Liquids near the glass transition exhibit dynamical heterogeneity, i.e. correlated regions in the liquid relax at either a much faster rate or a much slower rate than the average. This collective phenomenon has been characterized by measurements of a dynamic susceptibility $χ_4(t)$, which are sometimes interpreted in terms of the size of those relaxing regions and the intensity of the fluctuations. We show that the results of those measurements can be affected not only by the collective fluctuations in the relaxation rate, but also by density fluctuations in the initial state and by single-particle fluctuations. We also show that at very long times the average overlap $C(t)$ probing the similarity between an initial and a final state separated by a time interval $t$ decays as a power law $C(t) \sim t^{-d/2}$. This is much slower than the stretched exponential behavior $C(t) \sim {\rm e}^{-(t/τ)^β}$ previously observed at times within one or two orders of magnitude of the $α$-relaxation time $τ_α$. We find that for times longer than $10-100 τ_α$, the dynamic susceptibility $χ_4(t)$ is dominated by single particle fluctuations, and that $χ_4(t) \approx C(t) \sim t^{-d/2}$. Finally, we introduce a method to extract the collective relaxation contribution to the dynamic susceptibility $χ_4(t)$ by subtracting the effects of single-particle fluctuations and initial state density fluctuations. We apply this method to numerical simulations of two glass forming models: a binary hard sphere system and a Kob-Andersen Lennard-Jones system. This allows us to extend the analysis of numerical data to timescales much longer than previously possible, and opens the door for further future progress in the study of dynamic heterogeneities, including the determination of the exchange time.
Clusters of fast and slow correlated particles, identified as dynamical heterogeneities (DHs), con-stitute a central aspect of glassy dynamics. A key ingredient of the glass transition scenario is asignificant increase of the cluster size $ξ$4 as the transition is approached. In need of easy-to-computetools to measure $ξ$4 , the dynamical susceptibility $χ$4 was introduced recently, and used in various ex-perimental works to probe DHs. Here, we investigate DHs in dense microgel suspensions using imagecorrelation analysis, and compute both $χ$4 and the four-point correlation function G4 . The s…
Glasses are ubiquitous in daily life and technology. However the microscopic mechanisms generating this state of matter remain subject to debate: Glasses are considered either as merely hyper-viscous liquids or as resulting from a genuine thermodynamic phase transition towards a rigid state. We show that third- and fifth-order susceptibilities provide a definite answer to this longstanding controversy. Performing the corresponding high-precision nonlinear dielectric experiments for supercooled glycerol and propylene carbonate, we find strong support for theories based upon thermodynamic amorph…
Existence and growth of amorphous order in supercooled liquids approaching glass transition is a subject of intense research. Even after decades of work, there is still no clear consensus on the molecular mechanisms that lead to a rapid slowing down of liquid dynamics approaching this putative transition. The existence of a correlation length associated with amorphous order has recently been postulated and also been estimated using multi-point correlation functions which cannot be calculated easily in experiments. Thus the study of growing amorphous order remains mostly restricted to systems l…
We investigate the growth of dynamic heterogeneity in a glassy hard-sphere mixture for volume fractions up to and including the mode-coupling transition. We use an 80 000 particle system to test a new procedure to evaluate a dynamic correlation length xi(t): we determine the ensemble independent dynamic susceptibility chi_4(t) and use it to facilitate evaluation of xi(t) from the small wave vector behavior of the four-point structure factor. We analyze relations between the alpha relaxation time tau_alpha, chi_4(tau_alpha), and xi(tau_alpha). We find that mode-coupling like power laws provide …
Active glassy systems can be thought of as simple model systems that imitate complex biological systems. Sometimes, it becomes crucial to estimate the amount of the activity present in such biological systems, such as predicting the progression rate of the cancer cells or the healing time of the wound. In this work, we study a model active glassy system to understand a possible quantification of the degree of activity from the collective, long-range phonon response in the system. We find that the four-point dynamic susceptibility, $χ_4(t)$ at the phonon timescale, grows with increased activity…
