Random quench predicts universal properties of amorphous solids

TL;DR

This paper introduces a field-theoretic model of the quenching process in amorphous solids, unifying various universal properties and explaining vibrational anomalies from initial structureless states.

Contribution

It develops a comprehensive theoretical framework linking the quenching process to the universal features of amorphous solids, extending previous mean-field results.

Findings

Unified description of elastic heterogeneity and vibrational anomalies

Relation of amorphous properties to initial medium and quench process

Generalization of previous mean-field results

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.