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.