Abstract Floquet engineering consists in the modification of physical systems by application periodic time-dependent perturbations. The search for shape perturbation that best modifies properties a system order to achieve some predefined metastable target behavior can be formulated as an optimal control problem. We discuss several ways formulate and solve this present, examples, applications co...

We present an effective field theory approach to the topological response of Floquet systems with symmetry group $G$. This is achieved by introducing a background $G$ gauge in Schwinger-Keldysh formalism, which suitable for far from equilibrium systems. carry out this program chiral (anomalous Floquet-Anderson insulators) two spatial dimensions, and cohomology models unitaries. These actions se...

The exchange of power between two identical coupled waveguides with embedded periodic structure along the z direction is studied in the framework of Floquet–Bloch theory. A one-period propagator is calculated and a spectrum of its eigenvalues (eigenphases) is studied. We show that due to special symmetry properties of the Floquet–Bloch operator, a strong enhancement or a total suppression of po...

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...

2 Linear Equations 14 2.1 Matrix Exponentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Normal Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Non-Autonomous Linear Equations . . . . . . . . . . . . . . . . . . . . . 19 2.4 Inhomogeneous Linear Equations . . . . . . . . . . . . . . . . . . . . . . 20 2.5 Stability and Boundedness . . . . . . ....

The dynamic response of an axially translating continuum subjected to the combined effects of a pair of spring supported frictional guides and axial acceleration is investigated; such systems are both non-conservative and gyroscopic. The continuum is modeled as a tensioned string translating between two rigid supports with a time dependent velocity profile. The equations of motion are derived w...

A primer on the Floquet theory of periodically time-dependent quantum systems is provided, and it is shown how to apply this framework for computing the quasienergy band structure governing the dynamics of ultracold atoms in driven optical cosine lattices. Such systems are viewed here as spatially and temporally periodic structures living in an extended Hilbert space, giving rise to spatio-temp...