Dissecting mode-coupling theory for supercooled liquids

TL;DR

This paper critically evaluates the approximations in mode-coupling theory for supercooled liquids using simulations, revealing that certain errors cancel out over time and that the theory remains accurate in the supercooled regime, with improvements possible through minor corrections.

Contribution

The study provides a detailed assessment of MCT approximations, highlighting error cancellations and suggesting avenues for refining the theory's predictive capabilities.

Findings

Long-time error cancellations occur due to static and dynamic approximations.

MCT's memory functional remains highly accurate in the supercooled regime.

Minor errors in the memory kernel are amplified by the self-consistent equations.

Abstract

The mode-coupling theory (MCT) of the glass transition ranks among the most successful first-principles kinetic theories to describe glassy dynamics. However, MCT does not fully account for crucial aspects of the dynamics near the glass transition. To facilitate improving the theory, we critically test the approximations inherent in MCT for a supercooled mixture using Brownian dynamics simulations. Although each MCT approximation significantly impacts the predicted dynamics, our findings show that long-time cancellations of errors occur due to static and dynamic approximations of four-point correlation functions, with the validity of these approximations remaining relatively constant across different temperatures. Notably, the MCT form of the memory functional maintains remarkably high accuracy even in the supercooled regime when evaluated with the intermediate scattering function from simulations. The primary discrepancies between theoretical predictions and experimental results arise from the self-consistent nature of the MCT equations, which amplify minor errors in the memory kernel. This suggests that minor corrections to the memory functional could substantially enhance the theory's predictive accuracy.