# Effect of instantaneous and continuous quenches on the density of vibrational modes in model glasses

## TL;DR

This study examines how the method of quenching affects the vibrational mode density in model glasses, revealing a transition from a $eta ext{≈}3$ to a universal $eta ext{= }4$ as quench rates slow down.

## Contribution

It demonstrates that the vibrational mode density exponent depends on quench rate and parent temperature, connecting instantaneous quenches to realistic slow cooling.

## Key findings

- Instantaneous quenches from high T yield $eta ext{≈}3$.
- As parent temperature approaches glass transition, $eta$ approaches 4.
- Slower, physically realistic quenches produce a universal $eta=4$.

## Abstract

Computational studies of supercooled liquids often focus on various analyses of their "underlying inherent states" --- the glassy configurations at zero temperature obtained by an infinitely-fast (instantaneous) quench from equilibrium supercooled states. Similar protocols are also regularly employed in investigations of the unjamming transition at which the rigidity of decompressed soft-sphere packings is lost. Here we investigate the statistics and localization properties of low-frequency vibrational modes of glassy configurations obtained by such instantaneous quenches. We show that the density of vibrational modes grows as $\omega^\beta$ with $\beta$ depending on the parent temperature $T_{0}$ from which the glassy configurations were instantaneously quenched. For quenches from high temperature liquid states we find $\beta\!\approx\!3$, whereas $\beta$ appears to approach the previously-observed value $\beta\!=\!4$ as $T_0$ approaches the glass transition temperature. We discuss the consistency of our findings with the theoretical framework of the Soft Potential Model, and contrast them with similar measurements performed on configurations obtained by continuous quenches at finite cooling rates. Our results suggest that any physical quench at rates sufficiently slower than the inverse vibrational timescale --- including all physically-realistic quenching rates of molecular or atomistic glasses --- would result in a glass whose density of vibrational modes is universally characterized by $\beta\!=\!4$.