Fluctuation-dissipation relations in trap models

Abstract

Trap models are intuitively appealing and often solvable models of glassy dynamics. In particular, they have been used to study aging and the resulting out-of-equilibrium fluctuation-dissipation relations between correlations and response functions. In this note I show briefly that one such relation, first given by Bouchaud and Dean, is valid for a general class of mean-field trap models: it relies only on the way a perturbation affects the transition rates, but is independent of the distribution of trap depths and the form of the unperturbed transition rates, and holds for all observables that are uncorrelated with the energy. The model with Glauber dynamics and an exponential distribution of trap depths, as considered by Barrat and Mezard, does not fall into this class if the perturbation is introduced in the standard way by shifting all trap energies. I show that a similar relation between response and correlation nevertheless holds for the out-of-equilibrium dynamics at low temperatures. The results point to intriguing parallels between trap models with energetic and entropic barriers.

Extended introduction and discussion of relation to results of cond-mat/0303445. 13 pages, 2 figures, IOP style

References in corpus (14)

• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Energy flow, partial equilibration and effective temperatures in systems with slow dynamics
• Models of traps and glass phenomenology
• On the Out of Equilibrium Relaxation of the Sherrington - Kirkpatrick model
• Aging on Parisi's tree
• Observable-dependence of fluctuation-dissipation relations and effective temperatures
• Sub-diffusion and localization in the one dimensional trap model
• Multiple scaling regimes in simple aging models
• Hopping in the Glass Configuration Space: Subaging and Generalized Scaling Laws
• Fluctuation-dissipation relations and effective temperatures in simple non-mean field systems
• Phase space diffusion and low temperature aging
• ON A DYNAMICAL MODEL OF GLASSES
• Dynamical ultrametricity in the critical trap model
• Zero-temperature criticality in a simple glass model

Cited by in corpus (9)

• Activated dynamics: an intermediate model between REM and p-spin
• Microscopic realizations of the Trap Model
• Spectral properties of the trap model on sparse networks
• Out-of-equilibrium dynamics in a gaussian trap model
• A sluggish random walk with subdiffusive spread
• Aging effects in simple models for glassy relaxation
• Trap models with slowly decorrelating observables
• Dynamic phase diagram of the Number Partitioning Problem
• Local energy approach to the dynamic glass transition