arXiv subjects

Ludovic Berthier

Publications and source records attributed to Ludovic Berthier.

At least 91 records · Page 5Linked to original sources

arXiv2019

Lectures on non-equilibrium active systems

These notes are based on lectures given during the Summer School `Active matter and non-equilibrium statistical physics', held in Les Houches in September 2018. In these notes, we have merged our lectures into a single chapter broadly dedicated to `Non-equilibrium active systems'. We start with a discussion of generic features of non-equilibrium statistical mechanics, followed by a description of selected examples of the possible consequences of not being at thermal equilibrium. We then introduce the topic of dense glassy materials with a short review of glassy dynamics, rheology and jamming transitions for systems that are not active. We then discuss dense active materials, from simple mean-field theories to numerical models and experimental realizations. Finally, we discuss two examples of materials driven out of equilibrium by an oscillatory driving force.

cond-mat.stat-mech↗

arXiv2019

Perspective: Configurational entropy of glass-forming liquids

The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraud with difficulties, misconceptions and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain why the configurational entropy has become a key quantity to describe glassy materials, from early empirical observations to modern theoretical treatments. We explain why practical measurements necessarily require approximations that make its physical interpretation delicate. We then demonstrate that computer simulations have become an invaluable tool to obtain precise, non-ambiguous, and experimentally-relevant measurements of the configurational entropy. We describe a panel of available computational tools, offering for each method a critical discussion. This perspective should be useful to both experimentalists and theoreticians interested in glassy materials and complex systems.

cond-mat.stat-mech↗

arXiv2019

Sound attenuation in stable glasses

Understanding the difference between universal low-temperature properties of amorphous and crystalline solids requires an explanation of the stronger damping of long-wavelength phonons in amorphous solids. A longstanding sound attenuation scenario, resulting from a combination of experiments, theories, and simulations, leads to a quartic scaling of sound attenuation with the wavevector, which is commonly attributed to Rayleigh scattering of the sound. Modern computer simulations offer conflicting conclusions regarding the validity of this picture. We simulate glasses with an unprecedentedly broad range of stabilities to perform the first microscopic analysis of sound damping in model glass formers across a range of experimentally relevant preparation protocols. We present a convincing evidence that quartic scaling is recovered for small wavevectors irrespective of the glass's stability. With increasing stability, the wavevector where the quartic scaling begins increases by approximately a factor of three and the sound attenuation decreases by over an order of magnitude. Our results uncover an intimate connection between glass stability and sound damping.

cond-mat.soft↗

arXiv2019

Perspective: Gardner Physics in Amorphous Solids and Beyond

One of the most remarkable predictions to emerge out of the exact infinite-dimensional solution of the glass problem is the Gardner transition. Although this transition was first theoretically proposed a generation ago for certain mean-field spin glass models, its materials relevance was only realized when a systematic effort to relate glass formation and jamming was undertaken. A number of nontrivial physical signatures associated to the Gardner transition have since been considered in various areas, from models of structural glasses to constraint satisfaction problems. This Perspective surveys these recent advances and discusses the novel research opportunities that arise from them.

cond-mat.stat-mech↗

arXiv2019

Universal relaxation dynamics of sphere packings below jamming

We show that non-Brownian suspensions of repulsive spheres below jamming display a slow relaxational dynamics with a characteristic time scale that diverges at jamming. This slow time scale is fully encoded in the structure of the unjammed packing and can be readily measured via the vibrational density of states. We show that the corresponding dynamic critical exponent is the same for randomly generated and sheared packings. Our results show that a wide variety of physical situations, from suspension rheology to algorithmic studies of the jamming transition are controlled by a unique diverging timescale, with a universal critical exponent.

cond-mat.soft↗

arXiv2019

Hierarchical landscape of hard disk glasses

We numerically analyse the landscape governing the evolution of the vibrational dynamics of hard disk glasses as the density increases towards jamming. We find that the dynamics becomes slow, spatially correlated, and starts to display aging dynamics across an avoided Gardner transition, with a phenomenology that resembles three dimensional observations. We carefully analyse the behaviour of single glass samples, and find that the emergence of aging dynamics is controlled by the apparition of a complex organisation of the landscape that splits into a remarkable hierarchy of minima as jamming is approached. Our results show that the mean-field prediction of a Gardner phase characterized by an ultrametric structure of the landscape provides a useful description of finite dimensional systems, even when the Gardner transition is avoided.

cond-mat.dis-nn↗

arXiv2019

Perspective: Nonequilibrium glassy dynamics in dense systems of active particles

Despite the diversity of materials designated as active matter, virtually all active systems undergo a form of dynamic arrest when crowding and activity compete, reminiscent of the dynamic arrest observed in colloidal and molecular fluids undergoing a glass transition. We present a short perspective on recent and ongoing efforts to understand how activity competes with other physical interactions in dense systems. We first review recent experimental work on active materials that uncovered both classic signatures of glassy dynamics and intriguing novel phenomena at large density. We introduce a minimal model of self-propelled particles where the competition between interparticle interactions, crowding, and self-propulsion can be studied in great detail. We discuss more complex models that include some additional, material-specific ingredients. We end with some general perspectives on dense active materials, suggesting directions for future research, in particular for theoretical work.

