The Real Meaning of Complex Minkowski-Space World-Lines

In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.Comment: 16 page

Simplicial vs. Continuum String Theory and Loop Equations

We derive loop equations in a scalar matrix field theory. We discuss their solutions in terms of simplicial string theory -- the theory describing embeddings of two--dimensional simplicial complexes into the space--time of the matrix field theory. This relation between the loop equations and the simplicial string theory gives further arguments that favor one of the statements of the paper hep-th/0407018. The statement is that there is an equivalence between the partition function of the simplicial string theory and the functional integral in a continuum string theory -- the theory describing embeddings of smooth two--dimensional world--sheets into the space--time of the matrix field theory in question.Comment: 6 page

The Generalized Good Cut Equation

The properties of null geodesic congruences (NGCs) in Lorentzian manifolds are a topic of considerable importance. More specifically NGCs with the special property of being shear-free or asymptotically shear-free (as either infinity or a horizon is approached) have received a great deal of recent attention for a variety of reasons. Such congruences are most easily studied via solutions to what has been referred to as the 'good cut equation' or the 'generalization good cut equation'. It is the purpose of this note to study these equations and show their relationship to each other. In particular we show how they all have a four complex dimensional manifold (known as H-space, or in a special case as complex Minkowski space) as a solution space.Comment: 12 page

Multiexciton molecules in the hexaborides

We investigate multiexciton bound states in a semiconducting phase of divalent hexaborides. Due to three degenerate valleys in both the conduction and valence bands the binding energy of a 6-exciton molecule is greatly enhanced by the shell effect. The ground state energies of multiexciton molecules are calculated using the density functional formalism. We also show that charged impurities stabilize multiexciton complexes leading to condensation of localized excitons. These complexes can act as nucleation centers of local moments.Comment: RevTEX, 7 pages with 3 figure

(2,2) Supergravity in the Light-Cone gauge

Starting with the prepotential description of two-dimensional $(2,2)$ supergravity we use local supersymmetry transformations to go to light-cone gauge. We discuss properties of the theory in this gauge and derive Ward identities for correlation functions defined with respect to the induced supergravity action.Comment: Latex, 20 pages, 2 figures in separate compressed fil

Interband proximity effect and nodes of superconducting gap in Sr2RuO4

The power-law temperature dependences of the specific heat, the nuclear relaxation rate, and the thermal conductivity suggest the presence of line nodes in the superconducting gap of Sr2RuO4. These recent experimental observations contradict the scenario of a nodeless (k_x+ik_y)-type superconducting order parameter. We propose that interaction of superconducting order parameters on different sheets of the Fermi surface is a key to understanding the above discrepancy. A full gap exists in the active band, which drives the superconducting instability, while line nodes develop in passive bands by interband proximity effect.Comment: 4 pages, 1 figur

Predicting Category Intuitiveness With the Rational Model, the Simplicity Model, and the Generalized Context Model

Naïve observers typically perceive some groupings for a set of stimuli as more intuitive than others. The problem of predicting category intuitiveness has been historically considered the remit of models of unsupervised categorization. In contrast, this article develops a measure of category intuitiveness from one of the most widely supported models of supervised categorization, the generalized context model (GCM). Considering different category assignments for a set of instances, the authors asked how well the GCM can predict the classification of each instance on the basis of all the other instances. The category assignment that results in the smallest prediction error is interpreted as the most intuitive for the GCM—the authors refer to this way of applying the GCM as “unsupervised GCM.” The authors systematically compared predictions of category intuitiveness from the unsupervised GCM and two models of unsupervised categorization: the simplicity model and the rational model. The unsupervised GCM compared favorably with the simplicity model and the rational model. This success of the unsupervised GCM illustrates that the distinction between supervised and unsupervised categorization may need to be reconsidered. However, no model emerged as clearly superior, indicating that there is more work to be done in understanding and modeling category intuitiveness

Static and Dynamic Properties of Trapped Fermionic Tonks-Girardeau Gases

We investigate some exact static and dynamic properties of one-dimensional fermionic Tonks-Girardeau gases in tight de Broglie waveguides with attractive p-wave interactions induced by a Feshbach resonance. A closed form solution for the one-body density matrix for harmonic trapping is analyzed in terms of its natural orbitals, with the surprising result that for odd, but not for even, numbers of fermions the maximally occupied natural orbital coincides with the ground harmonic oscillator orbital and has the maximally allowed fermionic occupancy of unity. The exact dynamics of the trapped gas following turnoff of the p-wave interactions are explored.Comment: 4 pages, 2 figures, submitted to PR