Entangled spin clusters: some special features

In this paper, we study three specific aspects of entanglement in small spin clusters. We first study the effect of inhomogeneous exchange coupling strength on the entanglement properties of the S=1/2 antiferromagnetic linear chain tetramer compound NaCuAsO_{4}. The entanglement gap temperature, T_{E}, is found to have a non-monotonic dependence on the value of $\alpha$, the exchange coupling inhomogeneity parameter. We next determine the variation of T_{E} as a function of S for a spin dimer, a trimer and a tetrahedron. The temperature T_{E} is found to increase as a function of S, but the scaled entanglement gap temperature t_{E} goes to zero as S becomes large. Lastly, we study a spin-1 dimer compound to illustrate the quantum complementarity relation. We show that in the experimentally realizable parameter region, magnetization and entanglement plateaus appear simultaneously at low temperatures as a function of the magnetic field. Also, the sharp increase in one quantity as a function of the magnetic field is accompanied by a sharp decrease in the other so that the quantum complementarity relation is not violated.Comment: 17 pages, 6 figures. Accepted in Phys. Rev.

A k-essence Model Of Inflation, Dark Matter and Dark Energy

We investigate the possibility for \textit{k}-essence dynamics to reproduce the primary features of inflation in the early universe, generate dark matter subsequently, and finally account for the presently observed acceleration. We first show that for a purely kinetic \textit{k}-essence model the late time energy density of the universe when expressed simply as a sum of a cosmological constant and a dark matter term leads to a static universe. We then study another \textit{k}-essence model in which the Lagrangian contains a potential for the scalar field as well as a non-canonical kinetic term. We show that such a model generates the basic features of inflation in the early universe, and also gives rise to dark matter and dark energy at appropriate subsequent stages. Observational constraints on the parameters of this model are obtained.Comment: 8 pages, Latex, minor changes to match with published versio