Two dimensional Sen connections and quasi-local energy-momentum

The recently constructed two dimensional Sen connection is applied in the problem of quasi-local energy-momentum in general relativity. First it is shown that, because of one of the two 2 dimensional Sen--Witten identities, Penrose's quasi-local charge integral can be expressed as a Nester--Witten integral.Then, to find the appropriate spinor propagation laws to the Nester--Witten integral, all the possible first order linear differential operators that can be constructed only from the irreducible chiral parts of the Sen operator alone are determined and examined. It is only the holomorphy or anti-holomorphy operator that can define acceptable propagation laws. The 2 dimensional Sen connection thus naturally defines a quasi-local energy-momentum, which is precisely that of Dougan and Mason. Then provided the dominant energy condition holds and the 2-sphere S is convex we show that the next statements are equivalent: i. the quasi-local mass (energy-momentum) associated with S is zero; ii.the Cauchy development $D(\Sigma)$ is a pp-wave geometry with pure radiation ($D(\Sigma)$ is flat), where $\Sigma$ is a spacelike hypersurface whose boundary is S; iii. there exist a Sen--constant spinor field (two spinor fields) on S. Thus the pp-wave Cauchy developments can be characterized by the geometry of a two rather than a three dimensional submanifold.Comment: 20 pages, Plain Tex, I

Quasi-local mass in the covariant Newtonian space-time

In general relativity, quasi-local energy-momentum expressions have been constructed from various formulae. However, Newtonian theory of gravity gives a well known and an unique quasi-local mass expression (surface integration). Since geometrical formulation of Newtonian gravity has been established in the covariant Newtonian space-time, it provides a covariant approximation from relativistic to Newtonian theories. By using this approximation, we calculate Komar integral, Brown-York quasi-local energy and Dougan-Mason quasi-local mass in the covariant Newtonian space-time. It turns out that Komar integral naturally gives the Newtonian quasi-local mass expression, however, further conditions (spherical symmetry) need to be made for Brown-York and Dougan-Mason expressions.Comment: Submit to Class. Quantum Gra

Dientes de Abelisauridae y Carcharodontosauridae cf. (Theropoda, Dinosauria) del Campaniano-Maastrichtiano Formación Presidente Prudente (Suroeste Provincia de São Paulo, Brasil)

Isolated theropod teeth referable to Abelisauridae indet., and Carcharodontosauridae cf., from the Campanian-Maastrichtian Presidente Prudente Formation of the western São Paulo State, Brazil, are described. They are compared to the Late Cretaceous Gondwanan theropod dinosaur teeth and their affinities are discussed. These teeth are significant because carnivorous dinosaur remains are poorly known from the Late Cretaceous beds of Western São Paulo State except for a few isolated elements.Se describen dientes aislados de terópodos referidos a Abelisauridae indet. y Carcharodontosauridae cf., procedentes de la Formación Presidente Prudente del Campaniano-Maastrichtiano, en el oeste del estado de San Pablo, Brasil. Los materiales son comparados con dientes de dinosaurios gondwánicos del Cretácico tardío, y cuyas afinidades son aquí discutidas. Estos dientes de dinosaurios carnívoros son significativos debido a que su presencia es pobremente conocida en el Cretácico tardío del oeste del estado del San Pablo, excepto por unos pocos huesos

Kondo decoherence: finding the right spin model for iron impurities in gold and silver

We exploit the decoherence of electrons due to magnetic impurities, studied via weak localization, to resolve a longstanding question concerning the classic Kondo systems of Fe impurities in the noble metals gold and silver: which Kondo-type model yields a realistic description of the relevant multiple bands, spin and orbital degrees of freedom? Previous studies suggest a fully screened spin $S$ Kondo model, but the value of $S$ remained ambiguous. We perform density functional theory calculations that suggest $S = 3/2$. We also compare previous and new measurements of both the resistivity and decoherence rate in quasi 1-dimensional wires to numerical renormalization group predictions for $S=1/2,1$ and 3/2, finding excellent agreement for $S=3/2$.Comment: 4 pages, 4 figures, shortened for PR

