Energy landscape of a Lennard-Jones liquid: Statistics of stationary points

Abstract

Molecular dynamics simulations are used to generate an ensemble of saddles of the potential energy of a Lennard-Jones liquid. Classifying all extrema by their potential energy u and number of unstable directions k, a well defined relation k(u) is revealed. The degree of instability of typical stationary points vanishes at a threshold potential energy, which lies above the energy of the lowest glassy minima of the system. The energies of the inherent states, as obtained by the Stillinger-Weber method, approach the threshold energy at a temperature close to the mode-coupling transition temperature Tc.

4 RevTeX pages, 6 eps figures. Revised version

References in corpus (1)

• Evaluation of configurational entropy of a model liquid from computer simulations

Cited by in corpus (103)

• Supercooled Liquids for Pedestrians
• Spin-Glass Theory for Pedestrians
• Modeling the mechanics of amorphous solids at different length and time scales
• Energy Barriers and Activated Dynamics in a Supercooled Lennard-Jones Liquid
• Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids
• Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids
• Hopping in a Supercooled Lennard-Jones Liquid: Metabasins, Waiting Time Distribution, and Diffusion
• Geometric approach to the dynamic glass transition
• The statistics of critical points of Gaussian fields on large-dimensional spaces
• Schematic models for dynamic yielding of sheared colloidal glasses
• Real space origin of temperature crossovers in supercooled liquids
• Equilibrium phase diagram of a randomly pinned glass-former
• Thirty milliseconds in the life of a supercooled liquid
• Landscape equivalent of the shoving model
• Particle rearrangements during transitions between local minima of the potential energy landscape of a supercooled Lennard-Jones liquid
• Finding All the Stationary Points of a Potential Energy Landscape via Numerical Polynomial Homotopy Continuation Method
• Mean-Field Theory, Mode-Coupling Theory, and the Onset Temperature in Supercooled Liquids
• Critical Behaviour of the Number of Minima of a Random Landscape at the Glass Transition Point and the Tracy-Widom distribution
• Topological Signature of First Order Phase Transitions
• A characteristic energy scale in glasses
• Universal law for the vibrational density of states of liquids
• Does the potential energy landscape of a supercooled liquid resemble a collection of traps?
• Hopping in the Glass Configuration Space: Subaging and Generalized Scaling Laws
• Quasi-saddles as relevant points of the potential energy surface in the dynamics of supercooled liquids
• Theory for Swap Acceleration near the Glass and Jamming Transitions
• Configuration space connectivity across the fragile to strong transition in silica
• Role of saddles in mean-field dynamics above the glass transition
• General features of the energy landscape in Lennard-Jones like model liquids
• Finite-Size Effects in a Supercooled Liquid
• Structural and microscopic relaxations in a colloidal glass
• Vibrations in glasses and Euclidean Random Matrix theory
• Topological Description of the Aging Dynamics in Simple Glasses
• On the origine of the Boson peak
• A localization transition underlies the mode-coupling crossover of glasses
• Relaxation dynamics in the energy landscape of glass-forming liquids
• Large deviation function for the number of eigenvalues of sparse random graphs inside an interval
• High-Dimensional Random Fields and Random Matrix Theory
• Numerical Polynomial Homotopy Continuation Method and String Vacua
• Understanding fragility in supercooled Lennard-Jones mixtures. II. Potential energy surface
• Brillouin and Boson peaks in Glasses from vector Euclidean Random Matrix Theory
• Yield stress, heterogeneities and activated processes in soft glassy materials
• Complex dynamics and configurational entropy of spatial optical solitons in nonlocal media
• Non-affine deformations of inherent structure as signature of cooperativity in supercooled liquids
• Are there localized saddles behind the heterogeneous dynamics of supercooled liquids?
• Complex light: Dynamic phase transitions of a light beam in a nonlinear non-local disordered medium
• Potential Energy Landscape in Lennard-Jones binary mixture model
• Comment on ``Quasisaddles as relevant points of the potential energy surface in the dynamics of supercooled liquids'' [J. Chem. Phys. 116, 10297 (2002); cond-mat/0203301]
• Anderson Localization in Euclidean Random Matrices
