Using the parametrically driven harmonic oscillator as a working example, we study two different Markovian approaches to the quantum dynamics of a periodically driven system with dissipation. In the simpler approach, the driving enters the master equation for the reduced density operator only in the Hamiltonian term. An improved master equation is achieved by treating the entire driven system w...

We theoretically introduce a type of topological dipole soliton propagating in Floquet insulator based on kagome array helical waveguides. Such solitons bifurcate from two edge states belonging to different gaps and have bright envelopes symmetries: fundamental for one component, the other. The formation is enabled by unique spectral features which allow simultaneous coexistence at same boundar...

Using a suitable version of Mawhin’s continuation principle, we obtain an existence result for the Floquet boundary value problem for second order Carathéodory differential equations by means of strictly localized C2 bounding functions.

A mystery surrounds the stability properties of the splay-phase periodic solutions to a series array of N Josephson junction oscillators. Contrary to what one would expect from dynamical systems theory, the splay state appears to be neutrally stable for a wide range of system parameters. It has been explained why the splay state must be neutrally stable when the Stewart-McCumber parameter β (a ...

We present a brief overview of some the analytic perturbative techniques for computation Floquet Hamiltonian periodically driven, or Floquet, quantum many-body system. The key technical points about each methods discussed are presented in pedagogical manner. They followed by account chosen phenomena where these have provided useful insights. provide an extensive discussion Floquet-Magnus expans...

We consider an atomic beam reservoir as a source of quantum noise. The atoms are modelled as two-state systems and interact one-at-a-time with the system. The Floquet operators are described in terms of the Fermionic creation, annihilation and number operators associated with the two-state atom. In the limit where the time between interactions goes to zero and the interaction is suitably scaled...