We propose a model describing N spin-1/2 systems coupled through N-order homogeneous interaction terms, in presence of local time-dependent magnetic fields. This model can be experimentally implemented with current technologies in trapped ions and superconducting circuits. By introducing a chain of unitary transformations, we succeed in exactly converting the quantum dynamics of this system into that of 2 N−1 fictitious spin-1/2 dynamical problems. We bring to light the possibility of controlling the unitary evolution of the N spins generating GHZ states under specific time-dependent scenarios. Moreover, we show that by appropriately engineering the time-dependence of the coupling parameters, one may choose a specific subspace in which the N-spin system dynamics takes place. This dynamical feature, which we call time-dependent selective interaction, can generate a cooling effect of all spins in the system.

Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a noncanonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations. * asergi@unime.it †

Two coupled two-level systems placed under external time-dependent magnetic fields are modelled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics. Each of the sub-dynamics is shown to be brought into an exactly solvable form by appropriately engineering the magnetic fields and thus we obtain an exact time evolution of the compound system. Several physically relevant and interesting quantities are evaluated exactly to disclose intriguing phenomena in such a system.

An exact analytical treatment of the dynamical problem for time-dependent 2x2 pseudo-Hermitian su(1,1) Hamiltonians is reported. A class of exactly solvable and physically transparent new scenarios are identified within both classical and quantum contexts. Such a class is spanned by a positive parameter ν that allows to distinguish two different dynamical regimes. Our results are usefully employed for exactly solving a classical propagation problem in a guided wave optics scenario. The usefulness of our procedure in a quantum context is illustrated by defining and investigating the su(1,1) "Rabi" scenario bringing to light analogies and differences with the standard su(2) Rabi model. Our approach, conjugated with the generalized von Neumann equation describing open quantum systems through non-Hermitian Hamiltonians, succeeds in evidencing that the νdependent passage from a real to a complex energy spectrum is generally unrelated to the existence of the two dynamical regimes.