Continuous-time random-walk approach to supercooled liquids. I. Different definitions of particle jumps and their consequences

Microscopic dynamics of enhanced glass-forming ability with minor oxygen addition in bulk metallic glasses

Minor oxygen addition has been proposed as a promising strategy to enhance the performance of metallic glasses, particularly their glass-forming ability. In this work, we investigate the microscopic dynamics of a CuZr glass former with oxygen content up to 2 at. % using molecular dynamics simulations based on specially developed neural network interatomic potentials. Our findings indicate a gradual increase in the glass transition temperature with oxygen addition, with an anomalous peak at 0.4 at. % O. We reveal an anti-correlation of kinetic fragility and dynamic heterogeneity behind this unusual rise, where the system exhibits reduced kinetic fragility alongside more significant dynamic heterogeneity. Using the continuous time random walk method, we show that at 0.4 at. % O, a highly mobile Cu atomic layer forms around O-Zr clusters, resulting in notable dynamic heterogeneity. This dynamic behavior is closely linked to the bonding pattern within the O-Zr network, particularly favoring the configuration with edge and surface sharing. In addition, such structures contribute to a more compact O-Zr network, leading to lower kinetic fragility. These findings provide detailed insights into the microscopic dynamics behind the effects of minor oxygen additions.

Relaxation dynamics of a liquid in the vicinity of an attractive surface: The process of escaping from the surface

We analyze the displacements of the particles of a glass-forming molecular liquid perpendicular to a confining solid surface using extensive molecular dynamics simulations with atomistic models. In the vicinity of an attractive surface, the liquid molecules are trapped. Transient localization of liquid molecules near the surface introduces a relaxation process related to the escape of molecules from the surface into the dynamics of the interfacial liquid layer. To describe this process, we analyze several dynamical observables of the confined liquid. The self-intermediate scattering function and the mean-squared displacement of the particles located in the interfacial layer are dominated by the process of escaping from the surface. This relaxation process is also associated with a strong heterogeneity in the mobility of the interfacial particles. The studied model liquid is hydrogenated methyl methacrylate. For the confining wall, we consider different models, namely a periodic single layer of graphene and a frozen amorphous configuration of the bulk liquid (frozen wall). Near graphene, where the liquid molecules form a layered structure and adopt parallel-to-surface orientation, a clear separation between small-scale movements of the molecules near the surface and the process of escaping from the surface is observed. This is reflected in the three-step relaxation of the interfacial layer. However, near the frozen wall, where the liquid molecules do not have a preferential alignment, a clear three-step relaxation is not seen, even though the dynamical quantities are controlled by the process of escaping from the surface.

A Monte Carlo simulation of tracer diffusion in amorphous polymers

Tracer diffusion in amorphous polymers is a sought-after quantity for a range of technological applications. In this regard, a quantitative description of the so-called decoupling from the reverse proportionality between viscosity and diffusion coefficient into a fractional one remains a challenge requiring a deeper insight. This work employs a Monte Carlo simulation framework in 3 dimensions to investigate the consequences of different scenarios for estimating this fractional exponent on the diffusion coefficient of tracers in polymers near glass transition. To this end, we adopted a continuous-time random walk model for tracer diffusion in the supercooled liquid state. The waiting time distribution of the diffusants was computed based on the rotational correlation times of the polymer. This proposed procedure is of particular interest because it brings the quantity of waiting time (and its statistics) in connection with the measurable observable of rotational times. In the framework of our simulations the aforementioned fractional exponent appears in the relation between the diffusant's waiting time and the rotational time of the diffusion medium. A limited comparison with experimental diffusivities from the literature revealed a reasonable agreement with a fractional exponent on the basis of the molar volumes of the diffusant and the monomeric unit. Finally, an analysis of time-averaged mean squared displacement pointed to normal Brownian dynamics for tracer diffusion in polymers above the glass transition temperature.

