Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: The potential energy landscape ensemble

Abstract

In principle, all of the dynamical complexities of many-body systems are encapsulated in the potential energy landscapes on which the atoms move - an observation that suggests that the essentials of the dynamics ought to be determined by the geometry of those landscapes. But what are the principal geometric features that control the long-time dynamics? We suggest that the key lies not in the local minima and saddles of the landscape, but in a more global property of the surface: its accessible pathways. In order to make this notion more precise we introduce two ideas: (1) a switch to a new ensemble that removes the concept of potential barriers from the problem, and (2) a way of finding optimum pathways within this new ensemble. The potential energy landscape ensemble, which we describe in the current paper, regards the maximum accessible potential energy, rather than the temperature, as a control variable. We show here that while this approach is thermodynamically equivalent to the canonical ensemble, it not only sidesteps the idea of barriers, it allows us to be quantitative about the connectivity of a landscape. We illustrate these ideas with calculations on a simple atomic liquid and on the Kob-Andersen model of a glass-forming liquid, showing, in the process, that the landscape of the Kob-Anderson model appears to have a connectivity transition at the landscape energy associated with its mode-coupling transition. We turn to the problem of finding the most efficient pathways through potential energy landscapes in our companion paper.

arXiv comment43 pages, 7 figures

References in corpus (26)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• The relationship between fragility, configurational entropy and the potential energy landscape of glass forming liquids
• Models of traps and glass phenomenology
• Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems
• Inherent Structure Entropy of Supercooled Liquids
• Coarse-grained microscopic model of glass formers
• Space-time Thermodynamics of the Glass Transition
• Energy Barriers and Activated Dynamics in a Supercooled Lennard-Jones Liquid
• Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids
• Hopping in a Supercooled Lennard-Jones Liquid: Metabasins, Waiting Time Distribution, and Diffusion
• Real space origin of temperature crossovers in supercooled liquids
• What does the potential energy landscape tell us about the dynamics of supercooled liquids and glasses?
• Particle rearrangements during transitions between local minima of the potential energy landscape of a supercooled Lennard-Jones liquid
• Replica-exchange molecular dynamics simulation for supercooled liquids
• Non-topographic description of inherent structure dynamics in glass formers
• Density of states of a binary Lennard-Jones Glass
• On the inequivalence of statistical ensembles
• The Potential Energy Landscape and Mechanisms of Diffusion in Liquids
• Inherent-Structure Dynamics and Diffusion in Liquids
• Efficient Monte Carlo simulation of a glass forming binary mixture
• Geometrical properties of the potential energy of the soft-sphere binary mixture
• Conformational Temperature Characterizing the Folding of a Protein
• Monte-Carlo rejection as a tool for measuring the energy landscape scaling of simple fluids

Cited by in corpus (10)

• NVU perspective on simple liquids' quasiuniversality
• Echoes of the glass transition in athermal soft spheres
• NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface
• Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: Geodesic pathways through the potential energy landscape
• NVU dynamics. II. Comparing to four other dynamics
• Revisiting the Concept of Activation in Supercooled Liquids
• NVU dynamics. III. Simulating molecules at constant potential energy
• Discovery of a paired Gaussian and long-tailed distribution of potential energies in nanoglasses
• The potential energy landscape and inherent dynamics of a hard-sphere fluid
• Viscous liquid dynamics modeled as random walks within overlapping hyperspheres