We present a detailed numerical study of dynamical heterogeneities in the aging regime of a simple binary Lennard-Jones glass former. For most waiting times t_{w} and final times t , both the dynamical susceptibility chi_{4}(t,t_{w}) and the dynamical correlation length xi_{4}(t,t_{w}) can be approximated as products of two factors: (i) a waiting-time-dependent scale that grows as a power of t_{w} , and (ii) a scaling function dependent on t,t_{w} only through the value of the intermediate scattering function C(t,t_{w}) . We find that chi_{4}(t,t_{w}) is determined only in part by the correlation volume.

The presence of dynamical heterogeneities, i.e. nanometer-scale regions containing molecules rearranging cooperatively at very different rates compared to the bulk [3,4], is increasingly being recognized as crucial in our understanding of the glass transition, from the non-exponential nature of relaxation, to the divergence of the relaxation times [5]. Recently, dynamical heterogeneities have been directly observed experimentally [6,7,8,9] and in simulations [13]. However a clear physical picture for the origin of these heterogeneities is still lacking. Here we investigate a possible physical mechanism for the origin of dynamical heterogeneities in the non-equilibrium dynamics of structural glasses. We test the predictions regarding universal scaling of fluctuations derived from this mechanism against simulation results in a simple binary Lennard-Jones glass model, and find that to a first approximation they are satisfied. We also propose to apply the same kind of analysis to experimental data from confocal microscopy in colloidal glasses.Supercooled liquids approaching the glass transition display increasingly slow dynamics, until eventually they cannot equilibrate in laboratory timescales [1]. One consequence of this fact is physical aging, i.e. the breakdown of time translation invariance (TTI): the correlation C(t, t w ) between spontaneous fluctuations of an observable at times t (the final time) and t w (the waiting time) are nontrivial functions of t and t w , as opposed to being functions of the time difference t − t w . In many cases, the two-time correlation C(t, t w ) in an aging system separates into a fast, time translation invariant contribution C fast (t − t w ), and a slow contributionIn the case of a structural glass, two-step relaxation is observed: the fast term corresponds to localized fluctuations of individual particles inside their cages, and the slow term corresponds to longer time scales, in which cages break down and the system structurally relaxes. For some systems, the slow part of the correlation has the form [2] C slow (t, t w ) = C slow (h(t)/h(t w )), where h(t) is some monotonically increasing function. For example, in the case of domain growth, h(t) is proportional to the domain size [2].Recently, it has been proven that, in the limit of long times, the dynamics of a class of spin-glass models is invariant under global reparametrizations t → h(t) of the time [10]. This result has been used to predict the existence of a Goldstone mode in the nonequilibrium dynamics, associated with smoothly varying local fluctuations in the reparametrization of the time t → h r (t) = e ϕr(t) . These fluctuations have been physically interpreted to represent local fluctuations of the age of the sample [11,12]. In the cases where the global two-time correlation exhibits h(t)/h(t w ) scaling, a simple Landau theory approximation for the dynamical action predicts [11,12,14] that the full probability distribution ρ(C r (t, t w )) of local correlations C r (t, t w ) depends only on the global correlati...

Glass-forming liquids display strong fluctuations-dynamical heterogeneities-near their glass transition. By numerically simulating a binary Weeks-Chandler-Andersen liquid and varying both temperature and time scale, we investigate the probability distributions of two kinds of local fluctuations in the nonequilibrium (aging) regime and in the equilibrium regime, and find them to be very similar in the two regimes and across temperatures. We also observe that, when appropriately rescaled, the integrated dynamic susceptibility is very weakly dependent on temperature and very similar in both regimes.

Dynamical heterogeneities -strong fluctuations near the glass transition -are believed to be crucial to explain much of the glass transition phenomenology. One possible hypothesis for their origin is that they emerge from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. To test this hypothesis, we use numerical simulation data from four glass-forming models to construct coarse grained observables that probe the dynamical heterogeneity, and decompose the fluctuations of these observables into two transverse components associated with the postulated time-fluctuation soft modes and a longitudinal component unrelated to them. We find that as temperature is lowered and timescales are increased, the time reparametrization fluctuations become increasingly dominant, and that their correlation volumes grow together with the correlation volumes of the dynamical heterogeneities, while the correlation volumes for longitudinal fluctuations remain small.

We test a hypothesis for the origin of dynamical heterogeneity in slowly relaxing systems, namely that it emerges from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. We do this by constructing coarse grained observables and decomposing the fluctuations of these observables into transverse components, which are associated with the postulated time-fluctuation soft modes, and a longitudinal component, which represents the rest of the fluctuations. Our test is performed on data obtained in simulations of four models of structural glasses. As the hypothesis predicts, we find that the time reparametrization fluctuations become increasingly dominant as temperature is lowered and timescales are increased. More specifically, the ratio between the strengths of the transverse fluctuations and the longitudinal fluctuations grows as a function of the dynamical susceptibility, χ4, which represents the strength of the dynamical heterogeneity; and the correlation volumes for the transverse fluctuations are approximately proportional to those for the dynamical heterogeneity, while the correlation volumes for the longitudinal fluctuations remain small and approximately constant.