Anomalous Fluctuations in a Droplet of Chemically Active Colloids or Enzymes

Chemically active colloids or enzymes cluster into dense droplets driven by their phoretic response to collectively generated chemical gradients. Employing Brownian dynamics simulation techniques, our study of the dynamics of such a chemically active droplet uncovers a rich variety of structures and dynamical properties, including the full range of fluidlike to solidlike behavior, and non-Gaussian positional fluctuations. Our work sheds light on the complex dynamics of the active constituents of metabolic clusters, which are the main drivers of nonequilibrium activity in living systems.

The influence of molecular shape on glass-forming behavior in a minimalist trimer model

In this study, we employed molecular dynamics simulations to probe the influence of molecular morphological changes on the dynamic behavior of a model consisting of trimer molecules. This model, comprising a chain of three particles, facilitates the exploration of variations in the internal angle between these particles. Our findings highlight the significant impact of molecular conformation: systems with more linear conformations, characterized by larger internal angles, exhibit relaxation times several orders of magnitude greater than their counterparts with smaller internal angles. Furthermore, we delve into the role of angular interaction rigidity, uncovering a pronounced deceleration in dynamics and an increase in dynamic heterogeneity as rigidity escalates. This model not only provides insights into azobenzene-type systems but also sets the stage for subsequent research into the microscopic nuances of related systems, with potential extensions to composite systems.

Comparing Microscopic and Macroscopic Dynamics in a Paradigmatic Model of Glass-Forming Molecular Liquid

Glass transition is a most intriguing and long-standing open issue in the field of molecular liquids. From a macroscopic perspective, glass-forming systems display a dramatic slowing-down of the dynamics, with the inverse diffusion coefficient and the structural relaxation times increasing by orders of magnitude upon even modest supercooling. At the microscopic level, single-molecule motion becomes strongly intermittent, and can be conveniently described in terms of “cage-jump” events. In this work, we investigate a paradigmatic glass-forming liquid, the Kob–Andersen Lennard–Jones model, by means of Molecular Dynamics simulations, and compare the macroscopic and microscopic descriptions of its dynamics on approaching the glass-transition. We find that clear changes in the relations between macroscopic timescales and cage-jump quantities occur at the crossover temperature where Mode Coupling-like description starts failing. In fact, Continuous Time Random Walk and lattice model predictions based on cage-jump statistics are also violated below the crossover temperature, suggesting the onset of a qualitative change in cage-jump motion. Interestingly, we show that a fully microscopic relation linking cage-jump time- and length-scales instead holds throughout the investigated temperature range.

A model-system of Fickian yet non-Gaussian diffusion: light patterns in place of complex matter

Fickian yet non-Gaussian Diffusion (FnGD), widely observed for colloidal particles in a variety of complex and biological fluids, emerges as a most intriguing open issue in Soft Matter. To fully monitor FnGD and advance its understanding, recording many trajectories over a large time range is crucial, which makes experiments challenging. Here we exploit a recently introduced experimental model of finely tunable FnGD: a quasi-2d system of Brownian beads in water moving in a heterogeneous energy landscape generated by a static and spatially random optical force field (speckle pattern). By performing experiments at different optical power, we succeed in monitoring the evolution as well as the precursors of FnGD. Fickian scaling of the mean square displacement is always attained after a subdiffusive regime while the displacement distributions keep on being non-Gaussian, which allows for measuring a characteristic length- and time-scale for the onset of FnGD, ξ_f and t_f. We find that ξ_f stays constant, whereas t_f grows as the inverse of the long-time diffusion coefficient t_f ∝ D^-1 for increasing the optical power. Deviations from the standard Gaussian shape of the displacement distribution are neatly characterized on a broad range of times, focusing on the excess probability at small displacements and on the decay-length of the distinctive exponential tails. Such deviations are fully built in the subdiffusive regime and, at the FnGD onset, grow with the optical power. As time goes on, the small-displacement probability narrows and the exponential tails progressively break up, with a tendency to recover the Gaussian behaviour. Overall, both subdiffusion and FnGD become more marked and persistent on increasing the optical power, suggesting a strict relation between these two regimes. As clearly demonstrated by our results, the adopted model-system represents a privileged stage for in-depth study of FnGD and opens the way to unveil the nature of this phenomenon through finely tuned and well-controlled experiments.

Advances in the study of supercooled water

In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.

