Divergent Four-Point Dynamic Density Correlation Function of a Glassy Suspension

Abstract

We use a recently derived diagrammatic formulation of the dynamics of interacting Brownian particles [G. Szamel, J. Chem. Phys. 127, 084515 (2007)10.1063/1.2759487] to study a four-point dynamic density correlation function. We resum 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)10.1103/PhysRevLett.97.195701] 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)10.1126/science.1120714; J. Chem. Phys. 126, 184503 (2007)10.1063/1.2721554]. It exhibits a small wave vector divergence at the mode-coupling transition.