# On mean-field theories of dynamics in supercooled liquids

## TL;DR

This paper introduces a hybrid numerical method to precisely determine the memory function in supercooled liquids and compares it with existing mean-field theories, revealing both similarities and differences.

## Contribution

It develops a hybrid numerical approach to extract the exact memory function and compares it with two mean-field models, providing insights into their accuracy.

## Key findings

- The exact memory function shares traits with mean-field models.
- Quantitative differences highlight limitations of mean-field approximations.
- The approach aids in understanding dynamics of 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.