Mode-coupling theory and beyond: a diagrammatic approach

TL;DR

This paper reviews the history and controversy of mode-coupling theory for the glass transition, introduces a diagrammatic approach for deriving and extending the theory, and calculates specific corrections to improve its accuracy.

Contribution

It presents a new diagrammatic formulation that simplifies deriving the mode-coupling theory and enables calculation of corrections beyond the standard approximation.

Findings

Standard mode-coupling theory derived simply from the diagrammatic approach

Calculated two corrections involving non-mode-coupling diagrams

Highlights the potential for systematic improvements to the theory

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.