No abstract

We present a simple but efficient geometrical method for determining the inert states of spin-S systems. It can be used if the system is described by a spin vector of a spin-S particle and its energy is invariant in spin rotations and phase changes. Our method is applicable to an arbitrary S and it is based on the representation of a pure spin state of a spin-S particle in terms of 2S points on the surface of a sphere. We use this method to find candidates for some of the ground states of spinor Bose-Einstein condensates.

This article gives a brief overview of some recent progress in the characterization and parametrization of density matrices of finite dimensional systems. We discuss in some detail the Bloch-vector and Jarlskog parametrizations and mention briefly the coset parametrization. As applications of the Bloch parametrization we discuss the trace invariants for the case of time dependent Hamiltonians and in some detail the dynamics of three-level systems. Furthermore, the Bloch vector of two-qubit systems as well as the use of the polarization operator basis is indicated. As the main application of the Jarlskog parametrization we construct density matrices for composite systems. In addition, some recent related articles are mentioned without further discussion.

We study the effect of the rotating-wave approximation (RWA) and the secular approximation (SA) on the non-Markovian behavior in the spin-boson model at zero-temperature. We find that both the RWA and SA lead to a dramatic reduction in the observed non-Markovianity. In general, nonMarkovian dynamics is observed for the whole relaxation time of the system, whereas the RWA and SA lead to such dynamics only on the short time scale of the environmental correlation time. Thus, the RWA and SA are not necessarily justified in the studies of non-Markovianity although they can estimate the state of the system precisely. Furthermore, we derive an accurate analytical expression for the non-Markovianity measure without the RWA or SA. This expression yields important insight into the physics of the problem.