an observable time-scale. The result explains why the study of the FPU problem is meaningful also in the ill-posed case of the \(\alpha \)-model.