A scheme for generating a fractal butterfly Floquet spectrum, first proposed by Wang and Gong [Phys. Rev. A 77, 031405(R) (2008)], is extended to driven SU(2) systems such as a driven two-mode Bose-Einstein condensate. A class of driven systems without a link with the Harper-model context is shown to have an intriguing butterfly Floquet spectrum. The found butterfly spectrum shows remarkable de...

We consider the steady propagation of a light beam in a planar waveguide whose width and depth are periodically modulated in the propagation direction. Using methods of soliton theory, a class of periodic potentials is presented for which the complete set of Floquet solutions of the linear Schrödinger equation can be found exactly at a particular optical frequency. For potentials in this class,...

Avoided crossings are common in the quasienergy spectra of strongly driven nonlinear quantum wells. In this paper we examine the sinusoidally driven particle in a square potential well to show that avoided crossings can alter the structure of Floquet states in this system. Two types of avoided crossings are identi ed: one type leads only to temporary changes (as a function of driving eld streng...

2 The Floquet theory of the aktion potential 3 2.1 Periodic event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Tonic spikes are limit cycles . . . . . . . . . . . . . . . . . . . . . 3 2.3 Limit cycle stability . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3.1 Eigensystem of the Floquet matrix . . . . . . . . . . . . . 6 2.4 Neutral dimension and phase shifts . . . . ...

Quantum mechanics predicts that certain stationary potentials can sustain bound states with an energy buried in the continuous spectrum of scattered states, the so-called bound states in the continuum (BIC). Originally regarded as mathematical curiosities, BIC have found an increasing interest in recent years, particularly in quantum and classical transport of matter and optical waves in mesosc...

Recent advances in theory of solid state nuclear magnetic resonance (NMR) such as Floquet-Magnus expansion and Fer expansion, address alternative methods for solving a time-dependent linear differential equation which is a central problem in quantum physics in general and solid-state NMR in particular. The power and the salient features of these theoretical approaches that are helpful to descri...

The Bäcklund-Darboux transformations are successfully utilized to construct heteroclinic orbits of Davey-Stewartson II equations through an elegant iteration of the transformations. In [17], we successfully built Melnikov vectors with the gradients of Floquet discriminants. Since there is no Floquet discriminant for Davey-Stewartson equations (in contrast to nonlinear Schrödinger equations [17]...