Stability of particles in two-dimensional quasicrystals against phasonic perturbations

We investigate particles in two-dimensional quasicrystalline interference patterns and present a method to determine for each particle at which phasonic displacement a phasonic flip occurs. By mapping all particles into characteristic areas of reduced phononic and phasonic displacements, we identify the particles that are close to edges of these areas and can easily flip. In contrast, the particles in the center are hardly affected by phasonic fluctuations. Our results are important e.g. for light-induced colloidal structures or cold atomic gases in laser traps. In addition, our approach can help to predict how thermal fluctuations induce phasonic flips in intrinsic quasicrystals with structures close to interference patterns.