# Chopping time of the FPU $\alpha$-model

## TL;DR

This paper investigates the time it takes for an FPU α-model chain to break into pieces, revealing a temperature-dependent formula that explains the chain's stability and the relevance of FPU studies.

## Contribution

It provides a combined numerical and analytical analysis of the chain's breaking time, deriving an Arrhenius-Kramers type formula at low temperatures.

## Key findings

- Breaking time follows an Arrhenius-Kramers law at low temperatures.
- Chains remain unbroken on observable timescales at low temperatures.
- The results justify studying the FPU problem even in ill-posed cases.

## Abstract

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