Universal break law for chains of Brownian particles with nearest neighbour interaction

TL;DR

This paper analyzes the breaking behavior of a finite chain of Brownian particles under slow pulling and noise, revealing universal statistical laws for break time and position depending only on local potential curvature.

Contribution

It introduces a universal law governing break time and position distributions for chains of Brownian particles, independent of potential details, depending only on local curvature.

Findings

Break time distribution is universal and depends only on local curvature.

Break position distribution exhibits universality, unaffected by potential specifics.

Results hold in regimes where pulling and noise influence break behavior.

Abstract

We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise potential $U$, with one end of the chain fixed and the other end pulled away, in the limit of slow pulling speed and small Brownian noise. We study the instant when and the place where the chain "breaks", that is, the distance between two neighbouring particles becomes larger than a certain threshold. We assume $U$ to be attractive and strictly convex up to the break distance, and three times continuously differentiable. We consider the regime, where both the pulling and the noise significantly influence the distribution of the break time and break position. It turns out that in this regime there is a universality of both the break time distribution and the break position distribution, in the sense that the limiting quantities do not depend on the details of $U$, but only on its curvature at the break distance.