Replica symmetry breaking in trajectories of a driven Brownian particle

TL;DR

This paper investigates the phenomenon of replica symmetry breaking in the trajectories of a driven Brownian particle, revealing a connection to directed polymers through a boundary condition mapping.

Contribution

It demonstrates replica symmetry breaking in a Brownian particle system driven by a noisy Burgers field and establishes an exact mapping to directed polymer ensembles.

Findings

Replica symmetry breaking occurs in the path ensemble.

The path ensemble maps exactly to directed polymer canonical ensemble.

The system's behavior is influenced by boundary conditions.

Abstract

We study a Brownian particle passively driven by a field obeying the noisy Burgers equation. We demonstrate that the system exhibits replica symmetry breaking in the path ensemble with the initial position of the particle being fixed. The key step of the proof is that the path ensemble with a modified boundary condition can be exactly mapped to the canonical ensemble of directed polymers.