On the Ricci tensor in type II B string theory

Let $\nabla$ be a metric connection with totally skew-symmetric torsion \T on a Riemannian manifold. Given a spinor field $\Psi$ and a dilaton function $\Phi$, the basic equations in type II B string theory are \bdm \nabla \Psi = 0, \quad \delta(\T) = a \cdot \big(d \Phi \haken \T \big), \quad \T \cdot \Psi = b \cdot d \Phi \cdot \Psi + \mu \cdot \Psi . \edm We derive some relations between the length ||\T||^2 of the torsion form, the scalar curvature of $\nabla$, the dilaton function $\Phi$ and the parameters $a,b,\mu$. The main results deal with the divergence of the Ricci tensor \Ric^{\nabla} of the connection. In particular, if the supersymmetry $\Psi$ is non-trivial and if the conditions \bdm (d \Phi \haken \T) \haken \T = 0, \quad \delta^{\nabla}(d \T) \cdot \Psi = 0 \edm hold, then the energy-momentum tensor is divergence-free. We show that the latter condition is satisfied in many examples constructed out of special geometries. A special case is $a = b$. Then the divergence of the energy-momentum tensor vanishes if and only if one condition \delta^{\nabla}(d \T) \cdot \Psi = 0 holds. Strong models (d \T = 0) have this property, but there are examples with \delta^{\nabla}(d \T) \neq 0 and \delta^{\nabla}(d \T) \cdot \Psi = 0.Comment: 9 pages, Latex2

Emergent Form from Structural Optimisation of the Voronoi Polyhedra Structure

In the course of the exploration of computational means in the architectural design process, in order to investigate more complex, adaptive geometries, the Voronoi diagram has recently gained some attention, being a three-dimensional space-filling structure which is modular but not repetitive. The project looks at the Voronoi diagram as a load-bearing structure, and whether it can be useful for structural optimisation. Hereby the edges of the Voronoi polyhedra are regarded as structural members of a statical system, which then is assessed by structural analysis software. Results seem to indicate that the Voronoi approach produces a very specific structural as well as spatial type of order. Through the dislocation of the Voronoi cells, the statical structure becomes more complex through emergent topology changes, and the initially simple spatial system becomes much more complex through emerging adjacencies and interconnections between spaces. The characteristics of the emerging form, however, lie rather in the complexity how shifted spaces and parts are fitted together, than in a radical overall emergent geometry. Spatially as well as a structurally, the form moves from a simple modular repetitive system towards a more complex adaptive one, with interconnected parts which cannot stand alone but rather form an organic whole

Killing spinors in supergravity with 4-fluxes

We study the spinorial Killing equation of supergravity involving a torsion 3-form \T as well as a flux 4-form \F. In dimension seven, we construct explicit families of compact solutions out of 3-Sasakian geometries, nearly parallel \G_2-geometries and on the homogeneous Aloff-Wallach space. The constraint \F \cdot \Psi = 0 defines a non empty subfamily of solutions. We investigate the constraint \T \cdot \Psi = 0, too, and show that it singles out a very special choice of numerical parameters in the Killing equation, which can also be justified geometrically

A first-principles DFT+GW study of spin-filter and spin-gapless semiconducting Heusler compounds

Among Heusler compounds, the ones being magnetic semiconductors (also known as spin-filter materials) are widely studied as they offer novel functionalities in spintronic/magnetoelectronic devices. The spin-gapless semiconductors are a special case. They possess a zero or almost-zero energy gap in one of the two spin channels. We employ the $GW$ approximation, which allows an elaborate treatment of the electronic correlations, to simulate the electronic band structure of these materials. Our results suggest that in most cases the use of $GW$ self energy instead of the usual density functionals is important to accurately determine the electronic properties of magnetic semiconductors.Comment: Final version as publishe

A Method for Calculating the Structure of (Singular) Spacetimes in the Large

A formalism and its numerical implementation is presented which allows to calculate quantities determining the spacetime structure in the large directly. This is achieved by conformal techniques by which future null infinity (\Scri{}^+) and future timelike infinity ($i^+$) are mapped to grid points on the numerical grid. The determination of the causal structure of singularities, the localization of event horizons, the extraction of radiation, and the avoidance of unphysical reflections at the outer boundary of the grid, are demonstrated with calculations of spherically symmetric models with a scalar field as matter and radiation model.Comment: 29 pages, AGG2

Tomographic readout of an opto-mechanical interferometer

The quantum state of light changes its nature when being reflected off a mechanical oscillator due to the latter's susceptibility to radiation pressure. As a result, a coherent state can transform into a squeezed state and can get entangled with the motion of the oscillator. The complete tomographic reconstruction of the state of light requires the ability to readout arbitrary quadratures. Here we demonstrate such a readout by applying a balanced homodyne detector to an interferometric position measurement of a thermally excited high-Q silicon nitride membrane in a Michelson-Sagnac interferometer. A readout noise of \unit{1.9 \cdot 10^{-16}}{\metre/\sqrt{\hertz}} around the membrane's fundamental oscillation mode at \unit{133}{\kilo\hertz} has been achieved, going below the peak value of the standard quantum limit by a factor of 8.2 (9 dB). The readout noise was entirely dominated by shot noise in a rather broad frequency range around the mechanical resonance.Comment: 7 pages, 5 figure

General Relativistic Scalar Field Models in the Large

For a class of scalar fields including the massless Klein-Gordon field the general relativistic hyperboloidal initial value problems are equivalent in a certain sense. By using this equivalence and conformal techniques it is proven that the hyperboloidal initial value problem for those scalar fields has an unique solution which is weakly asymptotically flat. For data sufficiently close to data for flat spacetime there exist a smooth future null infinity and a regular future timelike infinity.Comment: 22 pages, latex, AGG 1