Cooperativity Beyond Caging: Generalized Mode Coupling Theory

Abstract

The validity of mode coupling theory (MCT) is restricted by an uncontrolled factorization approximation of density correlations. The factorization can be delayed and ultimately avoided, however, by explicitly including higher order correlations. We explore this approach within a microscopically motivated schematic model. Analytic tractability allows us to discuss in great detail the impact of factorization at arbitrary order, including the limit of avoided factorization. Our results indicate a coherent picture for the capabilities as well as limitations of MCT. Moreover, including higher order correlations systematically defers the transition and ultimately restores ergodicity. Power-law divergence of the relaxation time is then replaced by continuous but exponential growth.

4 pages, 2 figures

References in corpus (13)

• Scaling behavior in the $\beta$-relaxation regime of a supercooled Lennard-Jones mixture
• On the Adam-Gibbs-Wolynes scenario for the viscosity increase in glasses
• Fragilities of Liquids Predicted from the Random First Order Transition Theory of Glasses
• A quantitative test of the mode-coupling theory of the ideal glass transition for a binary Lennard-Jones system
• Relaxation in a glassy binary mixture: Comparison of the mode-coupling theory to a Brownian dynamics simulation
• Relaxation in a glassy binary mixture: Mode-coupling-like power laws, dynamic heterogeneity and a new non-Gaussian parameter
• Colloidal glass transition: Beyond mode-coupling theory
• Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry
• Independence of the relaxation of a supercooled fluid of its microscopic dynamics: need for yet another extension of the mode-coupling theory
• Gaussian density fluctuations and Mode Coupling Theory for supercooled liquids
• Do current-density nonlinearities cut off the glass transition?
• Quantitative tests of mode-coupling theory for fragile and strong glass-formers
• Gaussian density fluctuations, mode coupling theory, and all that

Cited by in corpus (55)

• Theoretical perspective on the glass transition and amorphous materials
• Molecular dynamics simulations of glassy polymers
• Mode-Coupling Theory of the Glass Transition: A Primer
• Connectivity of the Icosahedral Network and a Dramatically Growing Static Length Scale in Cu-Zr Binary Metallic Glasses
• Hopping and the Stokes-Einstein relation breakdown in simple glass formers
• Locally preferred structures and many-body static correlations in viscous liquids
• A critical test of the mode-coupling theory of the glass transition
• Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry
• Microscopic dynamics of supercooled liquids from first principles
• A New Theory of Dynamic Arrest in Colloidal Mixtures
• Mode-Coupling as a Landau Theory of the Glass Transition
• Dimensional dependence of the Stokes--Einstein relation and its violation
• Qualitative Features at the Glass Crossover
• Static triplet correlations in glass-forming liquids: A molecular dynamics study
• Numerical and Theoretical Study of a Monodisperse Hard-Sphere Glass Former
• Equilibrium dynamics of the Dean-Kawasaki model: MCT and beyond
• Slow Dynamics of the High Density Gaussian Core Model
• Dynamics of interacting Brownian particles: a diagrammatic formulation
• Long-wavelength fluctuations lead to a model of the glass crossover
• The role of pair correlation function in the dynamical transition predicted by the mode coupling theory
• Relaxation Patterns in Supercooled Liquids from Generalized Mode-Coupling Theory
• Dimensional study of the dynamical arrest in a random Lorentz gas
• Mode-coupling theory and beyond: a diagrammatic approach
• Microscopic Theory of the Influence of Strong Attractive Forces on the Activated Dynamics of Dense Glass and Gel Forming Fluids
• Generalized mode-coupling theory of the glass transition: schematic results at finite and infinite order
• Does Fluctuating Nonlinear Hydrodynamics Support an Ergodic-Nonergodic Transition?
• Many-body correlations are non-negligible in both fragile and strong glassformers
• Cooperative heterogeneous facilitation: multiple glassy states and glass-glass transition
• On mean-field theories of dynamics in supercooled liquids
• Generalized mode-coupling theory of the glass transition. I. Numerical results for Percus-Yevick hard spheres
• Nonequilibrium mode-coupling theory for uniformly sheared underdamped systems
• Generalized mode-coupling theory of the glass transition. II. Analytical scaling laws
• Multi-component generalized mode-coupling theory: Predicting dynamics from structure in glassy mixtures
• Microscopic models of mode-coupling theory: the $F_{12}$ scenario
• Mode-coupling theory for mixtures of athermal self-propelled particles
• Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra
• Generalized Mode-Coupling Theory for Mixtures of Brownian Particles
• Crossover behavior and multi-step relaxation in a schematic model of the cut-off glass transition
• Brownian dynamics: from glassy to trivial
• Dynamical Susceptibilities Near Ideal Glass Transitions
• Glass transitions and scaling laws within an alternative mode-coupling theory
• Unveiling the anatomy of mode-coupling theory
• Glassy dynamics from generalized mode-coupling theory: existence and uniqueness of solutions for hierarchically coupled integro-differential equations
• Density nonlinearities in field theories for a toy model of fluctuating nonlinear hydrodynamics of supercooled liquids
• 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
• Detection of hidden structures on all scales in amorphous materials and complex physical systems: basic notions and applications to networks, lattice systems, and glasses
• Revisiting the single-saddle model for the $\beta$-relaxation of supercooled liquids
• Dynamics of a noninteracting colloidal fluid in a quenched Gaussian random potential: A time-reversal-symmetry-preserving field-theoretic approach
• Breakdown of a renormalized perturbation expansion around mode-coupling theory of the glass transition
• Understanding the approximations of mode-coupling theory for sheared steady states of colloids
• Mode-coupling theory of the glass transition for a liquid in a periodic potential
• Theory of Kinetically-Constrained-Models Dynamics
• Microscopic Theory of a Fluctuation-Induced Dynamical Crossover in Supercooled Liquids
• Theory of the $\beta$-Relaxation Beyond Mode-Coupling Theory: A Microscopic Treatment