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

Abstract

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.

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

“…In the aging cases we can verify that Eq. ( 5) can be rewritten in the form C(t, t ) = f [h(t)/h(t )] [33], which is found in many aging systems [35]. Once the fitting procedure is performed for a given dataset, we can use the known values of the parameters q EA , β and θ 0 to compute…”

“…A summary of the results of an early version of our analysis was published in Ref. [33]. This manuscript is organized in the following way.…”

“…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.…”

Fluctuating phases and fluctuating relaxation times in glass forming liquids

“…Time reparametrization symmetry refers to an invariance under transformations of the time variable t → φ(t), where φ(t) is a continuous and monotonically increasing function of t. This symmetry has been shown to be present in the long-time dynamics of mean field spin glass models [30,31] and of short range spin glass models [17,19,21,25]. Numerical studies in spin glasses [19] and structural glasses [20,26] have given strong evidence supporting the presence of this symmetry. The symmetry has also been used, from a different point of view, to determine properties of symmetric observables whose full dynamical properties are hard to compute [32,33].…”

“…Another proposal is that as a liquid is supercooled it eventually undergoes a Random First Order Transition in which the liquid freezes into a mosaic of aperiodic crystals [15,16], which give rise to the heterogeneity that is observed. A third approach postulates that dynamical heterogeneity emerges from the presence of soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations t → φ(t) [17][18][19][20][21][22][23][24][25][26][27].…”