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 establish the theoretical foundation of Floquet graphene antidot lattice, whereby massless Dirac fermions are driven periodically by a circularly polarized electromagnetic field, while having their motion excluded from an array nanoholes. The properties interest encoded in quasienergy spectra, which computed non-perturbatively within formalism. find that rich phase diagram emerges as amplitu...

We revisit the computation of (2-modified) Fredholm determinants for operators with matrix-valued semi-separable integral kernels. The latter occur, for instance, in the form of Green’s functions associated with closed ordinary differential operators on arbitrary intervals on the real line. Our approach determines the (2-modified) Fredholm determinants in terms of solutions of closely associate...

In this article, we present an alternative expansion scheme called Floquet-Magnus expansion (FME) used to solve a time-dependent linear differential equation which is a central problem in quantum physics in general and solid-state nuclear magnetic resonance (NMR) in particular. The commonly used methods to treat theoretical problems in solid-state NMR are the average Hamiltonian theory (AHT) an...

Anyons have recently received great attention due to their promising application in topological quantum computation. The best validated system that enjoys the anyonic excitations are the Laughlin states. The quasi-particles in Laughlin states are neither fermions nor bosons but possess the discrete statistical angle θ = π/m, with m being an integer. Here we report a possible realization of the ...

We present an algorithm for determining the stability of delay differential equations (DDEs)with time-periodic coefficients and time-periodic delays. The DDEs are first posed as an equivalent system of partial differential equations (PDEs) along with a nonlinear boundary condition. A Galerkin approximation is then employed to discretize the PDEs into a set of time-periodic ordinary differential...

Photoinduced quantum molecular dynamics is numerically investigated using two different Schrödinger formulations based on adiabatic (“bare”) and Floquet (“dressed”) molecular state representations. Computer simulations for the two approaches are compared in terms of numerical accuracy and efficiency where special emphasis is laid on the limit of very short and intense laser pulses. The optical ...