Friedel Oscillations in Microwave Billiards

TL;DR

This paper investigates Friedel oscillations in microwave billiards, demonstrating that a random plane wave model effectively describes oscillations in pseudo-integrable systems and discusses methods to distinguish chaotic from regular states.

Contribution

It extends the application of the random plane wave model to non-purely-chaotic microwave billiards and introduces phase space projection techniques for mixed dynamical systems.

Findings

Oscillations match the random plane-wave model in pseudo-integrable cavities.

Phase space projection improves modeling of mixed systems.

Distinguishing chaotic and regular states enhances understanding of microwave billiard dynamics.

Abstract

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 pseudo-integrable and mixed dynamics geometries. It is found that the oscillations in the pseudo-integrable microwave cavity matches 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.