43 citations · 152 across the 26 of their papers we have counts for
6 papers · 1 filter
Quasicrystals
Uwe Grimm, Peter Kramer
Mathematicians have been interested in non-periodic tilings of space for decades; however, it was the unexpected discovery of non-periodically ordered structures in intermetallic a…
A new product on 2x2 matrices
Linus Kramer, Peter Kramer, Vladimir Man'ko
We study a bilinear multiplication rule on 2x2 matrices which is intermediate between the ordinary matrix product and the Hadamard matrix product, and we relate this to the hyperbo…
Platonic polyhedra tune the 3-sphere: III. Harmonic analysis on octahedral spherical 3-manifolds
Peter Kramer
From the homotopy groups of three distinct octahedral spherical 3-manifolds we construct the isomorphic groups H of deck transformations acting on the 3-sphere. The H-invariant pol…
Quasicrystals: Atomic coverings and windows are dual projects
Peter Kramer
In the window approach to quasicrystals, the atomic position space E_parallel is embedded into a space E^n = E_parallel + E_perp. Windows are attached to points of a lattice Lambda…
Exact electron states in 1D (quasi-) periodic arrays of delta-potentials
Peter Kramer, Tobias Kramer
Exact one-electron eigenstates in finite parts of 1D periodic and Fibonacci chains of attractive and repulsive delta potentials are computed and analyzed. Bloch and bound state bou…
Tiling theory applied to the surface structure of icosahedral AlPdMn quasicrystals
Peter Kramer, Zorka Papadopolos, Harald Teuscher
Surfaces in i-Al68Pd23Mn9 as observed with STM and LEED experiments show atomic terraces in a Fibonacci spacing. We analyze them in a bulk tiling model due to Elser which incorpora…