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Mode-coupling theory of the glass transition for polydisperse systems

Robert Schlothauer and Thomas Franosch

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Phys. Rev. E 114, 025412 – Published 18 August, 2026

DOI: https://doi.org/10.1103/586t-9ytz

Abstract

We develop a covariant formulation of the mode-coupling theory (MCT) for the glass transition in polydisperse suspensions. We show that the Mori-Zwanzig equations of motion and the MCT memory functional are invariant under arbitrary changes of basis in the space of species-resolved density fluctuations, provided the vertices are transformed consistently. Exploiting this symmetry, we construct a mode basis via a diameter-moment expansion and an orthonormalization with respect to the structure factor. In this basis, the leading mode is the total density, and higher modes encode systematic size-contrast corrections. Truncating to a few modes yields a controlled, numerically stable reduction of the multicomponent MCT while retaining quantitative accuracy for the total intermediate scattering function. Benchmarking against a ten-component discretization of continuously polydisperse hard-sphere-like fluids (Schulz-Zimm and inverse-cubic distributions), we find that three to six modes reproduce the critical packing fraction and the full shape of the total correlator with large computational savings. This reformulation provides an efficient framework for the MCT of polydisperse systems with controlled discretization and basis-truncation errors.

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Phys. Rev. E 114, 025412– Published 18 August, 2026
  • Received 18 May 2026
  • Accepted 27 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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