Distinct molecular dynamics dividing liquid-like and gas-like supercritical hydrogens

Understanding how a supercritical fluid is related to normal liquid and gas and separating it into liquid-like and gas-like regions are of fundamental and practical importance. Despite the usefulness of hydrogen storage, molecular dynamics images on supercritical hydrogens exhibiting strong nuclear quantum effects are scarce. Taking advantage of the non-empirical ab initio molecular dynamics method for hydrogen molecules, we found that, while radial distribution functions and diffusion show a monotonic change along the density, van Hove time correlation functions and intramolecular properties such as bond length and vibrational frequency exhibit the anomalous order crossing the Widom line. By demonstrating that the anomalous order stemmed from the largest deviations between liquid-like and gas-like solvations formed around the Widom line, we concluded that this supercritical fluid is a mixture of liquid and gas possessing heterogeneity. The obtained physical insights can be an index to monitor the supercriticality and to identify distinct liquid-like and gas-like supercritical fluids.

Breakdown of the Stokes-Einstein relation in supercooled liquids: A cage-jump perspective

The breakdown of the Stokes-Einstein relation in supercooled liquids, which is the increase in the ratio τ_ατ_D between the two macroscopic times for structural relaxation and diffusion on decreasing the temperature, is commonly ascribed to dynamic heterogeneities, but a clear-cut microscopic interpretation is still lacking. Here, we tackle this issue exploiting the single-particle cage-jump framework to analyze molecular dynamics simulations of soft disk assemblies and supercooled water. We find that τ_ατ_D∝⟨t_p⟩⟨t_c⟩, where ⟨t_p⟩ and ⟨t_c⟩ are the cage-jump times characterizing slow and fast particles, respectively. We further clarify that this scaling does not arise from a simple term-by-term proportionality; rather, the relations τ_α∝⟨t_p⟩⟨Δr_J ²⟩ and τ_D∝⟨t_c⟩⟨Δr_J ²⟩ effectively connect the macroscopic and microscopic timescales, with the mean square jump length ⟨Δr_J ²⟩ shrinking on cooling. Our work provides a microscopic perspective on the Stokes-Einstein breakdown and generalizes previous results on lattice models to the case of more realistic glass-formers.

Rapid Fickian Yet Non-Gaussian Diffusion after Subdiffusion

The recently discovered Fickian yet non-Gaussian diffusion (FnGD) is here finely tuned and investigated over a wide range of probabilities and timescales using a quasi-2D suspension of colloidal beads under the action of a static and spatially random optical force field. This experimental model allows one to demonstrate that a "rapid" FnGD regime with a diffusivity close to that of free suspension can originate from earlier subdiffusion. We show that these two regimes are strictly tangled: as subdiffusion deepens upon increasing the optical force, deviations from Gaussianity in the FnGD regime become larger and more persistent in time. In addition, the distinctive exponential tails of FnGD are quickly built up in the subdiffusive regime. Our results shed new light on previous experimental observations and suggest that FnGD may generally be a memory effect of earlier subdiffusive processes.

Decelerated Liquid Dynamics Induced by Component-Dependent Supercooling in Hydrogen and Deuterium Quantum Mixtures

Isotopic mixtures of p-H₂ and o-D₂ molecules have been an attractive binary system because they include two kinds of purely isotopic molecules which possess the same electronic potential but the twice different mass inducing differently pronounced nuclear quantum effects (NQEs). Accessing details of structures and dynamics in such quantum mixtures combining complex molecular dynamics with NQEs of different strengths remains a challenging problem. Taking advantage of the nonempirical molecular dynamics method which describes p-H₂ and o-D₂ molecules, we found that the liquid dynamics slows down at a specific mixing ratio, which can be connected to the observed anomalous slowdown of crystallization in the quantum mixtures. We attributed the decelerated dynamics to the component-dependent supercooling of p-H₂ taking place in the mixtures, demonstrating that there is an optimal mixing ratio to hinder crystallization. The obtained physical insights will help in experimentally controlling and achieving unknown quantum mixtures including superfluid.