Gravitational energy in a small region for the modified Einstein and Landau-Lifshitz pseudotensors

The purpose of the classical Einstein and Landau-Lifshitz pseudotensors is for determining the gravitational energy. Neither of them can guarantee a positive energy in holonomic frames. In the small sphere approximation, it has been required that the quasilocal expression for the gravitational energy-momentum density should be proportional to the Bel-Robinson tensor $B_{\alpha\beta\mu\nu}$. However, we propose a new tensor $V_{\alpha\beta\mu\nu}$ which is the sum of certain tensors $S_{\alpha\beta\mu\nu}$ and $K_{\alpha\beta\mu\nu}$, it has certain properties so that it gives the same gravitational "energy-momentum" content as $B_{\alpha\beta\mu\nu}$ does. Moreover, we show that a modified Einstein pseudotensor turns out to be one of the Chen-Nester quasilocal expressions, while the modified Landau-Lifshitz pseudotensor becomes the Papapetrou pseudotensor; these two modified pseudotensors have positive gravitational energy in a small region.Comment:

A polarizable interatomic force field for TiO2_2 parameterized using density functional theory

We report a classical interatomic force field for TiO$_2$, which has been parameterized using density functional theory forces, energies, and stresses in the rutile crystal structure. The reliability of this new classical potential is tested by evaluating the structural properties, equation of state, phonon properties, thermal expansion, and some thermodynamic quantities such as entropy, free energy, and specific heat under constant volume. The good agreement of our results with {\em ab initio} calculations and with experimental data, indicates that our force-field describes the atomic interactions of TiO$_2$ in the rutile structure very well. The force field can also describe the structures of the brookite and anatase crystals with good accuracy.Comment: Accepted for publication in Phys. Rev. B; Changes from v1 include multiple minor revisions and a re-write of the description of the force field in Section II

Conserved superenergy currents

We exploit once again the analogy between the energy-momentum tensor and the so-called ``superenergy'' tensors in order to build conserved currents in the presence of Killing vectors. First of all, we derive the divergence-free property of the gravitational superenergy currents under very general circumstances, even if the superenergy tensor is not divergence-free itself. The associated conserved quantities are explicitly computed for the Reissner-Nordstrom and Schwarzschild solutions. The remaining cases, when the above currents are not conserved, lead to the possibility of an interchange of some superenergy quantities between the gravitational and other physical fields in such a manner that the total, mixed, current may be conserved. Actually, this possibility has been recently proved to hold for the Einstein-Klein-Gordon system of field equations. By using an adequate family of known exact solutions, we present explicit and completely non-obvious examples of such mixed conserved currents.Comment: LaTeX, 19 pages; improved version adding new content to the second section and some minor correction

Two dimensional Sen connections in general relativity

The two dimensional version of the Sen connection for spinors and tensors on spacelike 2-surfaces is constructed. A complex metric $\gamma_{AB}$ on the spin spaces is found which characterizes both the algebraic and extrinsic geometrical properties of the 2-surface $\$$. The curvature of the two dimensional Sen operator $\Delta_e$ is the pull back to $\$$ of the anti-self-dual part of the spacetime curvature while its `torsion' is a boost gauge invariant expression of the extrinsic curvatures of $\$$. The difference of the 2 dimensional Sen and the induced spin connections is the anti-self-dual part of the `torsion'. The irreducible parts of $\Delta_e$ are shown to be the familiar 2-surface twistor and the Weyl--Sen--Witten operators. Two Sen--Witten type identities are derived, the first is an identity between the 2 dimensional twistor and the Weyl--Sen--Witten operators and the integrand of Penrose's charge integral, while the second contains the `torsion' as well. For spinor fields satisfying the 2-surface twistor equation the first reduces to Tod's formula for the kinematical twistor.Comment: 14 pages, Plain Tex, no report numbe