This paper has two purposes. Firstly, the paper is devoted to collecting basic facts about the Floquet theorem and various Floquet factorization algorithms claimed for finite-dimensional linear continuous-time periodic (FDLCP) systems. Secondly, the paper presents a unified representation framework for various Floquet factorizations in FDLCP systems, while structural and analytic characteristic...

This paper has two purposes. Firstly, the paper is devoted to collecting basic facts about the Floquet theorem and various Floquet factorization algorithms claimed for finite-dimensional linear continuous-time periodic (FDLCP) systems. Secondly, the paper presents a unified representation framework for various Floquet factorizations in FDLCP systems, while structural and analytic characteristic...

In this paper, we study periodic linear systems on periodic time scales which include not only discrete and continuous dynamical systems but also systems with a mixture of discrete and continuous parts (e.g. hybrid dynamical systems). We develop a comprehensive Floquet theory including Lyapunov transformations and their various stability preserving properties, a unified Floquet theorem which es...

Ultrafast materials science promises optical control of physical properties of solids. Continuous-wave circularly polarized laser driving was predicted to induce a light-matter coupled state with an energy gap and a quantum Hall effect, coined Floquet topological insulator. Whereas the envisioned Floquet topological insulator requires high-frequency pumping to obtain well-separated Floquet band...

We report on simulations of the dc conductance and quantum Hall response of a Floquet topological insulator using Floquet scattering theory. Our results reveal that laser-induced edge states lead to quantum Hall plateaus once imperfect matching with the nonilluminated leads is lessened. The magnitude of the Hall plateaus, however, is not directly related to the number and chirality of all the e...

We apply the Floquet theorem and the resonating averages method to solve the Schrödinger equation of the harmonic oscillator whose frequency varies periodically with time. We determine its Floquet states and its corresponding wave functions. The formalism provides an efficiency tool for analyzing the various transition probabilities as well as the uncertainty relation of the system. The effect ...

This paper proposes a new method to numerically obtain Floquet multipliers which characterize stability of periodic orbits of ordinary differential equations. For sufficiently smooth periodic orbits, we can compute Floquet multipliers using some standard numerical methods with enough accuracy. However, it has been reported that these methods may produce incorrect results under some conditions. ...

We present a Floquet treatment of multiphoton quantum interference in a strongly driven superconducting flux qubit. The periodically time-dependent Schrödinger equation can be reduced to an equivalent timeindependent infinite-dimensional Floquet matrix eigenvalue problem. For resonant or nearly resonant multiphoton transitions, we extend the generalized Van Vleck GVV nearly degenerate high-orde...

This note proposes a new approach to computing the Kalman canonical decomposition of finite-dimensional linear periodic continuous-time systems by extending the Floquet theory. Controllable and observable subspaces are characterized by factorizing the monodromy matrix. Then, the conditions for the existence of several periodic Kalman canonical decompositions are extensively studied. The relatio...