cond-mat.soft↗

arXiv2019

Rejuvenation and Memory Effects in a Structural Glass

We show numerically that a three-dimensional model for structural glass displays aging, rejuvenation and memory effects when submitted to a temperature cycle. These effects indicate that the free energy landscape of structural glasses may possess the complex hierarchical structure that characterize materials such as spin and polymer glasses. We use the theoretical concept of marginal stability to interpret our results, and explain in which physical conditions a complex aging dynamics can emerge in dense supercooled liquids, paving the way for future experimental studies of complex aging dynamics in colloidal and granular glasses.

cond-mat.soft↗

arXiv2019

Marginally stable phases in mean-field structural glasses

A novel form of amorphous matter characterized by marginal stability was recently discovered in the mean-field theory of structural glasses. Using this approach, we provide complete phase diagrams delimiting the location of the marginally stable glass phase for a large variety of pair interactions and physical conditions, extensively exploring physical regimes relevant to granular matter, foams, emulsions, hard and soft colloids, and molecular glasses. We find that all types of glasses may become marginally stable, but the extent of the marginally stable phase highly depends on the preparation protocol. Our results suggest that marginal phases should be observable for colloidal and non-Brownian particles near jamming, and poorly annealed glasses. For well-annealed glasses, two distinct marginal phases are predicted. Our study unifies previous results on marginal stability in mean-field models, and will be useful to guide numerical simulations and experiments aimed at detecting marginal stability in finite dimensional amorphous materials.

cond-mat.stat-mech↗

arXiv2019

Low-frequency vibrational modes of stable glasses

We numerically study the evolution of the vibrational density of states $D(ω)$ of zero-temperature glasses when their kinetic stability is varied over an extremely broad range, ranging from poorly annealed glasses obtained by instantaneous quenches from above the onset temperature, to ultrastable glasses obtained by quenching systems thermalised below the experimental glass temperature. The low-frequency part of the density of states splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behaviour ($D(ω) \sim ω^2$) at low-frequency, with a strong correlation between the two regimes. Quasi-localized modes instead obey $D(ω) \sim ω^4$, irrespective of the glass stability. However, the prefactor of this quartic law becomes smaller in more stable glasses, and the corresponding modes become more localized and sparser. Our work is the first numerical observation of quasi-localized modes in a regime relevant to experiments, and it establishes a direct connection between glass stability and soft vibrational motion in amorphous solids.

cond-mat.soft↗

arXiv2018

Efficient swap algorithms for molecular dynamics simulations of equilibrium supercooled liquids

It was recently demonstrated that a simple Monte Carlo (MC) algorithm involving the swap of particle pairs dramatically accelerates the equilibrium sampling of simulated supercooled liquids. We propose two numerical schemes integrating the efficiency of particle swaps into equilibrium molecular dynamics (MD) simulations. We first develop a hybrid MD/MC scheme combining molecular dynamics with the original swap Monte Carlo. We implement this hybrid method in LAMMPS, a software package employed by a large community of users. Secondly, we define a continuous time version of the swap algorithm where both the positions and diameters of the particles evolve via Hamilton's equations of motion. For both algorithms, we discuss in detail various technical issues as well as the optimisation of simulation parameters. We compare the numerical efficiency of all available swap algorithms and discuss their relative merits.

cond-mat.stat-mech↗

arXiv2018

Configurational entropy of polydisperse supercooled liquids

We propose a computational method to measure the configurational entropy in generic polydisperse glass-formers. In particular, our method resolves issues related to the diverging mixing entropy term due to a continuous polydispersity. The configurational entropy is measured as the difference between the well-defined fluid entropy and a more problematic glass entropy. We show that the glass entropy can be computed by a simple generalisation of the Frenkel-Ladd thermodynamic integration method, which includes permutations of the particle diameters. This approach automatically provides a physically meaningful mixing entropy, and includes contributions that are not purely vibrational. The proposed configurational entropy is thus devoid of conceptual and technical difficulties due to continuous polydispersity, while being conceptually closer and technically simpler than alternative free energy approaches.

cond-mat.stat-mech↗

arXiv2018

Bypassing sluggishness: SWAP algorithm and glassiness in high dimensions

The recent implementation of a swap Monte Carlo algorithm (SWAP) for polydisperse mixtures fully bypasses computational sluggishness and closes the gap between experimental and simulation timescales in physical dimensions $d=2$ and $3$. Here, we consider suitably optimized systems in $d=2, 3,\dots, 8$, to obtain insights into the performance and underlying physics of SWAP. We show that the speedup obtained decays rapidly with increasing the dimension. SWAP nonetheless delays systematically the onset of the activated dynamics by an amount that remains finite in the limit $d \to \infty$. This shows that the glassy dynamics in high dimensions $d>3$ is now computationally accessible using SWAP, thus opening the door for the systematic consideration of finite-dimensional deviations from the mean-field description.

