# Mode-coupling theory for the dynamic heterogeneity in an aging glass: How Do Glassy Domains Grow?

Source: [Mode-coupling theory for the dynamic heterogeneity in an aging glass: How Do Glassy Domains Grow?](<https://www.sota2.com/research/paper/68fa3fe01e209131ce8ef091>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T02:29:23.921Z

Authors: Saroj Kumar Nandi, Sriram Ramaswamy

Published: 2012-05-05T18:10:48.000Z

## Abstract

We construct the equations for the growth kinetics of an aging structural glass within mode-coupling theory through a non-stationary variant of the 3-density correlator defined in Phys. Rev. Lett. {\\bf 97}, 195701 (2006). We solve a schematic form of the resulting equations to obtain the coarsening of the dynamic heterogeneity, characterized via the 3-point correlator $\\chi\_3(t,t\_w)$, as a function of waiting time $t\_w$. For a quench into the glass, we find that $\\chi\_3$ attains a peak value $\\sim t\_w^{0.5}$ at $t -t\_w \\sim t\_w^{0.8}$, providing a theoretical basis for the numerical observations of Parisi \[J. Phys. Chem. B \\textbf{103}, 4128 (1999)\] and Kob and Barrat \[Phys. Rev. Lett. \\textbf{78}, 4581 (1997)\]. The aging is not "simple": the $t\_w$ dependence cannot be attributed to an evolving effective temperature.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1205.1152>)

[PDF](<https://arxiv.org/pdf/1205.1152.pdf>)