Finite time quantum-classical correspondence in quantum chaotic systems

TL;DR

This paper demonstrates a universal finite time quantum-classical correspondence in chaotic systems, showing that quantum measures reliably reflect classical chaos over finite times across different systems.

Contribution

It reveals the universal validity of finite time quantum-classical correspondence and introduces a system-independent function linking quantum chaos measures to classical chaoticity.

Findings

Quantum chaotic measure correlates with classical chaoticity in finite time.

The relationship is captured by a universal, system-independent function.

Supports the role of finite time analysis in quantum ergodicity studies.

Abstract

Although the importance of the quantum-classical correspondence has been recognized in numerous studies of quantum chaos, whether it still holds for finite time dynamics remains less known. 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 both time dependent and many-body systems. 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 provide a deeper understanding of the quantum-classical correspondence and highlight the role of time for studying quantum ergodicity.