  The dynamics of quasicrystals is characterized by the existence of phason
excitations in addition to the usual phonon modes. In order to investigate
their interplay on an elementary level we resort to various one-dimensional
model systems. The main observables are the static, the incoherent, and the
coherent structure factor, which are extracted from molecular dynamics
simulations. For the validation of the algorithms, results for the harmonic
periodic chain are presented. We then study the Fibonacci chain with harmonic
and anharmonic interaction potentials. In the dynamic Fibonacci chain
neighboring atoms interact by double-well potentials allowing for phason flips.
The difference between the structure factors of the dynamic and the harmonic
Fibonacci chain lies in the temperature dependence of the phonon line width. If
a bias is introduced in the well depth, dispersionless optic phonon bands split
off.
