In this paper we provide a microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses. We single out both the differences with the phenomenological master equation used in the literature and the approximations under which the phenomenological model correctly describes the dynamics of the atom-cavity system. Some examples wherein the phenomenological and the microscopic master equations give rise to different predictions are discussed in detail.

The dynamics of a typical open quantum system, namely a quantum Brownian particle in a harmonic\ud potential, is studied focusing on its non-Markovian regime. Both an analytic approach and a stochastic wavefunction approach are used to describe the exact time evolution of the system. The border between two very different dynamical regimes, the Lindblad and non-Lindblad regimes, is identified and the relevant physical variables governing the passage from one regime to the other are singled out. The non-Markovian short-time dynamics is studied in detail by looking at the mean energy, the squeezing, the Mandel parameter, and the Wigner function of the system

An original method to exactly solve the non-Markovian Master Equation describing the interaction of a single harmonic oscillator with a quantum environment in the weak coupling limit is reported. By using a superoperatorial approach we succeed in deriving the operatorial solution for the density matrix of the system. Our method is independent of the physical properties of the environment. We show the usefulness of our solution deriving explicit expressions for the dissipative time evolution of some observables of physical interest for the system, such as, for example, its mean energy.

A simple systematic way of obtaining analytically solvable Hamiltonians for quantum two-level systems is presented. In this method, a time-dependent Hamiltonian and the resulting unitary evolution operator are connected through an arbitrary function of time, furnishing us with new analytically solvable cases. The method is surprisingly simple, direct, and transparent and is applicable to a wide class of two-level Hamiltonians with no involved constraint on the input function. A few examples illustrate how the method leads to simple solvable Hamiltonians and dynamics.

A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated.\ud An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a\ud cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition\ud of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line\ud current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron’ko-Stroganov\ud model

We apply the time-convolutionless (TCL) projection operator technique to the model of a central spin, which is coupled to a spin bath via nonuniform Heisenberg interaction. The second-order results of the TCL method\ud for the coherences and populations of the central spin are determined analytically and compared to numerical simulations of the full von Neumann equation of the total system. The TCL approach is found to yield an excellent approximation in the strong field regime for the description of both the short-time dynamics and the long time behavior

We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an appropriate time-dependent Schrödinger operator.

Abstract. A microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis [Scala M. et al. 2007 Phys. Rev. A 75, 013811], where a microscopic derivation was given in the framework of the Rotating Wave Approximation.