Trap models with slowly decorrelating observables

TL;DR

This paper analyzes trap models of glassy dynamics with observables that slowly decorrelate, providing exact results and revealing how such observables detect persistent slow out-of-equilibrium behavior.

Contribution

It offers the first exact analytical results for correlation and response in trap models with slow decorrelation, including effects of different transition rates.

Findings

Exact zero-temperature results for arbitrary decorrelation factor

Analytical scaling behavior at nonzero temperature

Transition rate choice influences exponents and prefactors

Abstract

We study the correlation and response dynamics of trap models of glassy dynamics, considering observables that only partially decorrelate with every jump. This is inspired by recent work on a microscopic realization of such models, which found strikingly simple linear out-of-equilibrium fluctuation-dissipation relations in the limit of slow decorrelation. For the Barrat-Mezard model with its entropic barriers we obtain exact results at zero temperature $T$ for arbitrary decorrelation factor $\kappa$. These are then extended to nonzero $T$, where the qualitative scaling behaviour and all scaling exponents can still be found analytically. Unexpectedly, the choice of transition rates (Glauber versus Metropolis) affects not just prefactors but also some exponents. In the limit of slow decorrelation even complete scaling functions are accessible in closed form. The results show that slowly decorrelating observables detect persistently slow out-of-equilibrium dynamics, as opposed to intermittent behaviour punctuated by excursions into fast, effectively equilibrated states.