Abstract
Chaotic billiards are a paradigm of quantum chaos studied theoretically in numerous papers. In flat microwave resonators with cross-sections mimicking the billiard shape there is a one-to-one correspondence between the stationary Schrödinger equation and the Helmholtz equation. This allows an experimental access to questions hitherto studied exclusively theoretically. In the article various aspects of quantum chaos are presented and illustrated by experimental results. It continues with a discussion of random matrices and the universal features of wave functions of chaotic billiards. Next, semiclassical quantum mechanics is introduced, establishing a link between the quantummechanical Green function and the classical trajectories. The article ends with a presentation of recent applications of wave-chaos research.
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Stöckmann, HJ. (2013). Chaos in Microwave Resonators. In: Duplantier, B., Nonnenmacher, S., Rivasseau, V. (eds) Chaos. Progress in Mathematical Physics, vol 66. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0697-8_5
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