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.

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• Multi-time density correlation functions in glass-forming liquids: Probing dynamical heterogeneity and its lifetime
• Static replica approach to critical correlations in glassy systems
• Arrest of flow and emergence of activated processes at the glass transition of a suspension of particles with hard sphere-like interactions
• Anisotropic spatially heterogeneous dynamics on the $\alpha$ and $\beta$ relaxation time scales studied via a four-point correlation function
• Heterogeneous dynamics and its length scale in simple ionic liquid models: A computational study
• Connecting Relaxation Time to a Dynamical Length Scale in Athermal Active Glass Formers
• Three-point susceptibilities ${\chi }_n(k;t)$ and ${\chi }_n^s(k;t)$: mode-coupling approximation
• Breakdown of a renormalized perturbation expansion around mode-coupling theory of the glass transition
• Microscopic Theory of a Fluctuation-Induced Dynamical Crossover in Supercooled Liquids
• Theory of the $\beta$-Relaxation Beyond Mode-Coupling Theory: A Microscopic Treatment
• Glass and jamming transition of simple liquids: static and dynamic theory