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Unveiling the anatomy of mode-coupling theory

by I. Pihlajamaa, V. E. Debets, C. C. L. Laudicina, L. M. C. Janssen

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Submission summary

Authors (as registered SciPost users): Ilian Pihlajamaa
Submission information
Preprint Link: https://arxiv.org/abs/2307.03443v3  (pdf)
Date accepted: 2023-11-13
Date submitted: 2023-10-30 09:45
Submitted by: Pihlajamaa, Ilian
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational

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.

Published as SciPost Phys. 15, 217 (2023)



Author comments upon resubmission

Dear Editor,

After consideration of the second report of the anonymous referee, we have added a few sentences to the manuscript to elaborate on the points they raised. Please consider our resubmission for publication in SciPost Physics.

Sincerely,
on behalf of all authors,
Ilian Pihlajamaa

List of changes

We have added the following text to the appendix:

[...] Additionally, it can be shown that both the memory kernel itself and its time integral should scale with $k^2$ for small $k$ \cite{gotze2009complex, cichocki1990self}. While Eq.~[29] does show the correct scaling for the kernel itself, on first glance it does not for its time integral (each term scales with $k^0$). Nevertheless, together with Eq.~[30] and [26], the correct scaling should be recovered. Thus we expect that the $k^0$-scalings of each of the terms in the time integral of Eq.~[29] cancel to yield an overall correct $k^2$ proportionality. The low wavelength limit is an interesting regime, but we leave it for further study here. Its investigation in more supercooled systems could shed light on the failure of MCT to produce a breakdown of the Stokes-Einstein relation.

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