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Quantum chaos and semiclassical behavior in mushroom billiards I: Spectral statistics
Matic Orel, \v{C}rt Lozej, Marko Robnik, Hua Yan
https://arxiv.org/abs/2507.13823

Quantum chaos and semiclassical behavior in mushroom billiards I: Spectral statistics
We study the aspects of quantum chaos in mushroom billiards introduced by Bunimovich. This family of billiards classically has the property of mixed phase space with precisely one entirely regular and one fully chaotic (ergodic) component, whose size depends on the width w of the stem, and has two limiting geometries, namely the circle (as the integrable system) and stadium (as the fully chaotic system). Therefore, this one-parameter system is ideal to study the semiclassical behavior of the qu…