Quantum-classical correspondence in the vicinity of periodic orbits

TL;DR

This paper introduces a method to quantify quantum-classical correspondence near periodic orbits in Floquet systems, highlighting how classical stability influences quantum dynamics and identifying signatures of bifurcations even in deep quantum regimes.

Contribution

We develop a novel approach to quantify quantum-classical correspondence and analyze the impact of classical orbit stability on quantum dynamics in chaotic systems.

Findings

The method quantifies the quantum numbers for observable quantum-classical correspondence.

Classical bifurcations leave signatures in quantum dynamics even in deep quantum regimes.

The approach explains the breakdown of quantum-classical correspondence in chaotic systems.

Abstract

Quantum-classical correspondence in chaotic systems is a long-standing problem. We describe a method to quantify Bohr's correspondence principle and calculate the size of quantum numbers for which we can expect to observe quantum-classical correspondence near periodic orbits of Floquet systems. Our method shows how the stability of classical periodic orbits affects quantum dynamics. We demonstrate our method by analyzing quantum-classical correspondence in the quantum kicked top (QKT), which exhibits both regular and chaotic behavior. We use our correspondence conditions to identify signatures of classical bifurcations even in a deep quantum regime. Our method can be used to explain the breakdown of quantum-classical correspondence in chaotic systems.