Nonequilibrium steady states (NESSs) in periodically driven dissipative quantum systems are vital Floquet engineering. We develop a general theory for high-frequency drives with Lindblad-type dissipation to characterize and analyze NESSs. This is based on the (HF) expansion linear algebraic numerics without numerically solving time evolution. Using this theory, we show that NESSs can deviate fr...

Discrete algebraic Riccati equations and their fixed points are well understood arise in a variety of applications; however, the time-varying have not yet been fully explored literature. In this article we provide self-contained study discrete time matrix difference equations. particular, novel semigroup duality formula new Floquet-type representation for these Due to aperiodicity underlying fl...

We de ne a discrete (integer-valued) Lyapunov function V for cyclic nearest neighbor systems of di erential delay equations possessing a feedback condition. This extends analogous de nitions for cyclic systems of ODE's, and for scalar di erential delay equations. We relate the values of V to the real parts of the Floquet multipliers for such linear periodic systems, and thereby prove all Floque...

We report the results of a Floquet analysis of two-dimensional arrays of resistively and capacitively shunted Josephson junctions in an external transverse magnetic field. The Floquet analysis indicates stable phase locking of the active junctions over a finite range of values of the bias current and junction capacitance, even in the absence of an external load. This stable phase locking is rob...

Multiple scales phenomena are ubiquitous, ranging from mechanical properties of wood, turbulent flow in gases and fluids, combustion, remote sensing of earth to wave propagation or heat conduction in composite materials. The obstacle with multi-scale problems is that they, due to limited primary memory even in the largest computational clusters, can not easily be modeled in standard numerical a...

We present an algorithm for the computation of reducible invariant tori of discrete dynamical systems that is suitable for tori of dimensions larger than 1. It is based on a quadratically convergent scheme that approximates, at the same time, the Fourier series of the torus, its Floquet transformation, and its Floquet matrix. The Floquet matrix describes the linearization of the dynamics around...

Studying of mutual coupling parameters between the antenna elements in an array environment has been considered as the subject of feature research. That is why, in this paper, we present a new Floquet modal analysis procedure for analyzing almost periodic structures. Accurate evaluation of the mutual coupling could be achieved by this analysis. It is shown how Floquet analysis can be exploited ...

The linear stability of the flow in the annular gap between two infinitely long cylinders, driven by the constant rotation and harmonic oscillation in the axial direction of the inner cylinder, is analysed using Floquet theory. Closed form solutions for the basic flow are derived, both with and without the presence of endwalls. Recent experiments and theory using the narrow gap approximation ha...

The accurate characterization of eigenmodes and eigenfrequencies of two-dimensional ion crystals provides the foundation for the use of such structures for quantum simulation purposes. We present a combined experimental and theoretical study of two-dimensional ion crystals. We demonstrate that standard pseudopotential theory accurately predicts the positions of the ions and the location of stru...