Propagation in perturbed one-dimensional phononic or photonic crystals, with both compositional and positional disorder, is considered. The coherent potential approximation is used to obtain the band structure and the Floquet normal form of the periodic-on-average perturbed crystal, which is modified differently with respect to the two kinds of disorder. For finite size crystals, the transmissi...

Solving a time-dependent linear differential equation towards obtaining evolution operators is a central problem in solid-state nuclear magnetic resonance. To this end, average Hamiltonian theory and Floquet theory have been the two commonly used theoretically methods in spin dynamics of NMR. We recently introduced the Floquet-Magnus expansion approach and here, we present the methodology of po...

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 study the time evolution of a periodically driven quantummechanical system coupled to several reservoirs of free fermions at different temperatures and chemical potentials. This is a paradigm of a cyclic thermodynamic process. We introduce the notion of a Floquet Liouvillean as the generator of the dynamics of the coupled system on an extended Hilbert space. We show that the time-periodic st...

We study the time evolution of a periodically driven quantummechanical system coupled to several reservoirs of free fermions at different temperatures. This is a paradigm of a cyclic thermodynamic process. We introduce the notion of a Floquet Liouvillean as the generator of the dynamics of the coupled system on an extended Hilbert space. We show that the time-periodic state which the state of t...

A fractional generalization of the Floquet theorem is suggested for Schr\"odinger equations (FTSE)s with time-dependent periodic Hamiltonians. The obtained result, called (fFT), formulated in form Mittag-Leffler function, which considered as eigenfunction Caputo derivative. formula makes it possible to reduce FTSE standard quantum mechanics Hamiltonian, where valid. Two examples related resonan...

We study the response of driven, time dependent, quantum system whose instantaneous Hamiltonian has gaps in its spectrum. We consider the question if the breakdown of quantum transport, and in particular, the breakdown of the Integer Quantum Hall conductance, is a phase transition. We prove that, under mild conditions, quantum response has an isolated essential singularity and a vanishing holom...

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...