Hydrodynamic structure factor for two‐dimensional decagonal quasicrystals

Abstract

The dynamic and static structure factors for two‐dimensional decagonal quasicrystals (QCs) are calculated based on the hydrodynamic model. Explicit formulae with algebraic decay, which is characteristic in lower dimensions, are obtained. The sound‐wave and diffusive‐mode contributions are analyzed separately. It is shown that the phonon–phason coupling yields the characteristic anisotropy in the structure factors. If one assumes the phasonic diffusion constant of the order of magnitude typical for metallic QCs, however, the phasonic contribution is expected only at very small frequencies and hence more likely to be observed in the time domain than in the frequency domain.