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

Abstract

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.

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

“…We now turn to a more quantitative analysis of the connection between the transverse fluctuating variables π 1r , π 2r , the longitudinal fluctuating variables σ r , and the dynamical heterogeneity. A more detailed version of this analysis will be presented elsewhere [26]. Here we report results for fixed C(t 1 , t 3 ) = 0.23, but similar results are obtained for other values of C(t 1 , t 3 ) [26].…”

“…A more detailed version of this analysis will be presented elsewhere [26]. Here we report results for fixed C(t 1 , t 3 ) = 0.23, but similar results are obtained for other values of C(t 1 , t 3 ) [26]. In the top panel of Fig.…”

“…( 2) is satisfied, we have Φ ab ≈ h(t a )/h(t b ), and we therefore obtain a triangular relation [24] Φ 13 ≈ Φ 12 Φ 23 . In terms of the variables X ≡ Φ 23 / √ Φ 13 and Y ≡ Φ 12 / √ Φ 13 , this leads to the prediction that 1 ≈ XY , which is satisfied to a good approximation for all times and all of our datasets [26].…”

“…Here q EA , β and θ 0 are fitting parameters that vary little from one dataset to another. However, the dependence of the α relaxation time τ on t w is quite different in the different systems we consider [26], and this leads to different forms for h(t) [24]: for aging polymers h(t) = exp[ln α (t/t 0 )], for aging particles h(t) = exp[(t/t 0 ) α ], and in equilibrium h(t) = exp(t/t 0 ). We define…”

Effective temperatures in inhomogeneous passive and active bidimensional Brownian particle systems

“…Let us compare the fluctuations in the ABP model with the ones found in other out of equilibrium particle systems. Spatial fluctuations of the displacements, linear responses and effective temperature in glassy systems were considered in [73,74,101], see [78] for a review. In these articles an emerging time-reparametrisation symmetry, in the long time delay relaxation dynamics, was claimed to constrain the noise induced fluctuations to be such that the global χ(∆ 2 ) parametric relation remains satisfied even locally (after coarse-graining).…”