Related papers: Exactly solvable time-dependent models of two inte…
We present the theory of time-dependent point transformations to find independent dynamical normal modes for 2D systems subjected to time-dependent control in the limit of small oscillations. The condition that determines if the independent…
In this series of works, we study exactly solvable non-unitary time evolutions in one-dimensional quantum critical systems ranging from quantum quenches to time-dependent drivings. In this part I, we are motivated by the recent works of…
In this paper we demonstrate that there exists a close relationship between quasi-exactly solvable quantum models and two special classes of classical dynamical systems. One of these systems can be considered a natural generalization of the…
A general algebraic condition for the functional independence of 2n-1 constants of motion of an n-dimensional maximal superintegrable Hamiltonian system has been proved for an arbitrary finite n. This makes it possible to construct, in a…
We derive a new class of exact time dependent solutions in a warped six dimensional supergravity model. Under the assumptions we make for the form of the underlying moduli fields, we show that the only consistent time dependent solutions…
We describe some new exact solutions for two- and four-level systems. In all the cases, external fields have a restricted behavior in time. First, we consider two types of new solutions for one-spin equation, one of them is in a external…
Analytical solutions to the time-dependent Schrodinger equation describing a driven two-level system are invaluable to many areas of physics, but they are also extremely rare. Here, we present a simple algorithm that generates an unlimited…
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotically to functions periodic with the…
The dynamics of two-level systems in time-dependent backgrounds is under consideration. We present some new exact solutions in special backgrounds decaying in time. On the other hand, following ideas of Feynman, Vernon and Hellwarth, we…
It is well-known that time-dependent Schr\"{o}dinger equation can only be exactly solvable in very rare cases, even for two-level quantum systems. Therefore, finding exact quantum dynamics under time-dependent Hamiltonian is not only of…
We introduce and study an exactly solvable model of several species of fermions in which particles interact pairwise through a mutual magnetic field; the interaction operates only between particles belonging to different species. After an…
We construct complete sets of invariant quantities that are integrals of motion for two Hamiltonian systems obtained through a reduction procedure, thus proving that these systems are maximally superintegrable. We also discuss the reduction…
The dynamics of two ultra-cold bosons confined in a one-dimensional double-well potential is studied. We compare the exact dynamics governed by a full two-body Hamiltonian with the dynamics obtained in a two-mode model approximation. We…
A time-dependent completely integrable Hamiltonian system is quantized with respect to time-dependent action-angle variables near an instantly compact regular invariant manifold. Its Hamiltonian depends only on action variables, and has a…
A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…
We examine the dynamics of bipartite entanglement between a two-level atom and the electromagnetic field. We treat the Jaynes-Cummings model with a single field mode and examine in detail the exact time evolution of entanglement, including…
We consider the problem of two-level system dynamics induced by the time-dependent field B={a(t)cos\omega t,a(t)sin\omega t,\omega_0}, with a(t) \sim cn(\nu t,k). The problem is exactly analytically solvable and we propose the scheme for…
Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution…
The one-dimensional Ising model is easily generalized to a \textit{genuinely nonequilibrium} system by coupling alternating spins to two thermal baths at different temperatures. Here, we investigate the full time dependence of this system.…
We propose a new approximation-technique to deal with the exact macroscopic integro-differential evolution equations of statistical systems which self-consistently accounts for dissipative effects. Concentrating on one and two point…