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Register a new userThe Geometric Mean Squared Displacement and the Stokes-Einstein Scaling in a Supercooled Liquid
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It is proposed that the rate of relaxation in a liquid is better described by the geometric mean of the van Hove distribution function, rather than the standard arithmetic mean used to obtain the mean squared displacement. The difference between the two means is shown to increase significantly with an increase in the non-Gaussian character of the displacement distribution. Preliminary results indicate that the geometric diffusion constant results in a substantial reduction of the deviation from Stokes-Einstein scaling.
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It was recently shown that the real part of the frequency-dependent fluidity for several glass-forming liquids of different chemistry conforms to the prediction of the random barrier model (RBM) devised for ac electrical conduction in disordered solids [S. P. Bierwirth textit{et al.}, Phys. Rev. Lett. {bf 119}, 248001 (2017)]. Inspired by these results we introduce a crystallization-resistant modification of the Kob-Andersen binary Lennard-Jones mixture for which the results of extensive graphics-processing unit (GPU)-based molecular-dynamics simulations are presented. We find that the low-temperature mean-square displacement is fitted well by the RBM prediction, which involves no shape parameters. This finding highlights the challenge of explaining why a simple model based on hopping of non-interacting particles in a fixed random energy landscape can reproduce the complex and highly cooperative dynamics of glass-forming liquids.
The onset of rigidity in interacting liquids, as they undergo a transition to a disordered solid, is associated with a dramatic rearrangement of the low-frequency vibrational spectrum. In this letter, we derive scaling forms for the singular dynamical response of disordered viscoelastic networks near both jamming and rigidity percolation. Using effective-medium theory, we extract critical exponents, invariant scaling combinations and analytical formulas for universal scaling functions near these transitions. Our scaling forms describe the behavior in space and time near the various onsets of rigidity, for rigid and floppy phases and the crossover region, including diverging length and time scales at the transitions. We expect that these behaviors can be measured in systems ranging from colloidal suspensions to anomalous charge-density fluctuations of strange metals.
We report an analytical evaluation of the mean-squared displacement (MSD) of the particles in glasses based on their coarse grained trajectories. The calculation is conducted by means of a local random configuration-tree theory that was recently proposed by one of us [C.-H. Lam, J. Stat. Mech. textbf{2018}, 023301 (2018)]. Results are compared with the numerical simulations of a lattice glass model, and good quantitative agreement has been obtained over a wide range of temperatures in the entire region of time with virtually no free parameters. To the best of our knowledge, the calculation is the first in its kind.
In this work we revisit the description of dynamics based on the concepts of metabasins and activation in mildly supercooled liquids via the analysis of the dynamics of a paradigmatic glass former between its onset temperature $T_{o}$ and mode-coupling temperature $T_{c}$. First, we provide measures that demonstrate that the onset of glassiness is indeed connected to the landscape, and that metabasin waiting time distributions are so broad that the system can remain stuck in a metabasin for times that exceed $tau_alpha$ by orders of magnitude. We then reanalyze the transitions between metabasins, providing several indications that the standard picture of activated dynamics in terms of traps does not hold in this regime. Instead, we propose that here activation is principally driven by entropic instead of energetic barriers. In particular, we illustrate that activation is not controlled by the hopping of high energetic barriers, and should more properly be interpreted as the entropic selection of nearly barrierless but rare pathways connecting metabasins on the landscape.
Apparent critical phenomena, typically indicated by growing correlation lengths and dynamical slowing-down, are ubiquitous in non-equilibrium systems such as supercooled liquids, amorphous solids, active matter and spin glasses. It is often challenging to determine if such observations are related to a true second-order phase transition as in the equilibrium case, or simply a crossover, and even more so to measure the associated critical exponents. Here, we show that the simulation results of a hard-sphere glass in three dimensions, are consistent with the recent theoretical prediction of a Gardner transition, a continuous non-equilibrium phase transition. Using a hybrid molecular simulation-machine learning approach, we obtain scaling laws for both finite-size and aging effects, and determine the critical exponents that traditional methods fail to estimate. Our study provides a novel approach that is useful to understand the nature of glass transitions, and can be generalized to analyze other non-equilibrium phase transitions.
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