Breaking a chain of interacting Brownian particles

TL;DR

This paper analyzes the dynamics of a finite chain of Brownian particles under slow pulling, identifying regimes of chain breakage and providing probabilistic descriptions of break time and position.

Contribution

It introduces a detailed analysis of chain breakage behavior under different regimes of pulling speed and noise, with new limit theorems for break time and position.

Findings

Identifies three regimes based on pulling speed and noise.

Proves weak limit theorems for break time.

Proves weak limit theorems for break position.

Abstract

We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise quadratic potential, with one end of the chain fixed and the other end pulled away at slow speed, in the limit of slow speed and small Brownian noise. We study the instant when the chain "breaks", that is, the distance between two neighboring particles becomes larger than a certain limit. There are three different regimes depending on the relation between the speed of pulling and the Brownian noise. We prove weak limit theorems for the break time and the break position for each regime.