Quasiperiodic propagation in time of some classical/quantum systems: Nielsen's conserved quantity and Floquet properties

TL;DR

This paper investigates quasiperiodic time evolution in classical and quantum systems, revealing a conserved Nielsen quantity that governs commutativity and non-commutativity, and extends Floquet theory to quasiperiodic regimes.

Contribution

It introduces a Nielsen-based conserved quantity for quasiperiodic propagators and extends Floquet theory to quasiperiodic systems.

Findings

Nielsen's conserved quantity controls the transition between commutative and non-commutative propagation.

Quasiperiodically kicked oscillator exhibits Floquet-like properties in a quasiperiodic context.

The system demonstrates a novel form of quasiperiodic propagation in classical and quantum dynamics.

Abstract

We consider classical and quantum propagators for two different time intervals. If these propagators follow one another in a Fibonacci sequence we get a discrete quasiperiodic system. A theorem due to Nielsen provides a novel conserved quantity for this system. The Nielsen quantity controls the transition between commutative and non-commutative propagation in time. The quasiperiodically kicked oscillator moreover is dominated by quasiperiodic analogues of the Floquet theorem.