Mode-coupling theory and beyond: a diagrammatic approach

Abstract

For almost thirty years, mode-coupling theory has been the most widely discussed and used but also the most controversial theory of the glass transition. In this paper we briefly review the reasons for both its popularity and its controversy. We emphasize the need for the development of approaches that would be able to evaluate corrections to and extensions of the existing (standard) mode-coupling theory. Next, we review our diagrammatic formulation of the dynamics of interacting Brownian particles. We show that within this approach the standard mode-coupling theory can be derived in a very simple way. Finally, we use our diagrammatic approach to calculate two corrections to the mode-coupling theory's expression for the so-called irreducible memory function. These corrections involve re-summations of well defined classes of non-mode-coupling diagrams.

Invited paper; to be published in PTEP

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Cited by in corpus (14)

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• Relaxation Patterns in Supercooled Liquids from Generalized Mode-Coupling Theory
• Dimensional study of the dynamical arrest in a random Lorentz gas
• Morphometric approach to many-body correlations in hard spheres
• Generalized mode-coupling theory of the glass transition: schematic results at finite and infinite order
• Nonequilibrium mode-coupling theory for uniformly sheared underdamped systems
• Persistent anti-correlations in Brownian dynamics simulations of dense colloidal suspensions revealed by noise suppression
• Dynamical Susceptibilities Near Ideal Glass Transitions
• Self-Consistent Relaxation Theory of Collective Ion Dynamics in Yukawa One-Component Plasmas under Intermediate Screening Regimes
• A numerical study of longtime dynamics and ergodic-nonergodic transitions in dense simple fluids
• Breakdown of a renormalized perturbation expansion around mode-coupling theory of the glass transition