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Field Theory for Amorphous Solids.
1Institut de Physique Théorique Philippe Meyer, École Normale Supérieure, PSL University, Sorbonne Universités, CNRS, 75005 Paris, France.
Physical Review Letters
|September 29, 2018
Summary
Long-range stress correlations in glassy materials are explained by mechanical equilibrium alone. This study derives equations for stress fluctuations and spatial structures in 2D and 3D amorphous systems.
Area of Science:
- Condensed Matter Physics
- Materials Science
- Statistical Mechanics
Background:
- Glasses exhibit inherent states at low temperatures, with anomalies reflecting their structure.
- Recent observations show long-range stress correlations in diverse glassy systems (liquids, colloids, granular materials).
- A unified explanation for these correlations has been lacking.
Purpose of the Study:
- To provide a common explanation for long-range stress correlations in glassy materials.
- To derive explicit predictions for stress correlations in two and three dimensions.
- To identify new theoretical frameworks for understanding glassy systems.
Main Methods:
- Development of a field theory of inherent states.
- Derivation of "equations of state" relating fluctuations to imposed stresses.
- Formulation of field equations for stress spatial structure in arbitrary geometries.
Main Results:
- Demonstration that long-range stress correlations arise from mechanical equilibrium alone.
- Explicit predictions for stress correlations in 2D and 3D amorphous systems.
- Identification of a novel holographic quantity in 3D amorphous systems.
Conclusions:
- Mechanical equilibrium is sufficient to explain long-range stress correlations in glasses.
- The derived field theory provides a unified framework for understanding stress correlations.
- New theoretical tools are available for analyzing the structure of stresses in amorphous materials.
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