Replica symmetry breaking in trajectory space for diffusion in logarithmically correlated random potentials

Abstract

We study the dynamics of a particle in a one-dimensional Gaussian random potential with logarithmic correlations. It was shown in previous studies that the model exhibits a dynamical transition between two subdiffusive phases. We numerically investigate both phases by focusing on overlap between trajectories of two independent particles in a common random potential, and show that replica symmetry breaking in trajectory space occurs in the low-temperature phase.

9 pages, 7 figures

References in corpus (2)

• Replica symmetry breaking in trajectories of a driven Brownian particle
• Replica symmetry breaking in trajectory space for the trap model

Cited by in corpus (1)

• Numerical calculation of overlap distribution of $(2+1)$-dimensional directed polymer in random media