# Random quench predicts universal properties of amorphous solids

### Submission summary

 As Contributors: Masanari Shimada Preprint link: scipost_202112_00003v1 Date accepted: 2022-01-13 Date submitted: 2021-12-03 03:33 Submitted by: Shimada, Masanari Submitted to: SciPost Physics Academic field: Physics Specialties: Statistical and Soft Matter Physics Approach: Theoretical

### Abstract

Amorphous solids display numerous universal features in their mechanics, structure, and response. Current models assume heterogeneity in mesoscale elastic properties, but require fine-tuning in order to quantitatively explain vibrational properties. A complete model should derive the magnitude and character of elastic heterogeneity from an initially structureless medium, through a model of the quenching process during which the temperature is rapidly lowered and the solid is formed. Here we propose a field-theoretic model of a quench, and compute structural, mechanical, and vibrational observables in arbitrary dimension $d$. This allows us to relate the properties of the amorphous solid to those of the initial medium, and to those of the quench. We show that previous mean-field results are subsumed by our analysis and unify spatial fluctuations of elastic moduli, long-range correlations of inherent state stress, universal vibrational anomalies, and localized modes into one picture.

Published as SciPost Phys. 12, 090 (2022)

We thank the referees for their useful comments, which led to improvements in the manuscript. In the attached manuscript all changes appear in blue. Detailed replies to referee comments follow below.

### List of changes

Referee 1
1. Remove the word "universal" from the abstract.
2. Add an explanation of the word "quench".
3. Change the displacement field in Eq. (1) to a vector.
4. Add an explanation of Green's function.
5. Remove the bracket in Eq. (2).
6. Add the explicit expression of the elastic modulus tensor corresponding to a homogeneous elastic continuum.
7. Introduce the Levi-Civita symbol before Eq. (11).
8. Add an explanation of the necessity of the gauge fields below Eq. (15).
9. Align the expressions in Eq. (17).
10. Add an explanation of the symbols T and L below Eq. (19).
12. Change sigma to kappa in Eq. (21).
14. Move a sentence in the last paragraph of the appendix to page 5.

Referee 2
1. Add an explanation of the dynamics of our model below Eq. (2).
2. Mention the importance of fluctuations of elastic constants in the conclusion.
3. Remove the word "overdamped" from the abstract.
4. Remove the bracket in Eq. (2).
5. Cite a review paper by Kirkpatrick in Ref. [54].
6. Add an explanation of the correlation volume.
7. Modify the explanation of DMFT.
8. Modify the explanation of the expansion after Eq. (28).

### Submission & Refereeing History

Resubmission scipost_202112_00003v1 on 3 December 2021
Submission 2008.11896v2 on 2 September 2021

## Reports on this Submission

### Report

The authors satisfactorily answered comments of both referees. I recommend that the paper is accepted.

• validity: high
• significance: high
• originality: high
• clarity: high
• formatting: excellent
• grammar: excellent