Spatially heterogeneous ages in glassy dynamics

TL;DR

This paper develops a framework to analyze local fluctuations and heterogeneities in the aging dynamics of glassy systems, linking local correlations, responses, and disorder effects through a unified theoretical approach.

Contribution

It introduces a novel theoretical framework for characterizing spatial heterogeneities and fluctuations in nonequilibrium glassy dynamics, applicable to various disordered and non-disordered systems.

Findings

Large heterogeneities in system age persist long-term.

Local correlations obey a generalized fluctuation-dissipation relation.

Predicted probability distribution functions constrain fluctuation behaviors.

Abstract

We construct a framework for the study of fluctuations in the nonequilibrium relaxation of glassy systems with and without quenched disorder. We study two types of two-time local correlators with the aim of characterizing the heterogeneous evolution: in one case we average the local correlators over histories of the thermal noise, in the other case we simply coarse-grain the local correlators. We explain why the former describe the fingerprint of quenched disorder when it exists, while the latter are linked to noise-induced mesoscopic fluctuations. We predict constraints on the pdfs of the fluctuations of the coarse-grained quantities. We show that locally defined correlations and responses are connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. We argue that large-size heterogeneities in the age of the system survive in the long-time limit. The invariance of the theory under reparametrizations of time underlies these results. We relate the pdfs of local coarse-grained quantities and the theory of dynamic random manifolds. We define a two-time dependent correlation length from the spatial decay of the fluctuations in the two-time local functions. We present numerical tests performed on disordered spin models in finite and infinite dimensions. Finally, we explain how these ideas can be applied to the analysis of the dynamics of other glassy systems that can be either spin models without disorder or atomic and molecular glassy systems.