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

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.

References in corpus (5)

• Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids
• Spontaneous and induced dynamic fluctuations in glass-formers I: General results and dependence on ensemble and dynamics
• Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations
• Lengthscale dependence of dynamic four-point susceptibilities in glass formers
• Dynamics of interacting Brownian particles: a diagrammatic formulation

Cited by in corpus (1)

• Three-point susceptibilities ${\chi }_n(k;t)$ and ${\chi }_n^s(k;t)$: mode-coupling approximation