Continuous pole placement method is adapted to time-periodic states of systems with time delay. The method is applied for finding an optimal control matrix in the problem of stabilization of unstable periodic orbits of dynamical systems via time-delayed feedback control algorithm. The optimal control matrix ensures the fastest approach of a perturbed system to the stabilized orbit. An applicati...

We study the regimes of heating in the periodically driven O(N)-model, which is a well established model for interacting quantum many-body systems. By computing the absorbed energy with a non-equilibrium Keldysh Green's function approach, we establish three dynamical regimes: at short times a single-particle dominated regime, at intermediate times a stable Floquet prethermal regime in which the...

We refute an often invoked theorem which claims that a periodic orbit with an odd number of real Floquet multipliers greater than unity can never be stabilized by time-delayed feedback control in the form proposed by Pyragas. Using a generic normal form, we demonstrate that the unstable periodic orbit generated by a subcritical Hopf bifurcation, which has a single real unstable Floquet multipli...

We theoretically report an analog of photon-assisted tunneling (PAT) originated from dark Floquet state in a periodically driven lattice array without a static biased potential by studying a three-channel waveguide system in a non-high-frequency regime. This analog of PAT can be achieved by only periodically modulating the top waveguide and adjusting the distance between the bottom and its adja...

Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulse...

This short review article presents theories used in solid-state nuclear magnetic resonance spectroscopy. Main theories used in NMR include the average Hamiltonian theory, the Floquet theory and the developing theories are the Fer expansion or the Floquet-Magnus expansion. These approaches provide solutions to the time-dependent Schrodinger equation which is a central problem in quantum physics ...

The stability of dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of N globally pulse-coupled rotators (neurons) subject to a generic velocity field. In particular, we analyze short-wavelength modes that were known to be marginally stable in the infinite N limit and show that the corresponding Floquet exponent scale as 1/N2. Moreover, we find that ...

Topological phases of matter have captured our imagination over the past few years, with tantalizing properties such as robust edge modes and exotic non-Abelian excitations, and potential applications ranging from semiconductor spintronics to topological quantum computation. Despite recent advancements in the field, our ability to control topological transitions remains limited, and usually req...