Elementary excitations in quasicrystals

We present detailed ab-initio investigations of electron-and phonon spectra in realistic models for icosahedral and decagonal quasicrystals. We show that the hierarchical dense structure of quasi-Brillouin-zone centers and boundaries in wave-number space explains both the spiky nature of the density of states and the existence of both propagating and stationary (localized) eigenstates. The consequence of the character of the eigenstates for the anomalous electronic transport and magnetic properties are discussed.