We propose a microscopic model to study the avalanche problem of insulating glass deformed by external static uniform strain below $T=60$K. We use three-dimensional real-space renormalization procedure to carry out the glass mechanical susceptibility at macroscopic length scale. We prove the existence of irreversible stress drops in amorphous materials, corresponding to the steep positive-negative transitions in glass mechanical susceptibility. We also obtain the strain directions in which the glass system is brittle. The irreversible stress drops in glass essentially come from non-elastic str…
Existing theories explain spin glass transition in terms of a phase transition and order parameters, and assume the existence of a distinct spin glass phase. In addition to problems related to clarifying the nature of this phase, the common challenge is to explain profound dynamic effects. Here, we propose that the main experimental results of spin glass transition can be understood in an entirely dynamic picture, without a reference to a distinct spin glass phase, phase transition and order parameters. In this theory, the susceptibility cusp at the glass transition temperature is due to the d…
We investigate the heterogeneous dynamics in a model, where chemical gelation and glass transition interplay, focusing on the dynamical susceptibility. Two independent mechanisms give raise to the correlations, which are manifested in the dynamical susceptibility: one is related to the presence of permanent clusters, while the other is due to the increase of particle crowding as the glass transition is approached. The superposition of these two mechanisms originates a variety of different behaviours. We show that these two mechanisms can be unentangled considering the wave vector dependence of…
We study the growth kinetics of glassy correlations in a structural glass by monitoring the evolution, within mode-coupling theory, of a suitably defined three-point function $χ_C(t,t_w)$ with time $t$ and waiting time $t_w$. From the complete wave vector-dependent equations of motion for domain growth we pass to a schematic limit to obtain a numerically tractable form. We find that the peak value $χ_C^P$ of $χ_C(t,t_w)$, which can be viewed as a correlation volume, grows as $t_w^{0.5}$, and the relaxation time as $t_w^{0.8}$, following a quench to a point deep in the glassy state. These resul…
We report experimental evidence that a polymer stretched at constant strain rate $\dotλ$ presents complex memory effects after that $\dotλ$ is set to zero at a specific strain $λ_w$ for a duration $t_w$, ranging from $100$s to $ 2.2\times10^5$s. When the strain rate is resumed, both the stress and the dielectric constant relax to the unperturbed state non monotonically. The relaxations depend on the observable, on $λ_w$ and on $t_w$. Relaxation master curves are obtained by scaling the relaxation time as $t/\ln (t_w)$. The dielectric evolution also captures the distribution of the relaxation t…
The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and structural relaxation. The study of the dynamics allows for predictions on the system relaxation above the temperature of dynamic arrest in the mean-field approximation, that are compared with the outcomes of the equations of motion directly derived within the Mode Coupling Theory (MCT) for under-cooled viscous liquids. Varying the external thermodynamic par…
Motivated by the mean field prediction of a Gardner phase transition between a "normal glass" and a "marginally stable glass", we investigate the off-equilibrium dynamics of three-dimensional polydisperse hard spheres, used as a model for colloidal or granular glasses. Deep inside the glass phase, we find that a sharp crossover pressure $P_{\rm G}$ separates two distinct dynamical regimes. For pressure $P < P_{\rm G}$, the glass behaves as a normal solid, displaying fast dynamics that quickly equilibrates within the glass free energy basin. For $P>P_{\rm G}$, instead, the dynamics becomes stro…
We have measured, as a function of the age $t_a$, the aging of the nonlinear dielectric susceptibility $χ_3$ of glycerol below the glass transition. Whereas the linear susceptibility can be accurately accounted for in terms of an age dependent relaxation time $τ_α(t_a)$, this scaling breaks down for $χ_3$, suggesting an increase of the amplitude of $χ_3$. This is a strong indication that the number $N_{corr}$ of molecules involved in relaxation events increases with $t_a$. For $T=0.96 \times T_g$, we find that $N_{corr}$ increases by $\sim 10%$ when $t_a$ varies from $1\mathrm{ks}$ to $100\mat…
An advance was made by Guiselin et al. [arXiv:2103.01569 (2021)] in molecular dynamics simulations of the equilibrium dynamics of supercooled liquids near the experimental glass transition by utilizing the giant equilibration speedup provided by the swap Monte Carlo algorithm. The found emergence of a power law in relaxation spectra at lower temperatures on the high frequency flank of the alpha-loss peak in analogy to the excess wings observed experimentally in molecular glass-formers. Their remarkable finding leads to the question of where the excess wing is located relative to the alpha-loss…