cond-mat.stat-mech↗

arXiv2018

Discontinuous shear-thickening in Brownian suspensions

Discontinuous shear-thickening in dense suspensions naturally emerges from the activation of frictional forces by shear flow in non-Brownian systems close to jamming. Yet, this physical picture is incomplete as most experiments study soft colloidal particles subject to thermal fluctuations. To characterise discontinuous shear-thickening in colloidal suspensions we use computer simulations to provide a complete description of the competition between athermal jamming, frictional forces, thermal motion, particle softness, and shear flow. We intentionally neglect hydrodynamics, electrostatics, lubrication, and inertia, but can nevertheless achieve quantitative agreement with experimental findings. In particular, shear-thickening corresponds to a crossover between frictionless and frictional jamming regimes which is controlled by thermal fluctuations and particle softness and occurs at a softness dependent Péclet number. We also explore the consequences of our findings for constant pressure experiments, and critically discuss the reported emergence of `S-shaped' flow curves. Our work provides the minimal ingredients to quantitatively interpret a large body of experimental work on discontinuous shear-thickening in colloidal suspensions.

cond-mat.soft↗

arXiv2018

Can the glass transition be explained without a growing static length scale?

It was recently discovered that SWAP, a Monte Carlo algorithm that involves the exchange of pairs of particles of differing diameters, can dramatically accelerate the equilibration of simulated supercooled liquids in regimes where the normal dynamics is glassy. This spectacular effect was subsequently interpreted as direct evidence against a static, cooperative explanation of the glass transition such as the one offered by the random first-order transition (RFOT) theory. We review several empirical facts that support the opposite view, namely, that a local mechanism cannot explain the glass transition phenomenology. We explain the speedup induced by SWAP within the framework of the RFOT theory. We suggest that the efficiency of SWAP stems from a postponed onset of glassy dynamics, which allows the efficient exploration of configuration space even in the regime where the physical dynamics is dominated by activated events across free-energy barriers. We describe this effect in terms of `crumbling metastability' and use the example of nucleation to illustrate the possibility of circumventing free-energy barriers of thermodynamic origin by a change of the local dynamical rules.

cond-mat.stat-mech↗

arXiv2018

Zero-temperature glass transition in two dimensions

The nature of the glass transition is theoretically understood in the mean-field limit of infinite spatial dimensions, but the problem remains totally open in physical dimensions. Nontrivial finite-dimensional fluctuations are hard to control analytically, and experiments fail to provide conclusive evidence regarding the nature of the glass transition. Here, we use Monte Carlo simulations that fully bypass the glassy slowdown, and access equilibrium states in two-dimensional glass-forming liquids at low enough temperatures to directly probe the transition. We find that the liquid state terminates at a thermodynamic glass transition at zero temperature, which is associated with an entropy crisis and a diverging static correlation length.

cond-mat.stat-mech↗

arXiv2018

A random critical point separates brittle and ductile yielding transitions in amorphous materials

We combine an analytically solvable mean-field elasto-plastic model with molecular dynamics simulations of a generic glass-former to demonstrate that, depending on their preparation protocol, amorphous materials can yield in two qualitatively distinct ways. We show that well-annealed systems yield in a discontinuous brittle way, as metallic and molecular glasses do. Yielding corresponds in this case to a first-order nonequilibrium phase transition. As the degree of annealing decreases, the first-order character becomes weaker and the transition terminates in a second-order critical point in the universality class of an Ising model in a random field. For even more poorly annealed systems, yielding becomes a smooth crossover, representative of the ductile rheological behavior generically observed in foams, emulsions, and colloidal glasses. Our results show that the variety of yielding behavior found in amorphous materials does not result from the diversity of particle interactions or microscopic dynamics {\it per se}, but is instead unified by carefully considering the role of the initial stability of the system.

cond-mat.dis-nn↗

arXiv2018

Local order and crystallization of dense polydisperse hard spheres

Computer simulations give precious insight into the microscopic behavior of supercooled liquids and glasses, but their typical time scales are orders of magnitude shorter than the experimentally relevant ones. We recently closed this gap for a class of models of size polydisperse fluids, which we successfully equilibrate beyond laboratory time scales by means of the swap Monte Carlo algorithm. In this contribution, we study the interplay between compositional and geometric local orders in a model of polydisperse hard spheres equilibrated with this algorithm. Local compositional order has a weak state dependence, while local geometric order associated to icosahedral arrangements grows more markedly but only at very high density. We quantify the correlation lengths and the degree of sphericity associated to icosahedral structures and compare these results to those for the Wahnström Lennard-Jones mixture. Finally, we analyze the structure of very dense samples that partially crystallized following a pattern incompatible with conventional fractionation scenarios. The crystal structure has the symmetry of aluminum diboride and involves a subset of small and large particles with size ratio approximately equal to 0.5.

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