Dual variables and a connection picture for the Euclidean Barrett-Crane model

The partition function of the SO(4)- or Spin(4)-symmetric Euclidean Barrett-Crane model can be understood as a sum over all quantized geometries of a given triangulation of a four-manifold. In the original formulation, the variables of the model are balanced representations of SO(4) which describe the quantized areas of the triangles. We present an exact duality transformation for the full quantum theory and reformulate the model in terms of new variables which can be understood as variables conjugate to the quantized areas. The new variables are pairs of S^3-values associated to the tetrahedra. These S^3-variables parameterize the hyperplanes spanned by the tetrahedra (locally embedded in R^4), and the fact that there is a pair of variables for each tetrahedron can be viewed as a consequence of an SO(4)-valued parallel transport along the edges dual to the tetrahedra. We reconstruct the parallel transport of which only the action of SO(4) on S^3 is physically relevant and rewrite the Barrett-Crane model as an SO(4) lattice BF-theory living on the 2-complex dual to the triangulation subject to suitable constraints whose form we derive at the quantum level. Our reformulation of the Barrett-Crane model in terms of continuous variables is suitable for the application of various analytical and numerical techniques familiar from Statistical Mechanics.Comment: 33 pages, LaTeX, combined PiCTeX/postscript figures, v2: note added, TeX error correcte

The interaction between transpolar arcs and cusp spots

Transpolar arcs and cusp spots are both auroral phenomena which occur when the interplanetary magnetic field is northward. Transpolar arcs are associated with magnetic reconnection in the magnetotail, which closes magnetic flux and results in a "wedge" of closed flux which remains trapped, embedded in the magnetotail lobe. The cusp spot is an indicator of lobe reconnection at the high-latitude magnetopause; in its simplest case, lobe reconnection redistributes open flux without resulting in any net change in the open flux content of the magnetosphere. We present observations of the two phenomena interacting--i.e., a transpolar arc intersecting a cusp spot during part of its lifetime. The significance of this observation is that lobe reconnection can have the effect of opening closed magnetotail flux. We argue that such events should not be rare

Geometry of Deformations of Relativistic Membranes

A kinematical description of infinitesimal deformations of the worldsheet spanned in spacetime by a relativistic membrane is presented. This provides a framework for obtaining both the classical equations of motion and the equations describing infinitesimal deformations about solutions of these equations when the action describing the dynamics of this membrane is constructed using {\it any} local geometrical worldsheet scalars. As examples, we consider a Nambu membrane, and an action quadratic in the extrinsic curvature of the worldsheet.Comment: 20 pages, Plain Tex, sign errors corrected, many new references added. To appear in Physical Review

Stability of Solid State Reaction Fronts

We analyze the stability of a planar solid-solid interface at which a chemical reaction occurs. Examples include oxidation, nitridation, or silicide formation. Using a continuum model, including a general formula for the stress-dependence of the reaction rate, we show that stress effects can render a planar interface dynamically unstable with respect to perturbations of intermediate wavelength

Vorton Formation

In this paper we present the first analytic model for vorton formation. We start by deriving the microscopic string equations of motion in Witten's superconducting model, and show that in the relevant chiral limit these coincide with the ones obtained from the supersonic elastic models of Carter and Peter. We then numerically study a number of solutions of these equations of motion and thereby suggest criteria for deciding whether a given superconducting loop configuration can form a vorton. Finally, using a recently developed model for the evolution of currents in superconducting strings we conjecture, by comparison with these criteria, that string networks formed at the GUT phase transition should produce no vortons. On the other hand, a network formed at the electroweak scale can produce vortons accounting for up to 6% of the critical density. Some consequences of our results are discussed.Comment: 41 pages; color figures 3-6 not included, but available from authors. To appear in Phys. Rev.

Application of remote sensing to state and regional problems

There are no author-identified significant results in this report

Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way post-processing

We derive a bound for the security of QKD with finite resources under one-way post-processing, based on a definition of security that is composable and has an operational meaning. While our proof relies on the assumption of collective attacks, unconditional security follows immediately for standard protocols like Bennett-Brassard 1984 and six-states. For single-qubit implementations of such protocols, we find that the secret key rate becomes positive when at least N\sim 10^5 signals are exchanged and processed. For any other discrete-variable protocol, unconditional security can be obtained using the exponential de Finetti theorem, but the additional overhead leads to very pessimistic estimates

Localized versus itinerant magnetic moments in Na0.72CoO2

Based on experimental 59Co-NMR data in the temperature range between 0.1 and 300 K, we address the problem of the character of the Co 3d-electron based magnetism in Na0.7CoO2. Temperature dependent 59Co-NMR spectra reveal different Co environments below 300 K and their differentiation increases with decreasing temperature. We show that the 23Na- and 59Co-NMR data may consistently be interpreted by assuming that below room temperature the Co 3d-electrons are itinerant. Their magnetic interaction appears to favor an antiferromagnetic coupling, and we identify a substantial orbital contribution corb to the d-electron susceptibility. At low temperatures corb seems to acquire some temperature dependence, suggesting an increasing influence of spin-orbit coupling. The temperature dependence of the spin-lattice relaxation rate T1-1(T) confirms significant variations in the dynamics of this electronic subsystem between 200 and 300K, as previously suggested. Below 200 K, Na0.7CoO2 may be viewed as a weak antiferromagnet with TN below 1 K but this scenario still leaves a number of open questions.Comment: 8.7 pages, 6 Figures, submitted to Phys. Rev.

Two inequivalent sublattices and orbital ordering in MnV2O4 studied by 51V NMR

We report detailed 51V NMR spectra in a single crystal of MnV2O4. The vanadium spectrum reveals two peaks in the orbitally ordered state, which arise from different internal hyperfine fields at two different V sublattices. These internal fields evolve smoothly with externally applied field, and show no change in structure that would suggest a change of the orbital ordering. The result is consistent with the orbital ordering model recently proposed by Sarkar et al. [Phys. Rev. Lett. 102, 216405 (2009)] in which the same orbital that is a mixture of t_2g orbitals rotates by about 45$^\circ$ alternately within and between orbital chains in the I4_1/a tetragonal space group.Comment: 4 pages, 4 figures, title changed, published in PRB as a rapid com

Rotating Black Holes in Higher Dimensions with a Cosmological Constant

We present the metric for a rotating black hole with a cosmological constant and with arbitrary angular momenta in all higher dimensions. The metric is given in both Kerr-Schild and Boyer-Lindquist form. In the Euclidean-signature case, we also obtain smooth compact Einstein spaces on associated S^{D-2} bundles over S^2, infinitely many for each odd D\ge 5. Applications to string theory and M-theory are indicated.Comment: 8 pages, Latex. Short version, with more compact notation, of hep-th/0404008. To appear in Phys. Rev. Let