Mode-Coupling Theory (MCT) Lecture Notes

Abstract

In this set of lecture notes we review the mode-coupling theory of the glass transition from several perspectives. First, we derive mode-coupling equations for the description of density fluctuations from microscopic considerations with the use the Mori-Zwanzig projection operator technique. We also derive schematic mode-coupling equations of a similar form from a field-theoretic perspective. We review the successes and failures of mode-coupling theory, and discuss recent advances in the applications of the theory.

Lecture Notes (xx pages) given at "Unifying Concepts in Glass Physics III", Bangalore (2004). To get diagrams use feynmf package and uncomment fmf-type comments in the tex source file before using latex on it

References in corpus (1)

• Supercooled liquids, the glass transition, and computer simulations

Cited by in corpus (125)

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• The effective temperature
• Mode-Coupling Theory of the Glass Transition: A Primer
• Solution of the dynamics of liquids in the large-dimensional limit
• Field Theory of Fluctuations in Glasses
• Relaxation Scenarios in a Mixture of Large and Small Spheres: Dependence on the Size Disparity
• Active glasses
• Multiple length and time scales of dynamic heterogeneities in model glass-forming liquids: A systematic analysis of multi-point and multi-time correlations
• Approximate but Accurate Quantum Dynamics from the Mori Formalism: I. Nonequilibrium Dynamics
• Understanding, predicting, and tuning the fragility of vitrimeric polymers
• Nonequilibrium mode-coupling theory for dense active systems of self-propelled particles
• The race to the bottom: approaching the ideal glass?
• Particle jumps in structural glasses
• Superfragile glassy dynamics of onecomponent system with isotropic potential: competition of diffusion and frustration
• Deconstructing the glass transition through critical experiments on colloids
• Out-of-equilibrium dynamical mean-field equations for the perceptron model
• Understanding Dynamics in Coarse-Grained Models: I. Universal Excess Entropy Scaling Relationship
• Real Space Analysis of Colloidal Gels: Triumphs, Challenges and Future Directions
• Classical many-body chaos with and without quasiparticles
• On relation between generalized diffusion equations and subordination schemes
• Locally favoured structures and dynamic length scales in a simple glass-former
• Identifying anomalous diffusion and melting in dusty plasmas
• Theoretical tools for understanding the climate crisis from Hasselmann's program and beyond
• Approximate but accurate quantum dynamics from the Mori formalism: II. Equilibrium correlation functions
• Operator backflow and the classical simulation of quantum transport
• Slow Dynamics of the High Density Gaussian Core Model
• Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. I. The isotropic case
• Dynamics of interacting Brownian particles: a diagrammatic formulation
• Mode coupling theory in the FDR-preserving field theory of interacting Brownian particles
• Structural Fluctuation of Protein in Water around Its Native State: A New Statistical Mechanics Formulation
• Classical Glasses, Black Holes, and Strange Quantum Liquids
• Dynamic correlations in Brownian many-body systems
• On the Dynamics of Liquids in the Large-Dimensional Limit
• Predictive power of MCT: Numerics and Finite size scaling for a mean field spin glass
• The quantum Biroli-Mézard model: glass transition and superfluidity in a quantum lattice glass model
• Microscopic Theory of the Influence of Strong Attractive Forces on the Activated Dynamics of Dense Glass and Gel Forming Fluids
• The Role of Intramolecular Barriers on the Glass Transition of Polymers: Computer Simulations vs. Mode Coupling Theory
• Coarse-grained forms for equations describing the microscopic motion of particles in a fluid
• Self-Consistent Description of Local Density Dynamics in Simple Liquids. The Case of Molten Lithium
• Generalized mode-coupling theory of the glass transition: schematic results at finite and infinite order
• Many-body correlations are non-negligible in both fragile and strong glassformers
• From caging to Rouse dynamics in polymer melts with intramolecular barriers: a critical test of the Mode Coupling Theory
• Segment-Scale, Force-Level Theory of Mesoscopic Dynamic Localization and Entropic Elasticity in Entangled Chain Polymer Liquids
• Combining Machine Learning and Physics to Understand Glassy Systems
• Generalized mode-coupling theory of the glass transition. I. Numerical results for Percus-Yevick hard spheres
• Field theoretic formulation of a mode-coupling equation for colloids
• On mean-field theories of dynamics in supercooled liquids
• Observation and Characterization of the Vestige of the Jamming Transition in a Thermal 3D System
• A dynamical relation between dual finite temperature classical and zero temperature quantum systems: quantum critical jamming and quantum dynamical heterogeneities
• Quantum to classical crossover in many-body chaos and scrambling from relaxation in a glass
• The glass transition in molecules, colloids and grains: universality and specificity
• Mode-coupling theory of lattice dynamics for classical and quantum crystals
• Mode-coupling theory for the dynamic heterogeneity in an aging glass: How Do Glassy Domains Grow?
• Generalized mode-coupling theory of the glass transition. II. Analytical scaling laws
• Spatial correlations in sheared isothermal liquids : From elastic particles to granular particles
