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.

arXiv comment15 pages, 10 figures

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Cited by in corpus (9)

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• Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models
• Inference of Markov models from trajectories via Large Deviations at Level 2.5 with applications to random walks in disordered media
• Spectral properties of the trap model on sparse networks
• Glassy dynamics on networks: local spectra and return probabilities
• On the Kemeny time for continuous-time reversible and irreversible Markov processes with applications to stochastic resetting and to conditioning towards forever-survival
• Numerical calculation of overlap distribution of $(2+1)$-dimensional directed polymer in random media
• Replica symmetry breaking in trajectory space for diffusion in logarithmically correlated random potentials
• Markov dualities via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors