The reciprocal space properties of the electronic wave functions of the Penrose lattice

The spectral density of an electron in a Penrose lattice is investigated numerically. it is found that the profile of the spectral density of the energy versus the wavenumber plane exhibits a dispersion-relation-like pattern. The positions and the 'intensities' of the stationary points of the dispersion relation are accounted for by the ordinary structure factor, S(Q), and the 'optical structure factor' S opt (Q); the Penrose lattice is a 'non-Bravais type' quasilattice and the eigenstates near the top of the band are considered to be 'optical modes'.