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

TL;DR

This study investigates the decay of mixed eigenstates in a quantum chaos model, revealing a power-law scaling that supports semiclassical theories and extends computational capabilities using Krylov subspace techniques.

Contribution

It introduces an efficient method to analyze large quantum systems and demonstrates the power-law decay of mixed eigenstates, supporting semiclassical condensation principles.

Findings

Power-law decay of mixed eigenstates with system size

Husimi functions align with Berry-Robnik predictions

Enhanced computational method for large quantum systems

Abstract

By using the Krylov subspace technique to generate the spin coherent states in 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) [arXiv:2308.04824]. In the fully chaotic kicked top, we find that the mean Wehrl entropy localization measure approaches the prediction given by the Circular Unitary Ensemble. In the mixed-type case, 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 $j^{-\zeta}$, a power-law decay as the system size $j$ increases, across nearly two orders of magnitude. This provides supporting evidence for the principle of uniform semiclassical condensation of Husimi functions and the Berry-Robnik picture in the semiclassical limit.