Replica symmetry breaking in trajectory space for the trap model

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.

15 pages, 10 figures

References in corpus (4)

• Anomalous transport in the crowded world of biological cells
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Large-scale fluctuations of the largest Lyapunov exponent in diffusive systems

Cited by in corpus (3)

• Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models
• On the Kemeny time for continuous-time reversible and irreversible Markov processes with applications to stochastic resetting and to conditioning towards forever-survival
• Markov dualities via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors