Divergent four-point dynamic density correlation function of a glassy colloidal suspension: a diagrammatic approach

TL;DR

This paper develops a diagrammatic approach to analyze a four-point dynamic density correlation function in glassy colloidal suspensions, revealing divergence at the mode-coupling transition.

Contribution

It introduces a new diagrammatic formulation for the four-point correlation function, connecting it to three-point functions and revealing divergence behavior.

Findings

Four-point function expressed in terms of three-point functions.

Small wave vector divergence at the mode-coupling transition.

Structure similar to previous theoretical proposals.

Abstract

We use a recently derived diagrammatic formulation of the dynamics of interacting Brownian particles [G. Szamel, J. Chem. Phys. 127, 084515 (2007)] to study a four-point dynamic density correlation function. We re-sum a class of diagrams which separate into two disconnected components upon cutting a single propagator. The resulting formula for the four-point correlation function can be expressed in terms of three-point functions closely related to the three-point susceptibility introduced by Biroli et al. [Phys. Rev. Lett. 97, 195701 (2006)] and the standard two-point correlation function. The four-point function has a structure very similar to that proposed by Berthier and collaborators [Science 310, 1797 (2005), J. Chem. Phys. 126, 184503 (2007)]. It exhibits a small wave vector divergence at the mode-coupling transition.