Friedel oscillations in microwave billiards

Friedel oscillations of electron densities near step edges have an analog in microwave billiards. A random plane-wave model, normally only appropriate for the eigenfunctions of a purely chaotic system, can be applied and is tested for non-purely-chaotic dynamical systems with measurements on pseudointegrable and mixed dynamics geometries. It is found that the oscillations in the pseudointegrable microwave cavity match the random plane-wave modeling. Separating the chaotic from the regular states for the mixed system requires incorporating an appropriate phase-space projection into the modeling in multiple ways for good agreement with experiment.