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Quantum chaos and semiclassical behavior in mushroom billiards II: Structure of quantum eigenstates and their phase space localization properties

Matic Orel and Marko Robnik

  • CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia, European Union

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Phys. Rev. E 113, 044218 – Published 28 April, 2026

DOI: https://doi.org/10.1103/rwq2-rydx

Abstract

We investigate eigenstate localization in the phase space of the Bunimovich mushroom billiard, a paradigmatic mixed–phase–space system whose piecewiseC1 boundary yields a single clean separatrix between one regular and one chaotic region. By varying the stem half-width w, we continuously change the strength and extent of bouncing-ball stickiness in the stem, which for narrow stems gives rise to phase space localization of chaotic eigenstates. Using the Poincaré–Husimi (PH) representation of eigenstates, we quantify localization via information entropies and inverse participation ratios of PH functions. For sufficiently wide stems, the distribution of entropy localization measures converges to a two-parameter beta distribution, while entropy localization measures and inverse participation ratios across the chaotic ensemble exhibit an approximately linear relationship. Finally, the fraction of mixed (neither purely regular nor fully chaotic) eigenstates decays as a power-law in the effective semiclassical parameter, in precise agreement with the principle of uniform semiclassical condensation of Wigner functions [H.-J. Stöckmann (1999); F. Haake (2010)].

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Quantum chaos and semiclassical behavior in mushroom billiards I: Spectral statistics

Matic Orel, Črt Lozej, Marko Robnik, and Hua Yan
Phys. Rev. E 113, 044217 (2026)

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Phys. Rev. E 113, 044218– Published 28 April, 2026
  • Received 13 October 2025
  • Accepted 2 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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