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 onto the canonical ensemble of directed polymers.
Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
Masahiko
M
Ueda
Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
Shin-ichi
S
Sasa