Packets of Diffusing Particles Exhibit Universal Exponential Tails

Brownian motion is a Gaussian process described by the central limit theorem. However, exponential decays of the positional probability density function P(X,t) of packets of spreading random walkers, were observed in numerous situations that include glasses, live cells, and bacteria suspensions. We show that such exponential behavior is generally valid in a large class of problems of transport in random media. By extending the large deviations approach for a continuous time random walk, we uncover a general universal behavior for the decay of the density. It is found that fluctuations in the number of steps of the random walker, performed at finite time, lead to exponential decay (with logarithmic corrections) of P(X,t). This universal behavior also holds for short times, a fact that makes experimental observations readily achievable.

Brownian motion with alternately fluctuating diffusivity: Stretched-exponential and power-law relaxation

We investigate Brownian motion with diffusivity alternately fluctuating between fast and slow states. We assume that sojourn-time distributions of these two states are given by exponential or power-law distributions. We develop a theory of alternating renewal processes to study a relaxation function which is expressed with an integral of the diffusivity over time. This relaxation function can be related to a position correlation function if the particle is in a harmonic potential and to the self-intermediate scattering function if the potential force is absent. It is theoretically shown that, at short times, the exponential relaxation or the stretched-exponential relaxation are observed depending on the power-law index of the sojourn-time distributions. In contrast, at long times, a power-law decay with an exponential cutoff is observed. The dependencies on the initial ensembles (i.e., equilibrium or nonequilibrium initial ensembles) are also elucidated. These theoretical results are consistent with numerical simulations.

Automated detection of many-particle solvation states for accurate characterizations of diffusion kinetics

Discrete-space kinetic models, i.e., Markov state models, have emerged as powerful tools for reducing the complexity of trajectories generated from molecular dynamics simulations. These models require configuration-space representations that accurately characterize the relevant dynamics. Well-established, low-dimensional order parameters for constructing this representation have led to widespread application of Markov state models to study conformational dynamics in biomolecular systems. On the contrary, applications to characterize single-molecule diffusion processes have been scarce and typically employ system-specific, higher-dimensional order parameters to characterize the local solvation state of the molecule. In this work, we propose an automated method for generating a coarse configuration-space representation, using generic features of the solvation structure-the coordination numbers about each particle. To overcome the inherent noisy behavior of these low-dimensional observables, we treat the features as indicators of an underlying, latent Markov process. The resulting hidden Markov models filter the trajectories of each feature into the most likely latent solvation state at each time step. The filtered trajectories are then used to construct a configuration-space discretization, which accurately describes the diffusion kinetics. The method is validated on a standard model for glassy liquids, where particle jumps between local cages determine the diffusion properties of the system. Not only do the resulting models provide quantitatively accurate characterizations of the diffusion constant, but they also reveal a mechanistic description of diffusive jumps, quantifying the heterogeneity of local diffusion.

Isotopic Effects on Intermolecular and Intramolecular Structure and Dynamics in Hydrogen, Deuterium, and Tritium Liquids: Normal Liquid and Weakly and Strongly Cooled Liquids

Differences in properties such as phase-transition temperature and transport coefficients among liquids of different isotopic compositions, hydrogen, deuterium, and tritium, should originate from their differently pronounced nuclear quantum effects (NQEs) rather than from any subtle difference in the electronic interaction potentials. Accurate and efficient determination of structural and dynamical isotopic effects in the quantum liquids still remains as one of the challenging problems in condensed-phase physics. With a recently developed nonempirical real-time molecular dynamics method which describes nonspherical molecules with the NQEs, we computationally realized and investigated dynamical and quantum isotopic effects of not only traditionally studied isotopes, hydrogen, and deuterium but also a lesser known radioisotope, tritium, in broad thermodynamic conditions from normal liquid to weakly and strongly cooled liquids, which have been hindered by rapid crystallization in spite of numerous experimental attempts at supercooling. Reproducing the previously reported experimental isotope dependence on the bond length and vibrational frequencies of hydrogen, deuterium, and tritium liquids, we further demonstrate that distinctive isotope effects appear in their intermolecular and intramolecular structure and dynamics not only at lower temperature but also at higher temperature, which none has so far been able to obtain quantitative results for realistic systems. Rationalization of their physical origins and the obtained physical insights will help future experimental searching and monitoring intermolecular and intramolecular dynamics and structures of these isotopes not only in normal liquid but also in supercooled liquid.

Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing

We examine renewal processes with power-law waiting time distributions (WTDs) and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics. All possible values of the scaling exponent α are considered for the WTD ψ(t) ∼ 1/t1+α. We treat continuous-time random walks (CTRWs) with 0 < α < 1 for which the mean waiting time diverges, and investigate the behaviour of the process for both ordinary and equilibrium CTRWs for 1 < α < 2 and α > 2. We demonstrate that in the presence of a drift CTRWs with α < 1 are ageing and non-ergodic in the sense of the non-equivalence of their ensemble and time averaged displacement characteristics in the limit of lag times much shorter than the trajectory length. In the sense of the equivalence of ensemble and time averages, CTRW processes with 1 < α < 2 are ergodic for the equilibrium and non-ergodic for the ordinary situation. Lastly, CTRW renewal processes with α > 2-both for the equilibrium and ordinary situation-are always ergodic. For the situations 1 < α < 2 and α > 2 the variance of the diffusion process, however, depends on the initial ensemble. For biased CTRWs with α > 1 we also investigate the behaviour of the ergodicity breaking parameter. In addition, we demonstrate that for biased CTRWs the Einstein relation is valid on the level of the ensemble and time averaged displacements, in the entire range of the WTD exponent α.

Single molecule translocation in smectics illustrates the challenge for time-mapping in simulations on multiple scales

Understanding the connections between the characteristic dynamical time scales associated with a coarse-grained (CG) and a detailed representation is central to the applicability of the coarse-graining methods to understand molecular processes. The process of coarse graining leads to an accelerated dynamics, owing to the smoothening of the underlying free-energy landscapes. Often a single time-mapping factor is used to relate the time scales associated with the two representations. We critically examine this idea using a model system ideally suited for this purpose. Single molecular transport properties are studied via molecular dynamics simulations of the CG and atomistic representations of a liquid crystalline, azobenzene containing mesogen, simulated in the smectic and the isotropic phases. The out-of-plane dynamics in the smectic phase occurs via molecular hops from one smectic layer to the next. Hopping can occur via two mechanisms, with and without significant reorientation. The out-of-plane transport can be understood as a superposition of two (one associated with each mode of transport) independent continuous time random walks for which a single time-mapping factor would be rather inadequate. A comparison of the free-energy surfaces, relevant to the out-of-plane transport, qualitatively supports the above observations. Thus, this work underlines the need for building CG models that exhibit both structural and dynamical consistency to the underlying atomistic model.

Continuous-time random-walk approach to supercooled liquids: Self-part of the van Hove function and related quantities

From equilibrium molecular dynamics (MD) simulations of a bead-spring model for short-chain glass-forming polymer melts we calculate several quantities characterizing the single-monomer dynamics near the (extrapolated) critical temperature [Formula: see text] of mode-coupling theory: the mean-square displacement g₀(t), the non-Gaussian parameter [Formula: see text] and the self-part of the van Hove function [Formula: see text] which measures the distribution of monomer displacements r in time t. We also determine these quantities from a continuous-time random walk (CTRW) approach. The CTRW is defined in terms of various probability distributions which we know from previous analysis. Utilizing these distributions the CTRW can be solved numerically and compared to the MD data with no adjustable parameter. The MD results reveal the heterogeneous and non-Gaussian single-particle dynamics of the supercooled melt near [Formula: see text]. In the time window of the early [Formula: see text] relaxation [Formula: see text] is large and [Formula: see text] is broad, reflecting the coexistence of monomer displacements that are much smaller ("slow particles") and much larger ("fast particles") than the average at time t, i.e. than [Formula: see text]. For large r the tail of [Formula: see text] is compatible with an exponential decay, as found for many glassy systems. The CTRW can reproduce the spatiotemporal dependence of [Formula: see text] at a qualitative to semiquantitative level. However, it is not quantitatively accurate in the studied temperature regime, although the agreement with the MD data improves upon cooling. In the early [Formula: see text] regime we also analyze the MD results for [Formula: see text] via the space-time factorization theorem predicted by ideal mode-coupling theory. While we find the factorization to be well satisfied for small r, both above and below [Formula: see text] , deviations occur for larger r comprising the tail of [Formula: see text]. The CTRW analysis suggests that single-particle "hops" are a contributing factor for these deviations.

