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Juan P. Garrahan

Publications and source records attributed to Juan P. Garrahan.

At least 181 records · Page 10Linked to original sources
arXiv2007

De-coupling of Exchange and Persistence Times in Atomistic Models of Glass Formers

With molecular dynamics simulations of a fluid mixture of classical particles interacting with pair-wise additive Weeks-Chandler-Andersen potentials, we consider the time series of particle displacements and thereby determine distributions for local persistence times and local exchange times. These basic characterizations of glassy dynamics are studied over a range of super-cooled conditions and shown to have behaviors, most notably de-coupling, similar to those found in kinetically constrained lattice models of structural glasses. Implications are noted.

cond-mat.stat-mech↗
arXiv2007

Dynamic facilitation explains democratic particle motion of metabasin transitions

Transitions between metabasins in supercooled liquids seem to occur through rapid "democratic" collective particle rearrangements. Here we show that this apparent homogeneous particle motion is a direct consequence of dynamic facilitation. We do so by studying metabasin transitions in facilitated spin models and constrained lattice gases. We find that metabasin transitions occur through a sequence of locally facilitated events taking place over a relatively short time frame. When observed on small enough spatial windows these events appear sudden and homogeneous. Our results indicate that metabasin transitions are essentially "non-democratic" in origin and yet another manifestation of dynamical heterogeneity in glass formers.

cond-mat.stat-mech↗
arXiv2007

Dynamic propensity in a kinetically constrained lattice gas

We apply the concept of dynamic propensity to a simple kinetically constrained model of glass formers, the two-vacancy assisted triangular lattice gas, or (2)-TLG. We find that the propensity field, defined in our case as the local root-mean square displacement averaged over the ensemble of trajectories with identical initial configurations, is a good measure of dynamical heterogeneity. This suggests a configurational origin for spatial fluctuations of the dynamics, but just as in the case of atomistic systems, we find that propensity is not correlated to any simple structural property. We show instead that certain extended clusters of particles connected to vacancies correlate well with propensity, indicating that these are the fundamental excitations of the (2)-TLG. We also discuss time-correlations and the correlation between configurations within the propensity ensemble.

cond-mat.stat-mech↗
arXiv2007

Non-equilibrium dynamics of spin facilitated glass models

We consider the dynamics of spin facilitated models of glasses in the non-equilibrium aging regime following a sudden quench from high to low temperatures. We briefly review known results obtained for the broad class of kinetically constrained models, and then present new results for the behaviour of the one-spin facilitated Fredrickson-Andersen and East models in various spatial dimensions. The time evolution of one-time quantities, such as the energy density, and the detailed properties of two-time correlation and response functions are studied using a combination of theoretical approaches, including exact mappings of master operators and reductions to integrable quantum spin chains, field theory and renormalization group, and independent interval and timescale separation methods. The resulting analytical predictions are confirmed by means of detailed numerical simulations. The models we consider are characterized by trivial static properties, with no finite temperature singularities, but they nevertheless display a surprising variety of dynamic behaviour during aging, which can be directly related to the existence and growth in time of dynamic lengthscales. Well-behaved fluctuation-dissipation ratios can be defined for these models, and we study their properties in detail. We confirm in particular the existence of negative fluctuation-dissipation ratios for a large number of observables. Our results suggest that well-defined violations of fluctuation-dissipation relations, of a purely dynamic origin and unrelated to the thermodynamic concept of effective temperatures, could in general be present in non-equilibrium glassy materials.

cond-mat.stat-mech↗
arXiv2006

Space-time thermodynamics and subsystem observables in a kinetically constrained model of glassy systems

In a recent article [M. Merolle et al., Proc. Natl. Acad. Sci. USA 102, 10837 (2005)] it was argued that dynamic heterogeneity in $d$-dimensional glass formers is a manifestation of an order-disorder phenomenon in the $d+1$ dimensions of spacetime. By considering a dynamical analogue of the free energy, evidence was found for phase coexistence between active and inactive regions of spacetime, and it was suggested that this phenomenon underlies the glass transition. Here we develop these ideas further by investigating in detail the one-dimensional Fredrickson-Andersen (FA) model in which the active and inactive phases originate in the reducibility of the dynamics. We illustrate the phase coexistence by considering the distributions of mesoscopic spacetime observables. We show how the analogy with phase coexistence can be strengthened by breaking microscopic reversibility in the FA model, leading to a non-equilibrium theory in the directed percolation universality class.

