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

TL;DR

This paper investigates the dynamics of particles in a one-dimensional logarithmically correlated random potential, revealing replica symmetry breaking in trajectory space during the low-temperature phase, which enhances understanding of complex disordered systems.

Contribution

It demonstrates the occurrence of replica symmetry breaking in trajectory space for a particle in a logarithmically correlated random potential, using numerical methods.

Findings

Replica symmetry breaking occurs in the low-temperature phase.

The model exhibits a dynamical transition between two subdiffusive phases.

Numerical analysis of trajectory overlaps supports the RSB phenomenon.

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.