On mean-field theories of dynamics in supercooled liquids

Abstract

We develop a hybrid numerical approach to extract the exact memory function K(t) of a tagged particle in three-dimensional glass-forming liquids. We compare the behavior of the exact memory kernel to two mean-field approaches, namely the standard mode-coupling theory and a recently proposed ansatz for the memory function that forms the basis of a new derivation of the exact form of K(t) for a fluid with short-ranged interactions in infinite dimensions. Each of the mean-field functions qualitatively and quantitatively share traits with the exact K(t), although several important quantitative differences are manifest.

arXiv comment11 pages, 11 figures

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• Comment on "Explicit Analytical Solution for Random Close Packing in $d=2$ and $d=3$"
• Active matter in infinite dimensions: Fokker-Planck equation and dynamical mean-field theory at low density
• An alternative, dynamic density functional-like theory for time-dependent density fluctuations in glass-forming fluids