2018/06/20 by Oğuz, Erdal C., Socolar, Joshua E. S., Steinhardt, Paul J. +1 · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.1806.10641
We consider the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long wavelength fluctuations in a broad class of one-dimensional substitution tilings. We present a simple argument that predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α>0 being hyperuniform, and confirm with numerical computations that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra, and limit-periodic tilings. Tilings with quasiperiodic or singular continuous spectra can be constructed with α arbitrarily close to any given value between -1 and 3. Limit-periodic tilings can be constructed with α between -1 and 1 or with Fourier intensities that approach zero faster than any power law.