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We analyze the slow, glassy structural relaxation as measured throughcollective and tagged-particle density correlation functions obtained fromBrownian dynamics simulations for a polydisperse system of quasi-hard spheresin the framework of the mode-coupling theory of the glass transition (MCT).Asymptotic analyses show good agreement for the collective dynamics whenpolydispersity effects are taken into account in a multi-component calculation,but qualitative disagreement at small $q$ when the system is treated aseffectively monodisperse. The origin of the different small-$q$ behaviour isattributed to the interplay between interdiffusion processes and structuralrelaxation. Numerical solutions of the MCT equations are obtained takingproperly binned partial static structure factors from the simulations as input.Accounting for a shift in the critical density, the collective densitycorrelation functions are well described by the theory at all densitiesinvestigated in the simulations, with quantitative agreement best around themaxima of the static structure factor, and worst around its minima. Aparameter-free comparison of the tagged-particle dynamics however reveals largequantiative errors for small wave numbers that are connected to the well-knowndecoupling of self-diffusion from structural relaxation and to dynamicalheterogeneities. While deviations from MCT behaviour are clearly seen in thetagged-particle quantities for densities close to and on the liquid side of theMCT glass transition, no such deviations are seen in the collective dynamics.

Structural relaxation of polydisperse hard spheres: comparison of the mode-coupling theory to a Langevin dynamics simulation