We demonstrate that the electronic structure of a material can be deformed into Floquet pseudobands with arbitrarily tailored shapes. achieve this goal combination quantum optimal control theory and engineering. The power versatility framework is demonstrated here by utilizing independent-electron tight-binding description $\ensuremath{\pi}$ system graphene. show several prototype examples focu...

Because of the periodically varying aerodynamic and inertial forces of the flapping wings, a hovering or constant-speed flying insect is a cyclically forcing system, and, generally, the flight is not in a fixed-point equilibrium, but in a cyclic-motion equilibrium. Current stability theory of insect flight is based on the averaged model and treats the flight as a fixed-point equilibrium. In the...

The Fourier series expansion method is a useful tool to approach the problems of discontinuities in optical waveguides, and it applies to analyze the Floquet-modes of photonic crystal waveguides. This paper shows that the Floquet-mode calculation with large truncation order is limited and explains the reason. Furthermore, two techniques of the formulation are presented to relieve this limitatio...

In this paper, a new efficient method is proposed to obtain the transient response of linear or piecewise linear dynamic systems with time delay and periodic coefficients under arbitrary control excitations via Chebyshev polynomial expansion. Since the time domain can be divided into intervals with length equal to the delay period, at each such interval the fundamental solution matrix for the c...

Floquet-Magnus (FM) expansion theory is a powerful tool in periodically driven (Floquet) systems under high-frequency drives. In closed systems, it dictates that their stroboscopic dynamics time-periodic Hamiltonian well captured by the FM expansion, which gives static effective Hamiltonian. On other hand, dissipative Liouvillian, remains an important and nontrivial problem whether Liouvillian ...

We study the problem of multiphoton processes for intense, long-wavelength irradiation of atomic and molecular electrons. An exact, nonperturbative approach is applied to the standard vector potential coupling Hamiltonian for a three-dimensional hydrogenlike atom in a microwave field treated semiclassically. Multiphoton probability exchange is calculated in both the velocity and the length gaug...

We show that the response to an electric field, in models of the Integral Quantum Hall effect, is analytic in the field and has isolated essential singularity at zero field. We also study the breakdown of Chern numbers associated with the response of Floquet states. We argue, and give evidence, that the breakdown of Chern numbers in Floquet states is a discontinuous transition at zero field. Th...

The calculation of orbital fluctuations and of the phase-orbital correlation within Floquet-based noise analysis of autonomous systems requires the availability of all the direct and adjoint Floquet eigenvectors associated with the noiseless limit cycle. Here the authors introduce a novel numerical technique for their frequency domain determination. The algorithm is entirely based on the Jacobi...

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...