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Quantum-classical correspondence between quantum chaos and finite-time classical dynamics
Qian Wang, Marko Robnik, 2025, original scientific article

Abstract: Although the importance of quantum-classical correspondence has been recognized in numerous studies of quantum chaos, its usefulness in understanding quantum chaos through finite-time classical dynamics remains less well understood.We address this question in this work by performing a detailed analysis of how the quantum chaotic measure relates to the chaoticity of the finite-time classical trajectories. A good correspondence between them has been revealed in time- dependent and many-body systems, both of them being of the mixed type. In particular, we show that the dependence of the quantum chaotic measure on the chaoticity of finite-time trajectories can be well captured by a function that is independent of the system. This strongly implies the universal validity of the finite-time quantum-classical correspondence. Our findings enhance the understanding of quantum-classical correspondence and provide a promising approach to explore the ergodic hierarchy in quantum systems.
Keywords: quantum chaos, finite-time classical dynamics, quantum-classical correspondence, dynamical chaos, mixed type, kicked top model, Dicke model
Published in DKUM: 03.11.2025; Views: 0; Downloads: 1
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Multifractality in quasienergy space of coherent states as a signature of quantum chaos
Qian Wang, Marko Robnik, 2021, original scientific article

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 the 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 a 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.
Keywords: quantum chaos, multifractal analysis, kicked top, coherent states
Published in DKUM: 13.10.2023; Views: 433; Downloads: 39
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