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

TL;DR

This paper investigates the decay of mixed eigenstates in the quantum kicked top model, revealing a power-law decrease with system size and confirming theoretical principles of quantum chaos and eigenstate classification.

Contribution

It demonstrates that the fraction of mixed eigenstates decays as a power law with system size, supporting the Berry-Robnik picture and the principle of semiclassical condensation.

Findings

Mixed eigenstates arise from tunneling between phase space structures.

The fraction of mixed states decreases as a power law with system size.

Results support the Berry-Robnik conjecture and semiclassical theories.

Abstract

The properties of mixed eigenstates in a generic quantum system with classical counterpart that has mixed-type phase space, although important to understand several fundamental questions that arise in both theoretical and experimental studies, are still not clear. Here, following a recent work [\v{C}.~Lozej {\it et al}. Phys. Rev. E {\bf 106}, 054203 (2022)], we perform an analysis of the features of mixed eigenstates in a time-dependent Hamiltonian system, the celebrated kicked top model. As a paradigmatic model for studying quantum chaos, kicked top model is known to exhibit both classical and quantum chaos. The types of eigenstates are identified by means of the phase space overlap index, which is defined as the overlap of the Husimi function with regular and chaotic regions in classical phase space. We show that the mixed eigenstates appear due to various tunneling precesses between different phase space structures, while the regular and chaotic eigenstates are, respectively, associated with invariant tori and chaotic component in phase space. We examine how the probability distribution of the phase space overlap index evolves with increasing system size for different kicking strengths. In particular, we find that the relative fraction of mixed states exhibits a power-law decay as the system size increases, indicating that only purely regular and chaotic eigenstates are left in the strict semiclassical limit. We thus provide further verification of the principle of uniform semiclassical condensation of Husimi functions and confirm the correctness of the Berry-Robnik picture.