Quantum chaos measures for Floquet dynamics

TL;DR

This paper analytically investigates chaos indicators like Loschmidt echo, autocorrelation, and OTOC in Floquet systems, especially the quantum kicked rotor, to understand quantum chaos transitions.

Contribution

It provides analytical expressions for chaos measures in Floquet systems and applies them to the quantum kicked rotor, including an integrable variant.

Findings

Derived explicit formulas for chaos measures in Floquet systems.

Analyzed time evolution of chaos indicators in the quantum kicked rotor.

Presented a representation theoretic derivation for an integrable kicked rotor variant.

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.