We study, both numerically and analytically, the time needed to observe the breaking of an FPU α-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 α-model.
Chopping Time of the FPU alpha-Model
Ponno, A.
2018
Abstract
We study, both numerically and analytically, the time needed to observe the breaking of an FPU α-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 α-model.
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