Field theoretic formulation of a mode-coupling equation for colloids

TL;DR

This paper introduces a field theoretic approach to derive the mode-coupling equation for colloids, providing a systematic and variational foundation that can be extended to higher orders and multipoint correlations.

Contribution

A novel field theoretic formulation of the mode-coupling equation based on a variational principle and controlled expansion, applicable to colloidal systems.

Findings

Derives mode-coupling equations from a systematic expansion

Applicable to colloids with mildly repulsive interactions

Framework can be extended to higher orders and multipoint correlations

Abstract

The only available quantitative description of the slowing down of the dynamics upon approaching the glass transition has been, so far, the mode-coupling theory, developed in the 80's by G\"otze and collaborators. The standard derivation of this theory does not result from a systematic expansion. We present a field theoretic formulation that arrives at very similar mode-coupling equation but which is based on a variational principle and on a controlled expansion in a small dimensioneless parameter. Our approach applies to such physical systems as colloids interacting via a mildly repulsive potential. It can in principle, with moderate efforts, be extended to higher orders and to multipoint correlation functions.