Quantum recurrences in the kicked top

Abstract

The emergence of classical chaos from an underlying quantum mechanics remains a challenging question due to the differences between dynamics driven by Schrödinger's equation versus Newton's equations. We present an infinite family of purely quantum recurrences that are not present in the classical limit of a chaotic system. They take the form of stroboscopic unitary evolutions in the quantum kicked top that act as the identity after a finite number of kicks. These state-independent recurrences are present in all finite dimensions and depend on the strength of the chaoticity parameter of the top. We further discuss the relationship of these periodicities to the quantum kicked rotor dynamics and the phenomenon of quantum antiresonance. Published by the American Physical Society 2024