arXiv subjects

Ludovic Berthier

Publications and source records attributed to Ludovic Berthier.

At least 199 records · Page 11Linked to original sources

arXiv2007

Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations

We study in detail the predictions of various theoretical approaches, in particular mode-coupling theory (MCT) and kinetically constrained models (KCMs), concerning the time, temperature, and wavevector dependence of multi-point correlation functions that quantify the strength of both induced and spontaneous dynamical fluctuations. We also discuss the precise predictions of MCT concerning the statistical ensemble and microscopic dynamics dependence of these multi-point correlation functions. These predictions are compared to simulations of model fragile and strong glass-forming liquids. Overall, MCT fares quite well in the fragile case, in particular explaining the observed crucial role of the statistical ensemble and microscopic dynamics, while MCT predictions do not seem to hold in the strong case. KCMs provide a simplified framework for understanding how these multi-point correlation functions may encode dynamic correlations in glassy materials. However, our analysis highlights important unresolved questions concerning the application of KCMs to supercooled liquids.

cond-mat.stat-mech↗

arXiv2007

Efficient measurement of linear susceptibilities in molecular simulations: Application to aging supercooled liquids

We propose a new method to measure time-dependent linear susceptibilities in molecular simulations, which does not require the use of nonequilibrium simulations, subtraction techniques, or fluctuation-dissipation theorems. The main idea is an exact reformulation of linearly perturbed quantities in terms of observables accessible in unperturbed trajectories. We have applied these ideas to two supercooled liquids in their nonequilibrium aging regime. We show that previous work had underestimated deviations from fluctuation-dissipation relations in the case of a Lennard-Jones system, while our results for silica are in qualitative disagreement with earlier results.

cond-mat.stat-mech↗

arXiv2006

The Monte-Carlo dynamics of a binary Lennard-Jones glass-forming mixture

We use a standard Monte-Carlo algorithm to study the slow dynamics of a binary Lennard-Jones glass-forming mixture at low temperature. We find that Monte-Carlo is by far the most efficient way to simulate a stochastic dynamics since relaxation is about 10 times faster than in Brownian Dynamics and about 30 times faster than in Stochastic Dynamics. Moreover, the average dynamical behaviour of the system is in quantitative agreement with the one obtained using Newtonian dynamics, apart at very short times where thermal vibrations are suppressed. We show, however, that dynamic fluctuations quantified by four-point dynamic susceptibilities do retain a dependence on the microscopic dynamics, as recently predicted theoretically.

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

Direct experimental evidence of a growing length scale accompanying the glass transition

Understanding glass formation is a challenge because the existence of a true glass state, distinct from liquid and solid, remains elusive: Glasses are liquids that have become too viscous to flow. An old idea, as yet unproven experimentally, is that the dynamics becomes sluggish as the glass transition approaches because increasingly larger regions of the material have to move simultaneously to allow flow. We introduce new multipoint dynamical susceptibilities to estimate quantitatively the size of these regions and provide direct experimental evidence that the glass formation of molecular liquids and colloidal suspensions is accompanied by growing dynamic correlation length scales.

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

Lifetime of dynamic heterogeneity in strong and fragile kinetically constrained spin models

Kinetically constrained spin models are schematic coarse-grained models for the glass transition which represent an efficient theoretical tool to study detailed spatio-temporal aspects of dynamic heterogeneity in supercooled liquids. Here, we study how spatially correlated dynamic domains evolve with time and compare our results to various experimental and numerical investigations. We find that strong and fragile models yield different results. In particular, the lifetime of dynamic heterogeneity remains constant and roughly equal to the alpha relaxation time in strong models, while it increases more rapidly in fragile models when the glass transition is approached.

cond-mat.stat-mech↗

arXiv2005

Aging and ultra-slow equilibration in concentrated colloidal hard spheres

We study the dynamic behaviour of concentrated colloidal hard spheres using Time Resolved Correlation, a light scattering technique that can detect the slow evolution of the dynamics in out-of-equilibrium systems. Surprisingly, equilibrium is reached a very long time after sample initialization, the non-stationary regime lasting up to three orders of magnitude more than the relaxation time of the system. Before reaching equilibrium, the system displays unusual aging behaviour. The intermediate scattering function decays faster than exponentially and its relaxation time evolves non-monotonically with sample age.

cond-mat.soft↗

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

Temperature Cycles in the Heisenberg Spin Glass

We study numerically the nonequilibrium dynamics of the three-dimensional Heisenberg Edwards-Anderson spin glass submitted to protocols during which temperature is shifted or cycled within the spin glass phase. We show that (partial) rejuvenation and (perfect) memory effects can be numerically observed and study both effects in detail. We quantitatively characterize their dependences on parameters such as the amplitude of the temperature changes, the timescale at which the changes are performed, and the cooling rates used to vary the temperature. We contrast our results both to those found numerically in the Ising version of the model, and to experimental results in different samples. We discuss the theoretical interpretations of our findings, arguing, in particular, that `full' rejuvenation can be observed in experiments even if temperature chaos is absent.

