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The properties of mixed eigenstates in a generic quantum system withclassical counterpart that has mixed-type phase space, although important tounderstand several fundamental questions that arise in both theoretical andexperimental studies, are still not clear. Here, following a recent work[\v{C}.~Lozej {\it et al}. Phys. Rev. E {\bf 106}, 054203 (2022)], we performan analysis of the features of mixed eigenstates in a time-dependentHamiltonian system, the celebrated kicked top model. As a paradigmatic modelfor studying quantum chaos, kicked top model is known to exhibit both classicaland quantum chaos. The types of eigenstates are identified by means of thephase space overlap index, which is defined as the overlap of the Husimifunction with regular and chaotic regions in classical phase space. We showthat the mixed eigenstates appear due to various tunneling precesses betweendifferent phase space structures, while the regular and chaotic eigenstatesare, respectively, associated with invariant tori and chaotic component inphase space. We examine how the probability distribution of the phase spaceoverlap index evolves with increasing system size for different kickingstrengths. In particular, we find that the relative fraction of mixed statesexhibits a power-law decay as the system size increases, indicating that onlypurely regular and chaotic eigenstates are left in the strict semiclassicallimit. We thus provide further verification of the principle of uniformsemiclassical condensation of Husimi functions and confirm the correctness ofthe Berry-Robnik picture.

Power-law decay of the fraction of the mixed eigenstates in kicked top model with mixed-type classical phase space