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Quantum-classical correspondence in chaotic systems is a long-standingproblem. We describe a method to quantify Bohr's correspondence principle andcalculate the size of quantum numbers for which we can expect to observequantum-classical correspondence near periodic orbits of Floquet systems. Ourmethod shows how the stability of classical periodic orbits affects quantumdynamics. We demonstrate our method by analyzing quantum-classicalcorrespondence in the quantum kicked top (QKT), which exhibits both regular andchaotic behavior. We use our correspondence conditions to identify signaturesof classical bifurcations even in a deep quantum regime. Our method can be usedto explain the breakdown of quantum-classical correspondence in chaoticsystems.

Quantum-classical correspondence in the vicinity of periodic orbits