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Edwards field theory for glasses and granular matter

E. DeGiuli
Phys. Rev. E 98, 033001 – Published 10 September 2018
Physics logo See Viewpoint: Constructing a Theory for Amorphous Solids
An article within the collection: Irwin Oppenheim Award

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 two and three dimensions, 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 holographic quantity in three-dimensional amorphous systems is identified.

  • Received 11 April 2018

DOI:https://doi.org/10.1103/PhysRevE.98.033001

©2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsPolymers & Soft Matter

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Irwin Oppenheim Award

Annual award recognizes outstanding contributions by early career scientists.

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Constructing a Theory for Amorphous Solids

Published 10 September 2018

Theorists are coming closer to a comprehensive description of the mechanics of solids with an amorphous structure, such as glass, cement, and compacted sand.

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Authors & Affiliations

E. DeGiuli

  • Institut de Physique Théorique Philippe Meyer, École Normale Supérieure, PSL University, Sorbonne Universités, Centre National de la Recherche Scientifique, 75005 Paris, France

See Also

Field Theory for Amorphous Solids

E. DeGiuli
Phys. Rev. Lett. 121, 118001 (2018)

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Issue

Vol. 98, Iss. 3 — September 2018

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