cond-mat.stat-mech↗
arXiv2006

Lengthscale dependence of dynamic four-point susceptibilities in glass formers

Dynamical four-point susceptibilities measure the extent of spatial correlations in the dynamics of glass forming systems. We show how these susceptibilities depend on the length scales that necessarily form part of their definition. The behaviour of these susceptibilities is estimated by means of an analysis in terms of renewal processes within the context of dynamic facilitation. The analytic results are confirmed by numerical simulations of an atomistic model glass-former, and of two kinetically constrained models. Hence we argue that the scenario predicted by the dynamic facilitation approach is generic.

cond-mat.stat-mech↗
arXiv2006

Fluctuation-dissipation relations in plaquette spin systems with multi-stage relaxation

We study aging dynamics in two non-disordered spin models with multi-spin interactions, following a sudden quench to low temperature. The models are relevant to the physics of supercooled liquids. Their low temperature dynamics resemble those of kinetically constrained models, and obey dynamical scaling, controlled by zero-temperature critical points. Dynamics in both models are thermally activated, resulting in multi-stage relaxation towards equilibrium. We study several two-time correlation and response functions. We find that equilibrium fluctuation-dissipation relations are generically not satisfied during the aging regime, but deviations from them are well described by fluctuation-dissipation ratios, as found numerically in supercooled liquids. These ratios are purely dynamic objects, containing information about the nature of relaxation in the models. They are non-universal, and can even be negative as a result of activated dynamics. Thus, effective temperatures are not well-defined in these models.

cond-mat.stat-mech↗
arXiv2006

Activated aging dynamics and negative fluctuation-dissipation ratios

In glassy materials aging proceeds at large times via thermal activation. We show that this can lead to negative dynamical response functions and novel and well-defined violations of the fluctuation-dissipation theorem, in particular, negative fluctuation-dissipation ratios. Our analysis is based on detailed theoretical and numerical results for the activated aging regime of simple kinetically constrained models. The results are relevant to a variety of physical situations such as aging in glass-formers, thermally activated domain growth and granular compaction.

cond-mat.stat-mech↗
arXiv2005

Fast Simulation of Facilitated Spin Models

We show how to apply the absorbing Markov chain Monte Carlo algorithm of Novotny to simulate kinetically constrained models of glasses. We consider in detail one-spin facilitated models, such as the East model and its generalizations to arbitrary dimensions. We investigate how to maximise the efficiency of the algorithms, and show that simulation times can be improved on standard continuous time Monte Carlo by several orders of magnitude. We illustrate the method with equilibrium and aging results. These include a study of relaxation times in the East model for dimensions d=1 to d=13, which provides further evidence that the hierarchical relaxation in this model is present in all dimensions. We discuss how the method can be applied to other kinetically constrained models.

cond-mat.stat-mech↗
arXiv2005

Dynamical Exchanges in Facilitated Models of Supercooled liquids

We investigate statistics of dynamical exchange events in coarse--grained models of supercooled liquids in spatial dimensions $d=1$, 2, and 3. The models, based upon the concept of dynamical facilitation, capture generic features of statistics of exchange times and persistence times. Here, distributions for both times are related, and calculated for cases of strong and fragile glass formers over a range of temperatures. Exchange time distributions are shown to be particularly sensitive to the model parameters and dimensions, and exhibit more structured and richer behavior than persistence time distributions. Mean exchange times are shown to be Arrhenius, regardless of models and spatial dimensions. Specifically, $ \sim c^{-2}$, with $c$ being the excitation concentration. Different dynamical exchange processes are identified and characterized from the underlying trajectories. We discuss experimental possibilities to test some of our theoretical findings.

cond-mat.stat-mech↗
arXiv2005

Space-time Thermodynamics of the Glass Transition

We consider the probability distribution for fluctuations in dynamical action and similar quantities related to dynamic heterogeneity. We argue that the so-called "glass transition" is a manifestation of low action tails in these distributions where the entropy of trajectory space is sub-extensive in time. These low action tails are a consequence of dynamic heterogeneity and an indication of phase coexistence in trajectory space. The glass transition, where the system falls out of equilibrium, is then an order-disorder phenomenon in space-time occurring at a temperature T_g which is a weak function of measurement time. We illustrate our perspective ideas with facilitated lattice models, and note how these ideas apply more generally.

cond-mat.stat-mech↗
arXiv2005

Static and dynamic lengthscales in a simple glassy plaquette model

We study static and dynamic spatial correlations in a two-dimensional spin model with four-body plaquette interactions and standard Glauber dynamics by means of analytic arguments and Monte Carlo simulations. We study in detail the dynamical behaviour which becomes glassy at low temperatures due to the emergence of effective kinetic constraints in a dual representation where spins are mapped to plaquette variables. We study the interplay between non-trivial static correlations of the spins and the dynamic `four-point' correlations usually studied in the context of supercooled liquids. We show that slow dynamics is spatially heterogeneous due to the presence of diverging lengthscales and scaling, as is also found in kinetically constrained models. This analogy is illustrated by a comparative study of a froth model where the kinetic constraints are imposed.

