Random quench predicts universal properties of amorphous solids

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.

19 pages, 3 figures, submission to SciPost

References in corpus (3)

• Invariant $\beta$-ensembles and the Gauss-Wigner crossover
• Connecting shear localization with the long-range correlated polarized stress fields in granular materials
• Elastic moduli fluctuations predict wave attenuation rates in glasses

Cited by in corpus (7)

• Low-energy quasilocalized excitations in structural glasses
• Density of States below the First Sound Mode in 3D Glasses
• Non-phononic density of states of two-dimensional glasses revealed by random pinning
• Low-Frequency Vibrational States in Ideal Glasses with Random Pinning
• Bose-Einstein-Like condensation of deformed random matrix: A replica approach
• Vibrational density of states of jammed packing: mean-field theory
• Note: Simple argument for emergent anisotropic stress correlations in disordered solids