Replica symmetry breaking in trajectories of a driven Brownian particle

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.

12 pages, 16 figures

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• Relative distance between tracers as a measure of diffusivity within moving aggregates
• Time evolution of intermittency in the passive slider problem
• Controlling conditional expectations by zero-determinant strategies
• Long-ranged correlations in large deviations of local clustering
• Comment on "Replica Symmetry Breaking in Trajectories of a Driven Brownian Particle"
• Reply to Comment on "Replica symmetry breaking in trajectories of a driven Brownian particle"
• Passive Tracer Dynamics in Slow-Bond Problem
• Replica symmetry breaking in trajectory space for diffusion in logarithmically correlated random potentials
• Numerical calculation of overlap distribution of $(2+1)$-dimensional directed polymer in random media