Ground state properties of the bond alternating spin-12\frac{1}{2} anisotropic Heisenberg chain

Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-$\frac{1}{2}$ anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases. The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains. Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization. Dispersion relations, spin gap and several ground state orders have been obtained. Dimer order and string orders are found to coexist in the ground state. Spin gap is found to develop as soon as the non-uniformity in alternating bond strength is introduced in the AFM-AFM chain which further remains non-zero for the AFM-FM chain. This spin gap along with the string orders attribute to the Haldane phase. The Haldane phase is found to exist in most of the anisotropic region similar to the isotropic point.Comment: 16 pages, 6 figures, 1 tabl

The Asymmetric Rotor. IX. The Heavy Water Bands at 2787 cm^–1 and 5373 cm^–1

The combination band (110) of the two stretching fundamentals of D2O is reported and analyzed to yield nu0=5373.2 cm^–1 and the excited state moments of inertia 1.910, 3.931, and 5.929×10^–40 g cm^2. The same method of analysis applied to the unsymmetrical fundamental band (100) envelope gives nu0=2787.5 cm^–1 and the excited state moments 1.881, 3.876, and 5.843×10^–40 g cm^2

Farthest point problem and M-compact sets

In this paper we give an elementary proof of the fact that every uniquely remotal set is singleton in a finite dimensional strictly convex normed linear space. We show that if A is a uniquely remotal M-compact subset with the derived set of A non-empty then the derived set of A is M-compact and uniquely remotal. We also show that if A is a uniquely remotal M-compact set and the derived set of A is compact then A is singleton

Precision segmented reflector, figure verification sensor

The Precision Segmented Reflector (PSR) program currently under way at the Jet Propulsion Laboratory is a test bed and technology demonstration program designed to develop and study the structural and material technologies required for lightweight, precision segmented reflectors. A Figure Verification Sensor (FVS) which is designed to monitor the active control system of the segments is described, a best fit surface is defined, and an image or wavefront quality of the assembled array of reflecting panels is assesse

Gravitons in Flatland

We review some features of three-dimensional (3D) massive gravity theories. In particular, we stress the role of the Schouten tensor, explore an analogy with Lovelock gravity and discuss renormalizabilty.Comment: 11 pages, Contribution to proceedings of the workshop {\it Cosmology, the Quantum Vacuum and Zeta Functions} in celebration of the 60th birthday of Emilio Elizalde; Barcelona, 8-10 March, 2010. Additional references in v

More on Massive 3D Gravity

We explore the space of static solutions of the recently discovered three-dimensional `New Massive Gravity' (NMG), allowing for either sign of the Einstein-Hilbert term and a cosmological term parametrized by a dimensionless constant $\lambda$. For $\lambda=-1$ we find black hole solutions asymptotic (but not isometric) to the unique (anti) de Sitter vacuum, including extremal black holes that interpolate between this vacuum and (a)dS$_2 \times S^1$. We also investigate unitarity of linearized NMG in (a)dS vacua. We find unitary theories for some dS vacua, but (bulk) unitarity in adS implies negative central charge of the dual CFT, except for $\lambda=3$ where the central charge vanishes and the bulk gravitons are replaced by `massive photons'. A similar phenomenon is found in the massless limit of NMG, for which the linearized equations become equivalent to Maxwell's equations.Comment: 25 pages, 4 figures; v2: minor improvements and extensions, references added; v3: version to appear in PR

Massive Gravity in Three Dimensions

A particular higher-derivative extension of the Einstein-Hilbert action in three spacetime dimensions is shown to be equivalent at the linearized level to the (unitary) Pauli-Fierz action for a massive spin-2 field. A more general model, which also includes `topologically-massive' gravity as a special case, propagates the two spin 2 helicity states with different masses. We discuss the extension to massive ${\cal N}$-extended supergravity, and we present a `cosmological' extension that admits an anti-de Sitter vacuum.Comment: Minor corrections plus a further correction to discussion of supersymmetry in adS vacua, Version to be publishe