Experimental Confirmation of Hyperuniformity of torque fluctuations in Frictional Matter

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 $R^{d-1}$, satisfying the definition of hyperuniformity.