Floquet states are signatured by pseudoeigenvalues which are discretely separated by the photon energy. Similarly, the laser-assisted photoemission effect (LAPE) induces electron-photon energy exchange (with momentum change), and also results in a discrete energy distribution. Both effects result from coherent interactions of electrons and photons. Here, we investigate the coherent interference...

One of the classical topics in the qualitative theory of differential equations is the Floquet theory. It provides a means to represent solutions and helps in particular for stability analysis. In this paper first we shall study Floquet theory for integro-differential equations (IDE), and then employ it to address stability problems for linear and nonlinear equations.

Recent discoveries on topological characterization of gapless systems have attracted interest in both theoretical studies and experimental realizations. Examples of such gapless topological phases are Weyl semimetals, which exhibit three-dimensional (3D) Dirac cones (Weyl points), and nodal line semimetals, which are characterized by line nodes (two bands touching along a line). Inspired by our...

Floquet theory plays a ubiquitous role in the analysis and control of time-periodic systems. Its main result is that any fundamental matrix X(t, 0) of a linear system with T -periodic coefficients will have a (generally complex) Floquet factorization with one of the two factors being T -periodic. It is also well known that it is always possible to obtain a real Floquet factorization for the fun...

The existence and uniqueness of a periodic solution of the system of differential equations d dt x(t) = A(t)x(t − ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.  

In this paper, the Floquet theory is combined with harmonic balance for the in-depth analysis of a Chua’s family circuit, exhibiting intermittence. Floquet multipliers are calculated along the periodic solution paths obtained through harmonic balance by means of a continuation algorithm. The analysis of both the stable and unstable solution sections enhances the information about the system and...

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...

We solve stabilization problems for linear time-varying systems under input delays. We show how changes of coordinates lead to systems with time invariant drifts, which are covered by the reduction model method and which lead to the problem of stabilizing a time-varying system without delay. For continuous time periodic systems, we can use Floquet theory to find the changes of coordinates. We a...