Self-consistent elastic continuum theory of degenerate, equilibrium aperiodic solids

TL;DR

This paper develops a continuum mechanics framework to describe the vibrational response of glassy liquids, incorporating built-in stress and degeneracy, and predicts a shear modulus jump at a key transition.

Contribution

It introduces a self-consistent elastic continuum theory for degenerate, aperiodic solids that accounts for built-in stress and predicts fixed points in elastic behavior.

Findings

Elastic constants are down-renormalized by built-in stress relaxation.

Identifies a nontrivial fixed point at Poisson ratio 1/5.

Predicts a discontinuous shear modulus jump at the transition.

Abstract

We show that the vibrational response of a glassy liquid at finite frequencies can be described by continuum mechanics despite the vast degeneracy of the vibrational ground state; standard continuum elasticity assumes a unique ground state. The effective elastic constants are determined by the bare elastic constants of individual free energy minima of the liquid, the magnitude of built-in stress, and temperature, analogously to how the dielectric response of a polar liquid is determined by the dipole moment of the constituent molecules and temperature. In contrast with the dielectric constant---which is enhanced by adding polar molecules to the system---the elastic constants are down-renormalized by the relaxation of the built-in stress. The renormalization flow of the elastic constants has three fixed points, two of which are trivial and correspond to the uniform liquid state and an infinitely compressible solid respectively. There is also a nontrivial fixed point at the Poisson ratio equal to 1/5, which corresponds to an isospin-like degeneracy between shear and uniform deformation. The present description predicts a discontinuous jump in the (finite frequency) shear modulus at the crossover from collisional to activated transport, consistent with the RFOT theory.