Potential-energy landscape of a supercooled liquid and its resemblance to a collection of traps.

It is analyzed whether the potential energy landscape of a glass-forming system can be effectively mapped on a random model which is described in statistical terms. For this purpose we generalize the simple trap model of Monthus and Bouchaud [J. Phys. A 29, 3847 (1996)] by dividing the total system into M weakly interacting identical subsystems, each being described in terms of a trap model. The distribution of traps in this extended trap model (ETM) is fully determined by the thermodynamics of the glass former. The dynamics is described by two adjustable parameters, one characterizing the common energy level of the barriers, the other the strength of the interaction. The comparison is performed for the standard binary mixture Lennard-Jones system with 65 particles. The metabasins, identified in our previous work, are chosen as traps. Comparing molecular dynamics simulations of the Lennard-Jones system with Monte Carlo calculations of the ETM allows one to determine the adjustable parameters. Analysis of the first moment of the waiting distribution yields an optimum agreement when choosing M approximately 3 subsystems. Comparison with the second moment of the waiting time distribution, reflecting dynamic heterogeneities, indicates that the sizes of the subsystems may fluctuate.

What does the potential energy landscape tell us about the dynamics of supercooled liquids and glasses?

For a model glass former we demonstrate via computer simulations how macroscopic dynamic quantities can be inferred from a potential energy landscape (PEL) analysis. The essential step is to consider whole superstructures of many PEL minima, called metabasins, rather than single minima. We show that two types of metabasins exist: some allowing for quasifree motion on the PEL (liquidlike), and the others acting as traps (solidlike). The activated, multistep escapes from the latter metabasins are found to dictate the slowing down of dynamics upon cooling over a much broader temperature range than is currently assumed.

Hopping in a supercooled Lennard-Jones liquid: metabasins, waiting time distribution, and diffusion.

We investigate the jump motion among potential energy minima of a Lennard-Jones model glass former by extensive computer simulation. From the time series of minima energies, it becomes clear that the energy landscape is organized in superstructures called metabasins. We show that diffusion can be pictured as a random walk among metabasins, and that the whole temperature dependence resides in the distribution of waiting times. The waiting time distribution exhibits algebraic decays: tau(-1/2) for very short times and tau(-alpha) for longer times, where alpha approximately 2 near T(c). We demonstrate that solely the waiting times in the very stable basins account for the temperature dependence of the diffusion constant.

Energy barriers and activated dynamics in a supercooled Lennard-Jones liquid.

We study the relation of the potential energy landscape (PEL) topography to relaxation dynamics of a small model glass former of Lennard-Jones type. The mechanism under investigation is the hopping between superstructures of PEL minima, called metabasins (MBs). Guided by the idea that the mean durations of visits to MBs should reflect the local PEL structure, we first derive the effective depths of MBs from dynamics, by the relation E(app)=d ln/dbeta, where beta=1/k(B)T. Second, we establish a connection of E(app) to the barriers that surround MBs. As the consequence of a rugged PEL, it turns out that escapes from MBs do not happen by single hops between PEL minima, but correspond to complicated multiminima sequences. We introduce the concept of return probabilities to the bottom of the MBs in order to judge when the attraction range of a MB has been left. The energy barriers overcome can then be identified. These turn out to be in good agreement with the effective depths E(app), calculated from dynamics. We are thus able to relate MB lifetimes to their local structure. Moreover, we can trace back the overall diffusive dynamics to the population of MBs and to their local topology, i.e., to purely thermodynamic and structural quantities. Single energy barriers are identified with the help of a new method, which accurately performs a descent along the ridge between two minima. We analyze the population of transition regions between minima, called basin borders. No indication for the mechanism of diffusion to change around the mode-coupling temperature can be found. We discuss the question whether the one-dimensional reaction paths connecting two minima are relevant for the calculation of reaction rates at the temperatures under study.

Cooperativity and spatial correlations near the glass transition: computer simulation results for hard spheres and disks.

We examine the dynamics of hard spheres and disks at high packing fractions in two and three dimensions, modeling the simplest systems exhibiting a glass transition. As it is well known, cooperativity and dynamic heterogeneity arise as central features when approaching the glass transition from the liquid phase, so an understanding of their underlying physics is of great interest. Cooperativity implies a reduction of the effective degrees of freedom, and we demonstrate a simple way of quantification in terms of the strength and the length scale of dynamic correlations among different particles. These correlations are obtained for different dynamical quantities X(i)(t) that are constructed from single-particle displacements during some observation time t. Of particular interest is the dependence on t. Interestingly, for appropriately chosen X(i)(t) we obtain finite cooperativity in the limit t-->infinity.