Replica symmetry breaking in trajectory space for the trap model

TL;DR

This paper investigates phase transitions in the one-dimensional trap model by analyzing trajectory localization and identifies a replica symmetry breaking phase at low temperatures through numerical methods.

Contribution

It introduces a novel approach to study localization in the trap model using trajectory space and characterizes the low temperature phase as replica symmetry breaking.

Findings

Discovered a phase transition in the path ensemble.

Identified a replica symmetry breaking phase at low temperatures.

Numerical evidence supports the phase transition in trajectory localization.

Abstract

We study the localization in the one-dimensional trap model in terms of statistical mechanics of trajectories. By numerically investigating overlap between trajectories of two particles on a common disordered potential, we find that there is a phase transition in the path ensemble. We characterize the low temperature phase as a replica symmetry breaking phase in trajectory space.