Mechanical analysis of a dynamical phase transition for particles in a channel

TL;DR

This paper investigates a dynamical phase transition in a particle system within a channel, where biasing the clustering leads to symmetry breaking and wall accumulation, analyzed through mechanical stress and control theory.

Contribution

It introduces a detailed mechanical analysis of the symmetry-breaking transition in biased particle trajectories using stress tensors and control theory.

Findings

Particles cluster at one wall under bias

Symmetry breaking occurs at high clustering bias

Finite average body forces are linked to thermal noise and bias

Abstract

We analyse biased ensembles of trajectories for a two-dimensional system of particles, evolving by Langevin dynamics in a channel geometry. This bias controls the degree of particle clustering. On biasing to large clustering, we observe a dynamical phase transition where the particles break symmetry and accumulate at one of the walls. We analyse the mechanical properties of this symmetry-broken state using the Irving-Kirkwood stress tensor. The biased ensemble is characterised by body forces which originate in random thermal noises, but have finite averages in the presence of the bias. We discuss the connection of these forces to Doob's transform and optimal control theory.