We investigate the Gross-Pitaevskii equation which describes an atomic Bose-Einstein condensate confined in an optical lattice and driven by a spatiotemporal periodic laser field. It is demonstrated that the exact Floquet states appear when the external time-dependent potential is balanced by the nonlinear mean-field interaction. The balance region of parameters is divided into a phase-continui...

Abstract This paper studies numerical methods for linear stability analysis of periodic solutions in codes for bifurcation analysis of small systems of ordinary differential equations (ODEs). Popular techniques in use today (including the AUTO97 method) produce very inaccurate Floquet multipliers if the system has very large or small multipliers. These codes compute the monodromy matrix explici...

Aims. We apply Floquet analysis to study the dynamical stability of two-dimensional axisymmetric Keplerian flows distorted by an m = 2 epicyclic periodic forcing term, representing a tidal perturbation in a thin accretion disk (AD) of a cataclysmic variable (CV). This tidal mode is responsible for the disk truncation mechanism. Methods. Floquet analysis reveals, with a positive Floquet exponent...

The linearized problem around a time-periodic parallel flow of the compressible Navier-Stokes equation in an infinite layer is investigated. By using the Floquet theory, spectral properties of the evolution operator associated with the linearized problem are studied in detail. The Floquet representation of low frequency part of the evolution operator, which plays an important role in the study ...

We study quasi-periodic tori under a normal-internal resonance, possibly with multiple eigenvalues. Two non-degeneracy conditions play a role. The first of these generalizes invertibility of the Floquet matrix and prevents drift of the lower dimensional torus. The second condition involves a Kolmogorovlike variation of the internal frequencies and simultaneously versality of the Floquet matrix ...

We investigate the correspondence between classical and quantum mechanics for periodically time dependent Hamiltonian systems, using the example of a periodically forced particle in a one-dimensional triangular well potential. In particular, we consider quantum mechanical Floquet states associated with resonances in the classical phase space. When the classical motion exhibits subharmonic reson...

1 Raison d’être 1 1.1 Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Schrödinger Operator with Periodic Potential . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Direct Integral Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Bloch Periodic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

We present a generalized Floquet formulation of time-dependent current-density-functional theory for nonperturbative treatment of multiphoton processes of many-electron systems in intense monochromatic electric and magnetic fields. It is shown that the time-dependent Kohn-Sham-like equation can be transformed into an equivalent time-independent Floquet Hamiltonian matrix eigenvalue problem. A p...

This article describes the use of an alternative expansion scheme called Floquet-Magnus expansion (FME) to study the dynamics of spin system in solid-state NMR. The main tool used to describe the effect of time-dependent interactions in NMR is the average Hamiltonian theory (AHT). However, some NMR experiments, such as sample rotation and pulse crafting, seem to be more conveniently described u...

For monotone linear differential systems with periodic coefficients, the (first) Floquet eigenvalue measures the growth rate of the system. We define an appropriate arithmetico-geometric time average of the coefficients for which we can prove that the Perron eigenvalue is smaller than the Floquet eigenvalue. We apply this method to Partial Differential Equations, and we use it for an age-struct...