Peter Kramer

The impact of quasicrystals (1984-2004) on theoretical physics

Since their discovery in 1984, quasicrystals have stimulated the search for aperiodic order in crystallography, mathematics and physics. Quasiperiodic point sets projected from lattices in higher dimension and quasiperiodic tiling models were introduced. Mathematical conditions for diffraction with pure point spectrum were found. The quantum theory of electrons in aperiodic systems goes beyond Bloch states. Scaling symmetries augment the non-crystallographic point groups, generate tiling models, and allow for the construction of wavelets. Covering units offer a novel way of atomic structure and surface description in quasicrystals.