Multiscale Relaxation Dynamics in Ultrathin Metallic Glass-Forming Films

The density layering phenomenon originating from a free surface gives rise to the layerlike dynamics and stress heterogeneity in ultrathin Cu-Zr glassy films, which facilitates the occurrence of multistep relaxations in the timescale of computer simulations. Taking advantage of this condition, we trace the relaxation decoupling and evolution with temperature simply via the intermediate scattering function. We show that the β relaxation hierarchically follows fast and slow modes in films, and there is a β-relaxation transition as the film is cooled close to the glass transition. We provide the direct observation of particle motions responsible for the β relaxation and reveal the dominant mechanism varying from the thermal activated to the cooperative jumps across the transition.

Cage Size and Jump Precursors in Glass-Forming Liquids: Experiment and Simulations

Glassy dynamics is intermittent, as particles suddenly jump out of the cage formed by their neighbors, and heterogeneous, as these jumps are not uniformly distributed across the system. Relating these features of the dynamics to the diverse local environments explored by the particles is essential to rationalize the relaxation process. Here we investigate this issue characterizing the local environment of a particle with the amplitude of its short time vibrational motion, as determined by segmenting in cages and jumps the particle trajectories. Both simulations of supercooled liquids and experiments on colloidal suspensions show that particles in large cages are likely to jump after a small time-lag, and that, on average, the cage enlarges shortly before the particle jumps. At large time-lags, the cage has essentially a constant size, which is smaller for longer-lasting cages. Finally, we clarify how this coupling between cage size and duration controls the average behavior and opens the way to a better understanding of the relaxation process in glass-forming liquids.

Particle dynamics in fluids with random interactions

We study the dynamics of particles in a multi-component 2d Lennard-Jones (LJ) fluid in the limiting case where all the particles are different (APD). The equilibrium properties of this APD system were studied in our earlier work [L. S. Shagolsem et al., J. Chem. Phys. 142, 051104 (2015).]. We use molecular dynamics simulations to investigate the statistical properties of particle trajectories in a temperature range covering both the fluid and the solid-fluid coexistence region. We calculate the mean-square displacement as well as displacement, angle, and waiting time distributions, and compare the results with those for one-component LJ fluid. As temperature is lowered, the dynamics of the APD system becomes increasingly complex, as the intrinsic difference between the particles is amplified by neighborhood identity ordering and by the inhomogeneous character of the solid-fluid coexistence region. The ramifications of our results for the analysis of protein tracking experiments in living cells are discussed.

Single-particle dynamics near the glass transition of a metallic glass

The single-particle dynamics of the glass-forming Cu_{50}Zr_{50} alloy, from the supercooled liquid well above the glass-transition temperature, T_{g} to the glassy state, is studied by using the molecular dynamics simulations. When the liquid is cooled below 1.2T_{g}, the dynamics heterogeneity characterized by the cage-jump motion becomes increasingly pronounced. The analyses based on the continuous time random walk method indicate that the liquid falls out of equilibrium in the present simulation time scale when it is cooled into the regime below 1.02T_{g}. However, we find that the jump length and the jump rate do not display the non-equilibrium behaviors even in the glassy state below T_{g}, which allows us to study the intrinsic dynamic characteristics through T_{g}. The mean waiting time between two successive jumps has a rapid growth following the Vogel-Fulcher-Tammann law as the non-equilibrium regime is approached, in analogy with the temperature behaviors of transport properties for fragile supercooled liquids. In contrast, the jump rate maintains the Arrhenius decay and the jump length has even a weaker temperature dependence when the liquid is cooled into glassy state. We find that a pronounced enhancement of the spatial correlation of jumps occurs accompanied by the glass transition: the string-like cooperative jumps dominate the fast motion instead of the uncorrelated and individual jumps. Our work offers an insight into the equilibrium effect of the single-particle dynamics in glass transition.

