Unveiling the anatomy of mode-coupling theory

TL;DR

This paper critically evaluates the approximations in mode-coupling theory of the glass transition using simulations, revealing which assumptions are accurate and guiding future theoretical improvements.

Contribution

It provides a detailed, quantitative assessment of each approximation in MCT, clarifying their validity and informing future research directions.

Findings

Some MCT approximations are highly accurate.

Other approximations are less valid, requiring refinement.

Results guide future development of glass transition theories.

Abstract

The mode-coupling theory of the glass transition (MCT) has been at the forefront of fundamental glass research for decades, yet the theory's underlying approximations remain obscure. Here we quantify and critically assess the effect of each MCT approximation separately. Using Brownian dynamics simulations, we compute the memory kernel predicted by MCT after each approximation in its derivation, and compare it with the exact one. We find that some often-criticized approximations are in fact very accurate, while the opposite is true for others, providing new guiding cues for further theory development.