cond-mat.stat-mech↗
arXiv2005

Heterogeneity and growing lengthscales in the dynamics of kinetically constrained lattice gases in two dimensions

We study dynamical heterogeneity and growing dynamical lengthscales in two kinetically constrained models, namely, the one- and two-vacancy assisted triangular lattice gases. One of the models is a strong glassformer and the other is a fragile glassformer. Both exhibit heterogeneous dynamics with broadly distributed timescales as seen in the distribution of persistence times. We show that the Stokes-Einstein relation is violated, to a greater degree in the fragile glassformer, and show how this violation is related to dynamic heterogeneity. We extract dynamical lengthscales from structure factors of mobile particles and show, quantitatively, the growth of this lengthscale as density increases. We comment on how the scaling of lengths and times in these models relates to that in facilitated spin models of glasses.

cond-mat.stat-mech↗
arXiv2005

Thermodynamics of Coarse Grained Models of Super-Cooled Liquids

In recent papers, we have argued that kinetically constrained coarse grained models can be applied to understand dynamic properties of glass forming materials, and we have used this approach in various applications that appear to validate this view. In one such paper [J.P. Garrahan and D. Chandler, Proc. Nat. Acad. Sci. USA 100, 9710 (2003)], among other things we argued that this approach also explains why the heat capacity discontinuity at the glass transition is generally larger for fragile materials than for strong materials. In the preceding article, Biroli, Bouchaud and Tarjus (BB&T) [cond-mat/0412024] have objected to our explanation on this point, arguing that the class of models we apply is inconsistent with both the absolute size and temperature dependence of the experimental specific heat. Their argument, however, neglects parameters associated with the coarse graining. Accounting for these parameters, we show here that our treatment of dynamics is not inconsistent with heat capacity discontinuities.

cond-mat.stat-mech↗
arXiv2005

Numerical study of a fragile three-dimensional kinetically constrained model

We numerically study the three-dimensional generalization of the kinetically constrained East model, the North-or-East-or-Front (NEF) model. We characterize the equilibrium behaviour of the NEF model in detail, measuring the temperature dependence of several quantities: alpha-relaxation time, distributions of relaxation times, dynamic susceptibility, dynamic correlation length, and four-point susceptibility. We show that the NEF model describes quantitatively experimental observations over an exceptionally wide range of timescales. We illustrate this by fitting experimental data obtained both in the mildly supercooled regime by optical Kerr effect, and close to the glass transition by dielectric spectroscopy.

cond-mat.stat-mech↗
arXiv2005

Glassy behaviour in an exactly solved spin system with a ferromagnetic transition

We show that applying simple dynamical rules to Baxter's eight-vertex model leads to a system which resembles a glass-forming liquid. There are analogies with liquid, supercooled liquid, glassy and crystalline states. The disordered phases exhibit strong dynamical heterogeneity at low temperatures, which may be described in terms of an emergent mobility field. Their dynamics are well-described by a simple model with trivial thermodynamics, but an emergent kinetic constraint. We show that the (second order) thermodynamic transition to the ordered phase may be interpreted in terms of confinement of the excitations in the mobility field. We also describe the aging of disordered states towards the ordered phase, in terms of simple rate equations.

cond-mat.stat-mech↗
arXiv2005

Dynamic Heterogeneity in the Glauber-Ising chain

In a recent paper [P. Mayer et al., Phys. Rev. Lett. 93, 115701 (2004)] it was shown, by means of experiments, theory and simulations, that coarsening systems display dynamic heterogeneity analogous to that of glass formers. Here, we present a detailed analysis of dynamic heterogeneities in the Glauber-Ising chain. We discuss how dynamic heterogeneity in Ising systems must be measured through connected multi-point correlation functions. We show that in the coarsening regime of the Ising chain these multi-point functions reveal the growth of spatial correlations in the dynamics, beyond what can be inferred from standard two-point correlations. They have non-trivial scaling properties, which we interpret in terms of the diffusion-annihilation dynamics of domain walls. In the equilibrium dynamics of the Ising chain, on the other hand, connected multi-point functions vanish exactly and dynamic heterogeneity is not observed. Our results highlight the similarities between coarsening systems and glass formers.

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