Optical and Acoustic Branches in the Vibrational Spectrum of aDiatomic Penrose Lattice

Vibrational densities of states for a diatomic Penrose lattice are calculated. They show apparently acoustic and optical branches. The acoustic branches appear smooth and continuous, while the optical branches are peakrich and have some small gaps. Detailed analysis shows that the density of states in the acoustic branches is attributed to the phonons and the fracton-like excitations and that in the optical branches clue to some localized vibrational model.