*Ｍasahiko Ueda, Shin-ichi Sasa,

Replica symmetry breaking in trajectory space for the trap model,

Journal of Physics A: Mathematical and Theoretical 50, 125001/1-14 (2017).

[Summary] 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.