Further results on the power-law decay of the fraction of the mixed eigenstates in kicked-top model with mixed-type classical phase space.

Abstract

By using the Krylov subspace technique to generate spin-coherent states in the kicked top model, a prototype model for studying quantum chaos, the accessible system size for studying the Husimi functions of eigenstates can be much larger than that reported in the literature and our previous study [Phys. Rev. E 108, 054217 (2023)10.1103/PhysRevE.108.054217]. In the fully chaotic kicked top, we show that the mean Wehrl entropy localization measure approaches the prediction given by the circular unitary ensemble, while the spectral statistics follows the circular orthogonal ensemble. For the mixed-type cases, we identify mixed eigenstates by the overlap of the Husimi function with regular and chaotic regions in classical compact phase space. Numerically, we show that the fraction of mixed eigenstates scales as j^{-ζ}, a power-law decay as the system size j increases, across nearly two orders of magnitude, expanding significantly beyond the previously limited range of system sizes. This provides supporting evidence for the principle of uniform semiclassical condensation of Husimi functions and the Berry-Robnik picture in the semiclassical limit.