Langevin equation with fluctuating diffusivity: A two-state model

Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.

Active cage model of glassy dynamics

We build up a phenomenological picture in terms of the effective dynamics of a tracer confined in a cage experiencing random hops to capture some characteristics of glassy systems. This minimal description exhibits scale invariance properties for the small-displacement distribution that echo experimental observations. We predict the existence of exponential tails as a crossover between two Gaussian regimes. Moreover, we demonstrate that the onset of glassy behavior is controlled only by two dimensionless numbers: the number of hops occurring during the relaxation of the particle within a local cage and the ratio of the hopping length to the cage size.

Distributional behaviors of time-averaged observables in the Langevin equation with fluctuating diffusivity: Normal diffusion but anomalous fluctuations

We consider the Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously over time, in order to study fluctuations of time-averaged observables in temporally heterogeneous diffusion processes. We find that the time-averaged mean-square displacement (TMSD) can be represented by the occupation time of a state in the asymptotic limit of the measurement time and hence occupation time statistics is a powerful tool for calculating the TMSD in the model. We show that the TMSD increases linearly with time (normal diffusion) but the time-averaged diffusion coefficients are intrinsically random when the mean sojourn time for one of the states diverges, i.e., intrinsic nonequilibrium processes. Thus, we find that temporally heterogeneous environments provide anomalous fluctuations of time-averaged diffusivity, which have relevance to large fluctuations of the diffusion coefficients obtained by single-particle-tracking trajectories in experiments.

Spectral decomposition of nonlinear systems with memory

We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.

Distinct structural and dynamical difference between supercooled and normal liquids of hydrogen molecules

Supercooled hydrogen liquid as well as superfluid have continued to elude experimental observation due to rapid crystallization. We computationally realized and investigated supercooled hydrogen liquid by a recently developed non-empirical real-time molecular dynamics method, which describes non-spherical hydrogen molecules with the nuclear quantum effects. We demonstrated that the hydrogen supercooled liquid is not a simply cooled liquid but rather exhibits intrinsic structural and dynamical characters including a precursor of tunneling and superfluidity which neither normal hydrogen liquid nor solid possesses. All of the insights provide a milestone for planning experiments of metastable hydrogen systems like glassy and superfluid states and for identifying various unknown hydrogen phases.

Particle jumps in structural glasses

Particles in structural glasses rattle around temporary equilibrium positions, that seldom change through a process which is much faster than the relaxation time, known as particle jump. Since the relaxation of the system is due to the accumulation of many such jumps, it could be possible to connect the single particle short time motion to the macroscopic relaxation by understanding the features of the jump dynamics. Here we review recent results in this research direction, clarifying the features of particle jumps that have been understood and those that are still under investigation, and examining the role of particle jumps in different theories of the glass transition.

Spatial correlations of elementary relaxation events in glass-forming liquids

The dynamical facilitation scenario, by which localized relaxation events promote nearby relaxation events in an avalanche process, has been suggested as the key mechanism connecting the microscopic and the macroscopic dynamics of structural glasses. Here we investigate the statistical features of this process via numerical simulations of a model structural glass. First we show that the relaxation dynamics of the system occurs through particle jumps that are irreversible, and that cannot be decomposed in smaller irreversible events. Then we show that each jump does actually trigger an avalanche. The characteristics of this avalanche change upon cooling, suggesting that the relaxation dynamics crossovers from a noise dominated regime, where jumps do not trigger other relaxation events, to a regime dominated by the facilitation process, where a jump triggers more relaxation events.

Computer simulations of glasses: the potential energy landscape

We review the current state of research on glasses, discussing the theoretical background and computational models employed to describe them. This article focuses on the use of the potential energy landscape (PEL) paradigm to account for the phenomenology of glassy systems, and the way in which it can be applied in simulations and the interpretation of their results. This article provides a broad overview of the rich phenomenology of glasses, followed by a summary of the theoretical frameworks developed to describe this phenomonology. We discuss the background of the PEL in detail, the onerous task of how to generate computer models of glasses, various methods of analysing numerical simulations, and the literature on the most commonly used model systems. Finally, we tackle the problem of how to distinguish a good glass former from a good crystal former from an analysis of the PEL. In summarising the state of the potential energy landscape picture, we develop the foundations for new theoretical methods that allow the ab initio prediction of the glass-forming ability of new materials by analysis of the PEL.

