First, the time evolution of an arbitrary finite-dimensional quantum system under frequent kicks, where each kick is a generic quantum operation, has been considered.  We develop a generalization of the Baker-Campbell-Hausdorff formula, allowing to reformulate such pulsed dynamics as a continuous one.  As a result, we obtain a general type of quantum Zeno dynamics, which unifies all known manifestations in the literature as well as describing new types.

Second, it has been theoretically demonstrated that two spins (qubits or qutrits), coupled by exchange interaction, undergo a coupling-based joint Landau-Majorana-Stückelberg-Zener transition when a linear ramp is applied  to one of the two spins.  Such a transition, under appropriate conditions, drives the two-spin system toward a maximally entangled state.  We have investigated effects, on the quantum dynamics of the two qudits, stemming from the Dzyaloshinskii-Moriya (DM) and dipole-dipole (d-d) interactions, qualitatively and quantitatively.  Since the Hamiltonian of the two spins has a symmetry, an exact treatment of the quantum dynamics is possible.  We have transparently revealed that the DM and d-d interactions generate independent, enhancing or hindering, modifications in the dynamical behavior predicted for the two spins coupled exclusively by the exchange interaction.