  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.
