Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids

Abstract

We present a numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids established in [Phys. Rev. Lett. 116, 015902 (2016)]. For soft sphere interactions, we obtain the numerical solution by an iterative algorithm and a straightforward discretization of time. We also discuss the case of hard spheres, for which we first derive analytically the dynamical mean field theory as a non-trivial limit of the soft sphere one. We present numerical results for the memory function and the mean square displacement. Our results reproduce and extend kinetic theory in the dilute or short-time limit, while they also describe dynamical arrest towards the glass phase in the dense strongly-interacting regime.

arXiv comment27 pages, 6 figures

References in corpus (40)

• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Cellular Dynamical Mean Field Approach to Strongly Correlated Systems
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Theory of nonlinear rheology and yielding of dense colloidal suspensions
• Nonequilibrium glass transitions in driven and active matter
• Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
• Two-time scales, two-temperature scenario for nonlinear rheology
• Universal microstructure and mechanical stability of jammed packings
• Glass Rheology: From mode-coupling theory to a dynamical yield criterion
• Exact theory of dense amorphous hard spheres in high dimension. II. The high density regime and the Gardner transition
• Glassy dynamics of athermal self-propelled particles: Computer simulations and a nonequilibrium microscopic theory
• Hopping and the Stokes-Einstein relation breakdown in simple glass formers
• Solution of the dynamics of liquids in the large-dimensional limit
• Numerical implementation of dynamical mean field theory for disordered systems: application to the Lotka-Volterra model of ecosystems
• Field Theory of Fluctuations in Glasses
• Mode-Coupling Theory for Active Brownian Particles
• Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry
• Critical fluctuations and breakdown of Stokes-Einstein relation in the Mode-Coupling Theory of glasses
• Microscopic dynamics of supercooled liquids from first principles
• Dimensional dependence of the Stokes--Einstein relation and its violation
• Out-of-equilibrium dynamical mean-field equations for the perceptron model
• Comparison of structure and transport properties of concentrated hard and soft sphere fluids
• The dynamics of the spherical p-spin model: from microscopic to asymptotics
• A simple theory for the dynamics of mean-field-like models of glass-forming fluids
• Qualitative Features at the Glass Crossover
• Marginally stable phases in mean-field structural glasses
• First-Principles Constitutive Equation for Suspension Rheology
• Active hard-spheres in infinitely many dimensions
• Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. I. The isotropic case
• A Microscopic Model of the Stokes-Einstein Relation in Arbitrary Dimension
• Mode coupling theory in the FDR-preserving field theory of interacting Brownian particles
• Exact Short Time Dynamics for Steeply Repulsive Potentials
• Predictive power of MCT: Numerics and Finite size scaling for a mean field spin glass
• Shear Stress Correlations in Hard and Soft Sphere Fluids
• Field theoretic formulation of a mode-coupling equation for colloids
• On mean-field theories of dynamics in supercooled liquids
• Critical force in active microrheology
• Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain
• First-passage and extreme-value statistics of a particle subject to a constant force plus a random force
• Square root singularity in the viscosity of neutral colloidal suspensions at large frequencies

Cited by in corpus (19)

• Sampling efficiency of transverse forces in dense liquids
• On the Dynamics of Liquids in the Large-Dimensional Limit
• Path Integral Approach Unveils the Role of Complex Energy Landscape for Activated Dynamics of Glassy Systems
• Local dynamical heterogeneity in glass formers
• Mean-field caging in a random Lorentz gas
• The dimensional evolution of structure and dynamics in hard sphere liquids
• Rigorous dynamical mean field theory for stochastic gradient descent methods
• Jamming, relaxation, and memory in a structureless glass former
• Dynamical mean-field theory for stochastic gradient descent in Gaussian mixture classification
• Transverse forces and glassy liquids in infinite dimensions
• Dynamic Gardner crossover in a simple structural glass
• Dynamics and fluctuations of minimally-structured glass formers
• Tagged-particle dynamics in confined colloidal liquids
• Not-so-glass-like Caging and Fluctuations of an Active Matter Model
• Comment on "Explicit Analytical Solution for Random Close Packing in $d=2$ and $d=3$"
• Tagged-particle motion in quasi-confined colloidal hard-sphere liquids
• An alternative, dynamic density functional-like theory for time-dependent density fluctuations in glass-forming fluids
• Active matter in infinite dimensions: Fokker-Planck equation and dynamical mean-field theory at low density
• Gradient descent dynamics and the jamming transition in infinite dimensions