• Model for the free-volume distributions of equilibrium fluids
• Multi-component generalized mode-coupling theory: Predicting dynamics from structure in glassy mixtures
• Systematic expansion in the order parameter for replica theory of the dynamical glass transition
• Emergence of bacterial glass
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Microscopic models of mode-coupling theory: the $F_{12}$ scenario
• Activated dynamics: an intermediate model between REM and p-spin
• Memory effects in the Fermi-Pasta-Ulam Model
• Generalized Langevin equations for systems with local interactions
• Spectral properties of the trap model on sparse networks
• Mode-coupling theory for mixtures of athermal self-propelled particles
• Analytical Calculation of Four-Point Correlations for a Simple Model of Cages Involving Numerous Particles
• Mode-coupling approach for the slow dynamics of a liquid on a spherical substrate
• Insights from Single-File Diffusion into Cooperativity in Higher Dimensions
• The mode-coupling glass transition in a fluid confined by a periodic potential
• Generalized Mode-Coupling Theory for Mixtures of Brownian Particles
• Finite-size critical fluctuations in microscopic models of mode-coupling theory
• Crossover behavior and multi-step relaxation in a schematic model of the cut-off glass transition
• Correlation function and linear response function of homogeneous isotropic turbulence in the Eulerian and Lagrangian coordinates
• Dynamical Susceptibilities Near Ideal Glass Transitions
• Ideal glass transition in a simple 2D lattice model
• Large deviations of glassy effective potentials
• Quantum fluctuations lead to glassy electron dynamics in the good metal regime of electron doped KTaO3
• Unveiling the anatomy of mode-coupling theory
• Machine learning glass caging order parameters with an artificial nested neural network
• Glassy dynamics of a binary Voronoi fluid: A mode-coupling analysis
• Glassy dynamics from generalized mode-coupling theory: existence and uniqueness of solutions for hierarchically coupled integro-differential equations
• Restricted equilibrium ensembles: Exact equation of state of a model glass
• Inherent-State Melting and the Onset of Glassy Dynamics in Two-Dimensional Supercooled Liquids
• Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking
• A Dramatically Growing Shear Rigidity Length Scale in a Supercooled Glass Former ($NiZ{r}_2$)
• A deep learning approach to the measurement of long-lived memory kernels from Generalised Langevin Dynamics
• Size-Stretched Exponential Relaxation in a Model with Arrested States
• Self-Consistent Relaxation Theory of Collective Ion Dynamics in Yukawa One-Component Plasmas under Intermediate Screening Regimes
• Linking density functional and mode coupling models for supercooled liquids
• Density nonlinearities in field theories for a toy model of fluctuating nonlinear hydrodynamics of supercooled liquids
• Time reparametrization invariance in arbitrary range p-spin models: symmetric versus non-symmetric dynamics
• Rheology of Hard Glassy Materials
• Tagged-particle motion of Percus-Yevick hard spheres from first principles
• Microscopic Theory of the Elastic Shear Modulus and Length-Scale-Dependent Dynamic Re-Entrancy Phenomena in Very Dense Sticky Particle Fluids
• Probing Local Structure in Glass by the Application of Shear
• Fast logarithmic Fourier-Laplace transform of nonintegrable functions
• Supercooled superfluids in Monte Carlo simulations
• Structural relaxation in quantum supercooled liquids: A mode-coupling approach
• The glass susceptibility: growth kinetics and saturation under shear
• Understanding the approximations of mode-coupling theory for sheared steady states of colloids
• Predicting the structure of fluids with piecewise constant interactions: Comparing the accuracy of five efficient integral equation theories
• A numerical study of longtime dynamics and ergodic-nonergodic transitions in dense simple fluids
• A simple closure procedure for the study of velocity autocorrelation functions in fluids as a "bridge" between different theoretical approaches
• Modeling the Dielectric Relaxation in Semicrystalline Polymers -- Understanding the Role of the Interphase between the Amorphous and Crystalline Domains
• General Two-Parameter Model of Alpha-Relaxation in Glasses
• Graph-Dynamics correspondence in metallic glass-forming liquids
• Fragility index of a simple liquid from structural inputs
• Effective one-component model of binary mixture: molecular arrest induced by the spatially correlated stochastic dynamics
• Information scrambling and butterfly velocity in quantum spin glass chains
• Controlling the Glass Transition through Active Fluctuating Interactions
• Glass theory: ground and excited states of coupled electron pairs
• Quantum fluctuations can enhance or reduce positional uncertainty at finite temperature
• Following the evolution of metastable glassy states under external perturbations: compression and shear-strain
• Model dielectric functions for fluctuation potential calculations in electron gas: a critical assessment
• An alternative, dynamic density functional-like theory for time-dependent density fluctuations in glass-forming fluids
• Ergodicity in glass relaxation
• Unifying atoms and colloids near the glass transition through bond-order topology
• Frequency-dependent specific heat in quantum supercooled liquids: A mode-coupling study
• Dynamics of wire frame glasses in two dimensions
• Relaxation Dynamics of a Liquid in the Vicinity of an Attractive Surface: The Process of Escaping from the Surface