Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings
Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings
This work considers the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long-wavelength fluctuations in a broad class of one-dimensional substitution tilings. A simple argument is presented which predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α > 0 being hyperuniform, and numerical …