Characterization of the Dynamics of Glass-forming Liquids from the Properties of the Potential Energy Landscape

We develop a framework for understanding the difference between strong and fragile behavior in the dynamics of glass-forming liquids from the properties of the potential energy landscape. Our approach is based on a master equation description of the activated jump dynamics among the local minima of the potential energy (the so-called inherent structures) that characterize the potential energy landscape of the system. We study the dynamics of a small atomic cluster using this description as well as molecular dynamics simulations and demonstrate the usefulness of our approach for this system. Many of the remarkable features of the complex dynamics of glassy systems emerge from the activated dynamics in the potential energy landscape of the atomic cluster. The dynamics of the system exhibits typical characteristics of a strong supercooled liquid when the system is allowed to explore the full configuration space. This behavior arises because the dynamics is dominated by a few lowest-lying minima of the potential energy and the potential energy barriers between these minima. When the system is constrained to explore only a limited region of the potential energy landscape that excludes the basins of attraction of a few lowest-lying minima, the dynamics is found to exhibit the characteristics of a fragile liquid.Comment: 13 pages, 6 figure

Saddles on the potential energy landscape of a Lennard-Jones liquid

By means of molecular dynamics simulations, we study the stationary points of the potential energy in a Lennard-Jones liquid, giving a purely geometric characterization of the energy landscape of the system. We find a linear relation between the degree of instability of the stationary points and their potential energy, and we locate the energy where the instability vanishes. This threshold energy marks the border between saddle-dominated and minima-dominated regions of the energy landscape. The temperature where the potential energy of the Stillinger-Weber minima becomes equal to the threshold energy turns out to be very close to the mode-coupling transition temperature.Comment: Invited talk presented by A.C. at the Conference: Disordered and Complex Systems, King's College London, July 200

Inflation in Random Landscapes with two energy scales

We investigate inflation in a multi-dimensional landscape with a hierarchy of energy scales, motivated by the string theory, where the energy scale of Kahler moduli is usually assumed to be much lower than that of complex structure moduli and dilaton field. We argue that in such a landscape, the dynamics of slow-roll inflation is governed by the low-energy potential, while the initial condition for inflation are determined by tunneling through high-energy barriers. We then use the scale factor cutoff measure to calculate the probability distribution for the number of inflationary e-folds and the amplitude of density fluctuations $Q$, assuming that the low-energy landscape is described by a random Gaussian potential with a correlation length much smaller than $M_{\rm pl}$. We find that the distribution for $Q$ has a unique shape and a preferred domain, which depends on the parameters of the low-energy landscape. We discuss some observational implications of this distribution and the constraints it imposes on the landscape parameters.Comment: 39 pages, 3 figures; (v2) minor change

Metastable states as a key to the dynamics of supercooled liquids

Computer simulations of a model glass-forming system are presented, which are particularly sensitive to the correlation between the dynamics and the topography of the potential energy landscape. This analysis clearly reveals that in the supercooled regime the dynamics is strongly influenced by the presence of deep valleys in the energy landscape, corresponding to long-lived metastable amorphous states. We explicitly relate non-exponential relaxation effects and dynamic heterogeneities to these metastable states and thus to the specific topography of the energy landscape

Potential Energy Landscape Equation of State

Depth, number, and shape of the basins of the potential energy landscape are the key ingredients of the inherent structure thermodynamic formalism introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys. Rev. A 25, 978 (1982)]. Within this formalism, an equation of state based only on the volume dependence of these landscape properties is derived. Vibrational and configurational contributions to pressure are sorted out in a transparent way. Predictions are successfully compared with data from extensive molecular dynamics simulations of a simple model for the fragile liquid orthoterphenyl.Comment: RevTeX4, 4 pages, 5 figure

Quasi-saddles as relevant points of the potential energy surface in the dynamics of supercooled liquids

The supercooled dynamics of a Lennard-Jones model liquid is numerically investigated studying relevant points of the potential energy surface, i.e. the minima of the square gradient of total potential energy $V$. The main findings are: ({\it i}) the number of negative curvatures $n$ of these sampled points appears to extrapolate to zero at the mode coupling critical temperature $T_c$; ({\it ii}) the temperature behavior of $n(T)$ has a close relationship with the temperature behavior of the diffusivity; ({\it iii}) the potential energy landscape shows an high regularity in the distances among the relevant points and in their energy location. Finally we discuss a model of the landscape, previously introduced by Madan and Keyes [J. Chem. Phys. {\bf 98}, 3342 (1993)], able to reproduce the previous findings.Comment: To be published in J. Chem. Phy

Geometric approach to the dynamic glass transition

We numerically study the potential energy landscape of a fragile glassy system and find that the dynamic crossover corresponding to the glass transition is actually the effect of an underlying geometric transition caused by a qualitative change in the topological properties of the landscape. Furthermore, we show that the potential energy barriers connecting local glassy minima increase with decreasing energy of the minima, and we relate this behaviour to the fragility of the system. Finally, we analyze the real space structure of activated processes by studying the distribution of particle displacements for local minima connected by simple saddles

Landscapes and Fragilities

The concept of fragility provides a possibility to rank different supercooled liquids on the basis of the temperature dependence of dynamic and/or thermodynamic quantities. We recall here the definitions of kinetic and thermodynamic fragility proposed in the last years and discuss their interrelations. At the same time we analyze some recently introduced models for the statistical properties of the potential energy landscape. Building on the Adam-Gibbs relation, which connects structural relaxation times to configurational entropy, we analyze the relation between statistical properties of the landscape and fragility. We call attention to the fact that the knowledge of number, energy depth and shape of the basins of the potential energy landscape may not be sufficient for predicting fragility. Finally, we discuss two different possibilities for generating strong behavior.Comment: 17 pages, 10 figures; accepted version, minor correction