2025/10/13 by Matic Orel, Orel, Matic, Marko Robnik +1
Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Quantum many-body systems
paper · doi:10.48550/arxiv.2510.11412
openalex publication_date 2025/10/13 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28
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)].