Experimental confirmation of hyperuniformity of torque fluctuations in frictional matter

¹ Hangzhou International Innovation Institute, Beihang University - Hangzhou 311115, China
² School of Physics and Astronomy, Shanghai Jiao Tong University - Shanghai 200240, China
³ Institute of Natural Sciences, Shanghai Jiao Tong University - Shanghai 200240, China
⁴ Department of Chemical Physics, the Weizmann Institute of Science - Rehovot 7610001, Israel

Received: 5 December 2025
Accepted: 30 January 2026

Abstract

A recent purely theoretical prediction stated that in frictional granular packings, mechanical balance and material isotropy constrain the stress auto-correlation matrix to be fully determined by two spatially isotropic functions: the pressure and torque auto-correlations. Moreover, and unexpectedly, the torque fluctuations were predicted to be hyperuniform, a condition for the stress auto-correlation to decay as the elastic Green's function. In this letter we present first experimental evidence for the hyperuniformity of the stress fluctuations. We propose that quite generally the variance of torque fluctuations in a d-dimensional ball of radius R will increase exactly like , satisfying the definition of hyperuniformity.