Edwards field theory for glasses and granular matter
arXiv:1804.04834 · doi:10.1103/PhysRevE.98.033001
Abstract
A minimal description of the inherent states of amorphous solids is presented. Using field theory, applicable when a system is probed at long length scales, it is shown that athermal amorphous solids have long-range correlations in their stresses, as recently observed in supercooled liquids, colloids, and granular matter. Explicit predictions for the correlators are presented, in both 2D and 3D, in excellent agreement with simulation data on supercooled liquids. It is shown that when applied to solids with strictly repulsive interactions, the simplest, naïve theory leads to a paradox. This paradox is resolved, and it is shown that a nontrivial, non-Gaussian theory is necessary for such materials. Modifications to the correlators are shown, at the saddle-point level. In all cases, `equations of state' relating fluctuations to imposed stresses are derived, as well as field equations that fix the spatial structure of stresses in arbitrary geometries. A new holographic quantity in 3D amorphous systems is identified.
11 pages + 9 pages SI
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Cited by in corpus (12)
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- Emergent Elasticity in Amorphous Solids
- Connecting shear localization with the long-range correlated polarized stress fields in granular materials
- Field theory for amorphous solids
- Protocol-Dependence and State Variables in the Force-Moment Ensemble
- Stress Correlations in Frictional Granular Media
- Yielding is an absorbing phase transition with vanishing critical fluctuations
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- Random quench predicts universal properties of amorphous solids
- Note: Simple argument for emergent anisotropic stress correlations in disordered solids
- Uncertainty Relations for Mesoscopic Coherent Light
- Stress-stress correlations in two-dimensional amorphous and crystalline solids