Spatially heterogeneous ages in glassy systems

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 these systems: 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 obtained for a given noise realization. We explain why the noise-averaged correlators describe the fingerprint of quenched disorder when it exists, while the coarse-grained correlators are linked to noise-induced mesoscopic fluctuations. We predict constraints on the distribution of the fluctuations of the coarse-grained quantities. In particular, 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. A symmetry of the underlying theory, namely invariance under reparametrizations of the time coordinates, underlies these results. We establish a connection between the probabilities of spatial distributions of local coarse-grained quantities and the theory of dynamic random manifolds. We define, and discuss the behavior of, a two-time dependent correlation length from the spatial decay of the fluctuations in the two-time local functions. We characterize the fluctuations in the system in terms of their fractal properties. For concreteness, 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.

Fluctuations in the time variable and dynamical heterogeneity in glass-forming systems

“…The understanding of dynamical heterogeneity is believed to be crucial to explain anomalous behavior of materials near the glass transition, and even possibly to explain the very presence of the glass transition itself [2]. Despite many efforts trying to address the origin of dynamical heterogeneity, this question still remains open [4,[17][18][19][20].…”

“…This framework is based on the hypothesis that in glassy systems the long time dynamics is invariant under reparametrizations of the time variable [20][21][22][23][24][25][26][27][28], but this invariance is broken, giving rise to Goldstone modes that manifest themselves with the emerge of heterogeneous dynamics [20][21][22][23][24][29][30][31][32][33][34]. The Goldstone modes correspond to fluctuations in the time reparametrization t → φ r (t), i.e.…”

Mapping Dynamical Heterogeneity in Structural Glasses to Correlated Fluctuations of the Time Variables

“…SHD is believed to be crucial to the understanding of non-exponential relaxation, the breakdown of the coupling between translational diffusion and viscosity, and even possibly the slowdown of the dynamics itself [1,2]. The origin of SHD is still uncertain, in part because of the lack of direct microscopic tests to attempt to disprove proposed theories [6,[9][10][11]. Here we apply one such test [12] for the hypothesis that SHD is associated with fluctuations in the time variable [11,13,14], and find that our molecular dynamics data are consistent with the hypothesis.…”

“…Thus the fluctuations of C r (t, t w ) represent the dynamical heterogeneity, and theories attempting to explain SHD should be able to explain those fluctuations. One of the proposed mechanisms for the origin of dynamical heterogeneity postulates that they are associated with local fluctuations in the time variable [11,[13][14][15][16][17][18][19], t → h r (t), i.e.…”

Fluctuations in Finite-dimensional Spin-glass Dynamics

“…A possible family of models in which this action could be computed are spin-glass models with Kac-type interactions [17]. In practice, in the past we have just proposed an action S[L r ] requiring it to be (i) global time-reversal invariant; (ii) local in space; (iii) positive definite [10,11,12,16]. We have derived from it some predictions that we checked numerically in disordered finite dimensional spin models [10,11,12,15] and kinetically constrained models [16].…”