• Thermodynamic-Dynamic Interrelations in Glass-Forming Polymer Fluids
• The distance between Inherent Structures and the influence of saddles on approaching the mode coupling transition in a simple glass former
• Topological properties of the mean field phi^4 model
• Investigation of the relation between local diffusivity and local inherent structures in the Kob-Andersen Lennard-Jones model
• A model for the generic alpha relaxation of viscous liquids
• Saddles in the energy landscape: extensivity and thermodynamic formalism
• Energy landscape - a key concept for the dynamics of glasses and liquids
• Saddle index properties, singular topology, and its relation to thermodynamical singularities for a phi^4 mean field model
• Methods to locate Saddle Points in Complex Landscapes
• Geometrical properties of the potential energy of the soft-sphere binary mixture
• Local Properties of the Potential Energy Landscape of a Model Glass: Understanding the Low Temperature Anomalies
• A Collection of Challenging Optimization Problems in Science, Engineering and Economics
• On the high-density expansion for Euclidean Random Matrices
• Communication: Newton homotopies for sampling stationary points of potential energy landscapes
• Crossover from entropic to thermal dynamics in glassy models
• On the relationship between phase transitions and topological changes in one dimensional models
• A single saddle model for the beta-relaxation in supercooled liquids
• Heterogeneities in systems with quenched disorder
• Supercooled Lennard-Jones Liquids and Glasses: a Kinetic Monte Carlo Approach
• Realistic Tunneling States for the Magnetic Effects in Non-Metallic Real Glasses
• Saddles and softness in simple model liquids
• Energy landscape picture of supercooled liquids: Application of a generalized random energy model
• The density of stationary points in a high-dimensional random energy landscape and the onset of glassy behaviour
• Revisiting the Concept of Activation in Supercooled Liquids
• Index statistical properties of sparse random graphs
• Dynamics and geometric properties of the k-Trigonometric model
• Structural relaxation in a supercooled molecular liquid
• Potential Energy Landscape of the Two-Dimensional XY Model: Higher-Index Stationary Points
• Distributions of pore sizes and atomic densities in binary glasses revealed by molecular dynamics simulations
• Inherent Structures for Soft Long-Range Interactions in Two-Dimensional Many-Particle Systems
• Turbulence lifetimes: what we can learn from the physics of glasses
• Freezing of Triangulations
• Spatial structure of unstable normal modes in a glass-forming liquid
• Relationship between Fragility, Diffusive Directions and Energy Barriers in a Supercooled Liquid
• An Inversion-Relaxation Approach for Sampling Stationary Points of Spin Model Hamiltonians
• An energy-landscape-based crossover temperature in glass-forming liquids
• Energy landscape properties studied by symbolic sequences
• Quasi-saddles of Liquids: Computational Study of a bulk Lennard-Jones system
• Saddles and dynamics in a solvable mean-field model
• Spectral statistics of the quenched normal modes of a network-forming molecular liquid
• Density effects in a bulk binary Lennard-Jones system
• Voronoi Glass-Forming Liquids : A Structural Study
• Instantaneous normal modes of glass-forming liquids during the athermal relaxation process of the steepest descent algorithm
• Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors
• How Cooperative are the Dynamics in Tunneling Systems? A Computer Study for an Atomic Model Glass
• Dynamic phase diagram of the Number Partitioning Problem
• Universality in the vibrational spectra of weakly-disordered two-dimensional clusters
• The glass transition in a nutshell: a source of inspiration to describe the subcritical transition to turbulence
• Revisiting the question of what instantaneous normal modes tell us about liquid dynamics
• Off-equilibrium dynamics in the energy landscape of a simple model glass
• Rare Trajectories in a Prototypical Mean-field Disordered Model: Insights into Landscape and Instantons
• Universal distribution of the number of minima for random walks and Lévy flights
• The number of minima in random landscapes generated by constrained random walk and Lévy flights: universal properties
• Following the evolution of metastable glassy states under external perturbations: compression and shear-strain
• How non-equilibrium correlations in active matter reveal the topological crossover in glasses