Multifractality in quasienergy space of coherent states as a signature of quantum chaos

TL;DR

This paper investigates how multifractal analysis of coherent states in a kicked top model reveals phase space structures and transitions from regularity to chaos, providing a quantum chaos signature.

Contribution

It introduces a multifractal analysis approach of coherent states in the kicked top model to detect quantum chaos and phase space changes.

Findings

Multifractal dimensions vary with kicking strength, indicating phase space structure changes.

Onset of chaos identified by phase space averaged multifractal dimensions.

Deviation from random matrix theory predictions signals quantum chaos.

Abstract

We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase space averaged multifractal dimensions, which are well described by random matrix theory in strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.