Quantum chaos measures for Floquet dynamics

Abstract

Periodically kicked Floquet systems such as the kicked rotor are a paradigmatic and illustrative simple model of chaos. For non-integrable quantum dynamics there are several diagnostic measures of the presence of (or the transition to) chaotic behaviour including the Loschmidt echo, autocorrelation function and OTOC. We analytically compute these measures in terms of the eigensystem of the unitary Floquet operator of driven quantum systems. We use these expressions to determine the time variation of the measures for the quantum kicked rotor on the torus, for the integrable as well as the chaotic case. For a simpler integrable variant of the kicked rotor, we also give a representation theoretic derivation of its dynamics.