Colloquium on January 28th, 2008

Achim Richter
Technische Universität Darmstadt

Playing billiards with microwaves - Quantum manifestations of classical chaos

Sufficiently flat microwave resonators shaped in the form of billiards are particularly well suited to study the quantum mechanical behavior of classically chaotic systems because of the formal equivalence of the respective wave equations, i.e. the Helmholtz and the Schroedinger equation. With superconducting resonators characterized by high quality factors it has become possible for the first time to measure the spectrum of eigenmodes and their eigenfunctions completely and to determine their statistical properties. Two-dimensional billiards systems (stadium, mushroom, …) of different chaoticity are discussed and it is shown that they display universal features which are also evident in real physical systems like atoms, molecules and atomic nuclei. Special emphasis is placed on properties of spectra and wavefunctions, and on so called Friedel oscillations, known also from surface and condensed matter physics.