Connecting short and long time dynamics in hard-sphere-like colloidal glasses

Glass-forming materials are characterized by an intermittent motion at the microscopic scale. Particles spend most of their time rattling within the cages formed by their neighbors, and seldom jump to a different cage. In molecular glass formers the temperature dependence of the jump features, such as the average caging time and jump length, characterizes the relaxation processes and allows for a short-time prediction of the diffusivity. Here we experimentally investigate the cage-jump motion of a two-dimensional hard-sphere-like colloidal suspension, where the volume fraction is the relevant parameter controlling the slowing down of the dynamics. We characterize the volume fraction dependence of the cage-jump features and show that, as in molecular systems, they allow for a short time prediction of the diffusivity.

Hopping and the Stokes-Einstein relation breakdown in simple glass formers

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition--like that of other statistical systems--is exact when the spatial dimension d → ∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions,d = 2, 3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes-Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses.

Renewal events in glass-forming liquids

On cooling toward the glass transition temperature, glass-forming liquids display long periods of localized motion interrupted by fast "jumps" in the single-particle trajectories. Several theoretical models based on these single-particle jumps have been proposed, most prominently the continuous-time random walk (CTRW). The central assumption of the CTRW is that jumps are renewal events, i.e. that the internal clock of a particle can be reset upon a jump. In this paper, I present an easy-to-implement method to test whether jumps detected in a supercooled liquid or glass are renewal events or not. The test was applied to molecular dynamics simulations of a short-chain polymer melt, demonstrating that the jumps can in fact be treated as renewal events. The test further revealed that additional relaxation processes are present which are not accounted for in the CTRW picture, highlighting the limitations of this approach. The notion of renewal events in glass-forming systems could be a very important building block for the interpretation of aging and the glass transition. Furthermore, it could have practical implications for the study of non-equilibrium dynamics in glasses as well as mechanical rejuvenation.

New conserved structural fields for supercooled liquids

By considering Voronoi tessellations of the configurations of a fluid, we propose two new conserved fields, which provide structural information not fully accounted for by the usual 2-point density correlation functions. One of these fields is scalar and associated with the volume of the Voronoi cell, whereas the other one, termed the "geometric polarisation", is vectorial and related to the local anisotropy of the configurations. We study the static and dynamical properties of these fields in the supercooled regime of a model glass-forming liquid. We show that the geometric polarisation is statically correlated to the force field, but contrary to it develops a plateau regime when the temperature is lowered. This different relaxation is related to the cage effect in glass-forming liquids, which prevents a complete relaxation of the shape of the cage around particle on intermediate time scales.

Continuous-time random-walk approach to supercooled liquids. II. Mean-square displacements in polymer melts

The continuous-time random walk (CTRW) describes the single-particle dynamics as a series of jumps separated by random waiting times. This description is applied to analyze trajectories from molecular dynamics (MD) simulations of a supercooled polymer melt. Based on the algorithm presented by Helfferich et al. [Phys. Rev. E 89, 042603 (2014)], we detect jump events of the monomers. As a function of temperature and chain length, we examine key distributions of the CTRW: the jump-length distribution (JLD), the waiting-time distribution (WTD), and the persistence-time distribution (PTD), i.e., the distribution of waiting times for the first jump. For the equilibrium (polymer) liquid under consideration, we verify that the PTD is determined by the WTD. For the mean-square displacement (MSD) of a monomer, the results for the CTRW model are compared with the underlying MD data. The MD data exhibit two regimes of subdiffusive behavior, one for the early α process and another at later times due to chain connectivity. By contrast, the analytical solution of the CTRW yields diffusive behavior for the MSD at all times. Empirically, we can account for the effect of chain connectivity in Monte Carlo simulations of the CTRW. The results of these simulations are then in good agreement with the MD data in the connectivity-dominated regime, but not in the early α regime where they systematically underestimate the MSD from the MD.