Quantum-classical correspondence between quantum chaos and finite-time classical dynamics

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.