Emergent SO(3) Symmetry of the Frictionless Shear Jamming Transition

TL;DR

This paper reveals that shear jamming in frictionless soft spheres exhibits unique elastic properties and long-range correlations, yet shares underlying symmetry with isotropic jamming, explained through tensor basis rotation.

Contribution

It demonstrates the emergent SO(3) symmetry in shear jamming and connects it to isotropic jamming via elastic tensor basis rotation.

Findings

Shear-jammed states have non-zero residual shear stress.

The ratio of shear to bulk moduli approaches a constant near jamming.

Shear and isotropic jamming share the same underlying symmetry.

Abstract

We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. Despite these striking differences, we argue that in a deeper sense, the shear jamming and isotropic jamming transitions actually have the same symmetry, and that the differences can be fully understood by rotating the six-dimensional basis of the elastic modulus tensor.