Replica symmetry breaking in trajectories of a driven Brownian particle
  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. 
Masahiko Ueda and Shin-ichi Sasa
cond-mat.stat-mech cond-mat.dis-nn