20.500.12556/DKUM-86141 Phenomenology of quantum eigenstates in mixed-type systems: Lemon billiards with complex phase space structure The boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius with the distance 2B between their centers, as introduced by Heller and Tomsovic [E. J. Heller and S. Tomsovic, Phys. Today 46, 38 (1993)]. This paper is a continuation of our recent papers on a classical and quantum ergodic lemon billiard (B = 0.5) with strong stickiness effects [C. Lozej ˇ et al., Phys. Rev. E 103, 012204 (2021)], as well as on the three billiards with a simple mixed-type phase space and no stickiness [C. Lozej ˇ et al., Nonlin. Phenom. Complex Syst. 24, 1 (2021)]. Here we study two classical and quantum lemon billiards, for the cases B = 0.1953, 0.083, which are mixed-type billiards with a complex structure of phase space, without significant stickiness regions. A preliminary study of their spectra was published recently [ C. Lozej, D. Lukman, and M. ˇ Robnik, Physics 3, 888 (2021)]. We calculate a very large number (106) of consecutive eigenstates and their Poincaré-Husimi (PH) functions, and analyze their localization properties by studying the entropy localization measure and the normalized inverse participation ratio. We introduce an overlap index, which measures the degree of the overlap of PH functions with classically regular and chaotic regions. We observe the existence of regular states associated with invariant tori and chaotic states associated with the classically chaotic regions, and also the mixed-type states. We show that in accordance with the Berry-Robnik picture and the principle of uniform semiclassical condensation of PH functions, the relative fraction of mixed-type states decreases as a power law with increasing energy, thus, in the strict semiclassical limit, leaving only purely regular and chaotic states. Our approach offers a general phenomenological overview of the structural and localization properties of PH functions in quantum mixed-type Hamiltonian systems. quantum physics energy localization quantum chaos billiards chaotic systems kvantna fizika energija lokalizacija kvantni kaos biljardi kaotični sistemi true false true American Physical Society Angleški jezik Slovenski jezik Znanstveno delo 2023-10-12 10:20:22 2023-10-12 14:14:13 2023-10-16 09:40:58 0000-00-00 00:00:00 2022 0 0 Str. 1-15 Št 5, št. članka 054203 Letn. 106 2022 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2022-07-18 2022-10-20 2022-11-07 530.145:519.2 130231299 10.1103/PhysRevE.106.054203 2470-0053 Phenomenology_of_quantum_eigenstates_Crt_2022.pdf Phenomenology_of_quantum_eigenstates_Crt_2022.pdf 1 AE75CE08D60F9550B7820884337C4EC3 7a3a2ff6dbe858960ed7a20511b5424bcdd1539d8cbf7531a1faafef2e5e7cb8 498dfd0f-68d9-11ee-a17d-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=173509 https://journals.aps.org/pre/abstract/10.1103/PhysRevE.106.054203 0 62933c12-68d9-11ee-a17d-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=173510 Univerza v Mariboru 0 0 0