# The glass susceptibility: growth kinetics and saturation under shear

Source: [The glass susceptibility: growth kinetics and saturation under shear](<https://www.sota2.com/research/paper/68fa33b21e209131ce8922e0>)

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

Data updated: 2025-10-24T20:12:52.724Z

Authors: Saroj Kumar Nandi, Sriram Ramaswamy

Published: 2013-09-10T06:53:08.000Z

## Abstract

We study the growth kinetics of glassy correlations in a structural glass by monitoring the evolution, within mode-coupling theory, of a suitably defined three-point function $\\chi\_C(t,t\_w)$ with time $t$ and waiting time $t\_w$. From the complete wave vector-dependent equations of motion for domain growth we pass to a schematic limit to obtain a numerically tractable form. We find that the peak value $\\chi\_C^P$ of $\\chi\_C(t,t\_w)$, which can be viewed as a correlation volume, grows as $t\_w^{0.5}$, and the relaxation time as $t\_w^{0.8}$, following a quench to a point deep in the glassy state. These results constitute a theoretical explanation of the simulation findings of Parisi \[J. Phys. Chem. B {\\bf 103}, 4128 (1999)\] and Kob and Barrat \[Phys. Rev. Lett. {\\bf 78}, 4581 (1997)\] and are also in qualitative agreement with Parsaeian and Castillo \[Phys. Rev. E {\\bf 78}, 060105(R) (2008)\]. On the other hand, if the quench is to a point on the {\\em liquid side}, the correlation volume grows to saturation. We present a similar calculation for the growth kinetics in a $p$-spin spin glass mean-field model where we find a slower growth, $\\chi\_C^P \\sim t\_w^{0.13}$. Further, we show that a shear rate $\\gdot$ cuts off the growth of glassy correlations when $t\_w\\sim 1/\\gdot$ for quench in the glassy regime and $t\_w=\\min(t\_r,1/\\gdot)$ in the liquid, where $t\_r$ is the relaxation time of the unsheared liquid. The relaxation time of the steady state fluid in this case is $\\propto \\gdot^{-0.8}$.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1309.2389>)

[PDF](<https://arxiv.org/pdf/1309.2389.pdf>)