Universal dependence of the fluctuation-dissipation ratio on the transition rates in trap models

TL;DR

This paper explores how the fluctuation-dissipation ratio in trap models depends universally on transition rates, revealing mechanisms behind its limiting value and linking it to glassy system dynamics.

Contribution

It demonstrates that the fluctuation-dissipation ratio's limiting value depends on the form of perturbed transition rates and connects this to the exponential distribution of trap energies.

Findings

Limiting fluctuation-dissipation ratio exists for certain perturbed rates.

The ratio's value is linked to the exponential trap energy distribution.

FD plots resemble patterns in glassy systems.

Abstract

We investigate violations of the fluctuation-dissipation theorem in two classes of trap models by studying the influence of the perturbing field on the transition rates. We show that for perturbed rates depending upon the value of the observable at the arrival trap, a limiting value of the fluctuation-dissipation ratio does exist. However, the mechanism behind the emergence of this value is different in both classes of models. In particular, for an entropically governed dynamics (where the perturbing field shifts the relative population of traps according to the value of the observable) perturbed rates are argued to take a form that guarantees the existence of a limiting value for the effective temperature, utterly related to the exponential character of the distribution of trap energies. Fluctuation-dissipation (FD) plots reproduce some of the patterns found in a broad class of glassy systems, reinforcing the idea that structural glasses self-generate a dynamical measure that is captured by phenomenological trap models.