cond-mat.dis-nn↗

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.

cond-mat.stat-mech↗

arXiv2005

Length scale for the onset of Fickian diffusion in supercooled liquids

The interplay between self-diffusion and excitation lines in space-time was recently studied in kinetically constrained models to explain the breakdown of the Stokes-Einstein law in supercooled liquids. Here, we further examine this interplay and its manifestation in incoherent scattering functions. In particular, we establish a dynamic length scale below which Fickian diffusion breaks down, as is observed in experiments and simulations. We describe the temperature dependence of this length scale in liquids of various fragilities, and provide analytical estimates for the van Hove and self-intermediate scattering functions.

cond-mat.stat-mech↗

arXiv2004

What do we learn from the shape of the dynamical susceptibility of glass-formers?

We compute analytically and numerically the four-point correlation function that characterizes non-trivial cooperative dynamics in glassy systems within several models of glasses: elasto-plastic deformations, mode-coupling theory (MCT), collectively rearranging regions (CRR), diffusing defects and kinetically constrained models (KCM). Some features of the four-point susceptibility chi_4(t) are expected to be universal. at short times we expect an elastic regime characterized by a t or sqrt{t} growth. We find both in the beta, and the early alpha regime that chi_4 sim t^mu, where mu is directly related to the mechanism responsible for relaxation. This regime ends when a maximum of chi_4 is reached at a time t=t^* of the order of the relaxation time of the system. This maximum is followed by a fast decay to zero at large times. The height of the maximum also follows a power-law, chi_4(t^*) sim t^{*lambda}. The value of the exponents mu and lambda allows one to distinguish between different mechanisms. For example, freely diffusing defects in d=3 lead to mu=2 and lambda=1, whereas the CRR scenario rather predicts either mu=1 or a logarithmic behaviour depending on the nature of the nucleation events, and a logarithmic behaviour of chi_4(t^*). MCT leads to mu=b and lambda =1/gamma, where b and gamma are the standard MCT exponents. We compare our theoretical results with numerical simulations on a Lennard-Jones and a soft-sphere system. Within the limited time-scales accessible to numerical simulations, we find that the exponent mu is rather small, mu < 1, with a value in reasonable agreement with the MCT predictions.

cond-mat.dis-nn↗

arXiv2004

Spatially heterogeneous dynamics in granular compaction

We prove the emergence of spatially correlated dynamics in slowly compacting dense granular media by analyzing analytically and numerically multi-point correlation functions in a simple particle model characterized by slow non-equilibrium dynamics. We show that the logarithmically slow dynamics at large times is accompanied by spatially extended dynamic structures that resemble the ones observed in glass-forming liquids and dense colloidal suspensions. This suggests that dynamic heterogeneity is another key common feature present in very different jamming materials.

cond-mat.stat-mech↗

arXiv2004

A few bubbles in a glass

I briefly review a recent series of papers putting forward a coarse-grained theoretical approach to the physics of supercooled liquids approaching their glass transition. After a suitable coarse-graining, the dynamics of the liquid is replaced by that of a mobility field, which can then be analytically treated. The statistical properties of the mobility field then determine those of the liquid. Thermodynamic, spatial, topographic, dynamic properties of the liquid can then be quantitatively described within a single framework, and derive from the existence of an underlying dynamic critical point located at zero-temperature, where timescales and lengthscales diverge.

cond-mat.stat-mech↗

arXiv2004

Renormalization group study of a kinetically constrained model for strong glasses

We derive a dynamic field theory for a kinetically constrained model, based on the Fredrickson--Andersen model, which we expect to describe the properties of an Arrhenius (strong) supercooled liquid at the coarse-grained level. We study this field theory using the renormalization group. For mesoscopic length and time scales, and for space dimension d \geq 2, the behaviour of the model is governed by a zero-temperature dynamical critical point in the directed percolation universality class. We argue that in d=1 its behaviour is that of compact directed percolation. We perform detailed numerical simulations of the corresponding Fredrickson-Andersen model on the lattice in various dimensions, and find reasonable quantitative agreement with the field theory predictions.

cond-mat.stat-mech↗

arXiv2004

Heterogeneous Dynamics of Coarsening Systems

We show by means of experiments, theory and simulations, that the slow dynamics of coarsening systems displays dynamic heterogeneity similar to that observed in glass-forming systems. We measure dynamic heterogeneity via novel multi-point functions which quantify the emergence of dynamic, as opposed to static, correlations of fluctuations. Experiments are performed on a coarsening foam using Time Resolved Correlation, a recently introduced light scattering method. Theoretically we study the Ising model, and present exact results in one dimension, and numerical results in two dimensions. For all systems the same dynamic scaling of fluctuations with domain size is observed.

cond-mat.stat-mech↗