Equilibrium and non-equilibrium fluctuations in a glass-forming liquid

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 timescale, we investigate the probability distributions of two kinds of local fluctuations in the non-equilibrium (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.Comment: v1: 5 pages, 4 figures v2: 5 pages, 4 figures. Now includes results at three temperatures, two of them above T_{MCT} and one below T_{MCT}; and more extensive discussion of connections to experiment

Mapping dynamical heterogeneity in structural glasses to correlated fluctuations of the time variables

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.Comment: v4: Detailed analysis of transverse and longitudinal parts. One figure removed, two added. v3: Explicit decomposition into transverse and longitudinal parts, discussion of correlation volumes. One more figure v2: Modified introduction and forma

Slow and Long-ranged Dynamical Heterogeneities in Dissipative Fluids

A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow particles and determine their size, $N_c$, and their radius of gyration, $R_G$. We show that $N_c\propto R_G^{d_f}$, providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, $d_f$, that is observed to increase with packing fraction $\phi$. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., $\phi\to\phi_c$. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor $S_4(q,t)$ and the dynamical susceptibility $\chi_4(t)$. $S_4(q,t)$ is shown to obey scaling in the full range of packing fractions, $0.6\leq\phi\leq 0.805$, and to become increasingly long-ranged as $\phi\to\phi_c$. Finite size scaling of $\chi_4(t)$ provides a consistency check for the previously analyzed divergences of $\chi_4(t)\propto (\phi-\phi_c)^{-\gamma_{\chi}}$ and the correlation length $\xi\propto (\phi-\phi_c)^{-\gamma_{\xi}}$. We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for $\phi\to\phi_c$ suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.Comment: 14 pages, 25 figure

Universal Scaling in the Aging of the Strong Glass Former SiO2_2

We show that the aging dynamics of a strong glass former displays a strikingly simple scaling behavior, connecting the average dynamics with its fluctuations, namely the dynamical heterogeneities. We perform molecular dynamics simulations of SiO$_2$ with BKS interactions, quenching the system from high to low temperature, and study the evolution of the system as a function of the waiting time $t_{\rm w}$ measured from the instant of the quench. We find that both the aging behavior of the dynamic susceptibility $\chi_4$ and the aging behavior of the probability distribution $P(f_{{\rm s},{\mathbf r}})$ of the local incoherent intermediate scattering function $f_{{\rm s},{\mathbf r}}$ can be described by simple scaling forms in terms of the global incoherent intermediate scattering function $C$. The scaling forms are the same that have been found to describe the aging of several fragile glass formers and that, in the case of $P(f_{{\rm s},{\mathbf r}})$, have been also predicted theoretically. A thorough study of the length scales involved highlights the importance of intermediate length scales. We also analyze directly the scaling dependence on particle type and on wavevector $q$, and find that both the average and the fluctuations of the slow aging dynamics are controlled by a unique aging clock, which is not only independent of the wavevector $q$, but is the same for O and Si atoms.Comment: 13 pages, 21 figures (postscript

A simple model for dynamic heterogeneity in glass-forming liquids

Liquids near the glass transition exhibit dynamical heterogeneity, i.e. local relaxation rates fluctuate strongly over space and time. Here we introduce a simple continuum model that allows for quantitative predictions for the correlators describing these fluctuations. We find remarkable agreement of the model predictions for the dynamic susceptibility $\chi_4(t)$ with numerical results for a binary hard-sphere (HARD) liquid and for a Kob-Andersen Lennard-Jones (KALJ) mixture. We explain why the existence and position of the peak of $\chi_4(t)$ provides no information about the lifetime $\tau_{\rm ex}$ of the heterogeneities. We show that $\chi_4(t)$ depends weakly on $\tau_{\rm ex}$, but find a way to use this weak dependence to estimate $\tau_{\rm ex}$ from $\chi_4(t)$.Comment: Main text: 5 pages, 3 figures. Supplemental material: 2 pages, 1 figur