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.

The role of spinning electrons in paramagnetic phenomena

An attempt is made to explain paramagnetic phenomena without assuming the orientation of a molecule or ion in a magnetic field. Only the spin angular momentum is assumed to be responsible. A derivative of the Gurie-Langevin law and the magnetic moments of ions are given as a function of the number of electrons in an inner, incomplete shell. An explanation of Gerlach's experiments with iron and nickel vapors is attempted. An explanation of magnetomechanical experiments with ferromagne elements is given

Conformal and Nonconformal Symmetries in 2d Dilaton gravity

We study finite-dimensional extra symmetries of generic 2D dilaton gravity models. Using a non-linear sigma model formulation we show that the unique theories admitting an extra (conformal) symmetry are the models with an exponential potential $V \propto e^{\beta\phi}$ ($S ={1\over2\pi} \int d^2 x \sqrt{-g} [ R \phi + 4 \lambda^2 e^{\beta\phi} ]$), which include the CGHS model as a particular though limiting ($\beta=0$) case. These models give rise to black hole solutions with a mass-dependent temperature. The underlying extra symmetry can be maintained in a natural way in the one-loop effective action, thus implying the exact solubility of the semiclassical theory including back-reaction. Moreover, we also introduce three different classes of (non-conformal) transformations which are extra symmetries for generic 2D dilaton gravity models. Special linear combinations of these transformations turn out to be the (conformal) symmetries of the CGHS and $V \propto e^{\beta\phi}$ models. We show that one of the non-conformal extra symmetries can be converted into a conformal one by means of adequate field redefinitions involving the metric and the derivatives of the dilaton. Finally, by expressing the Polyakov-Liouville effective action in terms of an invariant metric, we are able to provide semiclassical models which are also invariant. This generalizes the solvable semiclassical model of Bose, Parker and Peleg (BPP) for a generic 2D dilaton gravity model.Comment: Latex, no figures. Revised version published i