Networks, Fields and Organizations: Micro-Dynamics, Scale and Cohesive Embeddings

Social action is situated in fields that are simultaneously composed of interpersonal ties and relations among organizations, which are both usefully characterized as social networks. We introduce a novel approach to distinguishing different network macro-structures in terms of cohesive subsets and their overlaps. We develop a vocabulary that relates different forms of network cohesion to field properties as opposed to organizational constraints on ties and structures. We illustrate differences in probabilistic attachment processes in network evolution that link on the one hand to organizational constraints versus field properties and to cohesive network topologies on the other. This allows us to identify a set of important new micro-macro linkages between local behavior in networks and global network properties. The analytic strategy thus puts in place a methodology for Predictive Social Cohesion theory to be developed and tested in the context of informal and formal organizations and organizational fields. We also show how organizations and fields combine at different scales of cohesive depth and cohesive breadth. Operational measures and results are illustrated for three organizational examples, and analysis of these cases suggests that different structures of cohesive subsets and overlaps may be predictive in organizational contexts and similarly for the larger fields in which they are embedded. Useful predictions may also be based on feedback from level of cohesion in the larger field back to organizations, conditioned on the level of multiconnectivity to the field.     

Charge transfer excitons: dynamic theory of vibronic spectra

The vibronic spectra of charge transfer excitons (CTE) in a molecular one-component or alternatingly ordered two-component chain are treated in the framework of a dynamic approach (neglecting thermal excitations of the intramolecular vibrations). The model introduces two mechanisms of coupling between CTEs and vibrational quanta: (1) shift of the equilibrium positions of the nuclei in the ionized donor or acceptor; (2) change of the vibrational frequency in the ionized molecule. This model allows to generalize the simple CTE Hamiltonian and the vibronic Hamiltonian of Frenkel excitons. The linear optical susceptibility is calculated in the vibronic region (one CTE and one vibrational quantum). The double splitting of vibronics of CTEs was analyzed: (1) the splitting connected with the location of the intramolecular vibration on the donors or on the acceptors; (2) the splitting connected with the symmetry of the vibronic spectra (in the degenerate case). The general structure of the vibronic spectra of CTEs is established. It contains structureless absorption lines, which correspond to two-particle bands (the phonon is excited on a neutral molecule neighboring the donor or the acceptor) and Lorentz-type lines of one-particle states, which correspond to the bound propagation of the CTE and the phonon.     

Millimeter and submillimeter wave spectroscopic investigations into the rotation-tunneling spectrum of gGg ethylene glycol, HOCH2CH2OH

The rotation-tunneling spectrum of the second most stable gGg^′ conformer of ethylene glycol (1,2-ethanediol) in its ground vibrational state has been studied in selected regions between 77 and 579 GHz. Compared to the study of the more stable aGg^′ conformer, a much larger frequency range was studied, resulting in a much extended frequency list covering similar quantum numbers, J?55 and K_a?19. While the input data were reproduced within experimental uncertainties up to moderately high values of J and K_a larger residuals remain at higher quantum numbers. The severe mixing of the states caused by the Coriolis interaction between the two tunneling substates is suggested to provide a considerable part of the explanation. In addition, a Coriolis interaction of the gGg^′ ground vibrational state with an excited state of the aGg^′ conformer may also contribute. Relative intensities of closely spaced lines have been investigated to determine the signs of the Coriolis constants between the two tunneling substates relative to the dipole moment components and to estimate the magnitudes of the dipole moment components and the energy difference between the gGg^′ and the aGg^′ conformers. Results of ab initio calculations on the total dipole moment and the vibrational spectrum were needed for these estimates. The current analysis is limited to transitions with quantum numbers J?40 and K_a?6 plus those having J?22 and K_a?17 which could be reproduced within experimental uncertainties. The results are aimed at aiding radioastronomers to search for gGg^′ ethylene glycol in comets and in interstellar space.     

Sagnac Effect of Gödel's Universe

We present exact expressions for the Sagnac effect of Gödel's Universe. For this purpose we first derive a formula for the Sagnac time delay along a circular path in the presence of an arbitrary stationary metric in cylindrical coordinates. We then apply this result to Gödel's metric for two different experimental situations: First, the light source and the detector are at rest relative to the matter generating the gravitational field. In this case we find an expression that is formally equivalent to the familiar nonrelativistic Sagnac time delay. Second, the light source and the detector are rotating relative to the matter. Here we show that for a special rotation rate of the detector the Sagnac time delay vanishes. Finally we propose a formulation of the Sagnac time delay in terms of invariant physical quantities. We show that this result is very close to the analogous formula of the Sagnac time delay of a rotating coordinate system in Minkowski spacetime.     

On gravitational radiation and the energy flux of matter

A suitable derivative of Einstein's equations in the framework of the teleparallel equivalent of general relativity (TEGR) yields a continuity equation for the gravitational energy‐momentum. In particular, the time derivative of the total gravitational energy is given by the sum of the total fluxes of gravitational and matter fields energy. We carry out a detailed analysis of the continuity equation in the context of Bondi and Vaidya's metrics. In the former space‐time the flux of gravitational energy is given by the well known expression in terms of the square of the news function. It is known that the energy definition in the realm of the TEGR yields the ADM (Arnowitt‐Deser‐Misner) energy for appropriate boundary conditions. Here we show that the same energy definition also describes the Bondi energy. The analysis of the continuity equation in Vaidya's space‐time shows that the variation of the total gravitational energy is determined by the energy flux of matter only.     

The Two-Body Interaction with a Circle in Time

We complete our previous^{(1, 2)} demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,⁽⁴⁾ including fine structure. We complete our previous derivation⁽²⁾ of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.     

Simple Entanglement Measure for Multipartite Pure States

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.     

Supersymmetric large extra dimensions and the cosmological constant: an update

This article critically reviews the proposal for addressing the cosmological constant problem within the framework of supersymmetric large extra dimensions (SLED), as recently proposed in hep-th/0304256. After a brief restatement of the cosmological constant problem, a short summary of the proposed mechanism is given. The emphasis is on the perspective of the low-energy effective theory in order to see how it addresses the problem of why low-energy particles like the electron do not contribute too large a vacuum energy. This is followed by a discussion of the main objections, which are grouped into the following five topics: (1) Weinberg’s No-Go Theorem. (2) Are hidden tunings of the theory required, and are these stable under renormalization? (3) Why should the mechanism apply only now and not rule out possible earlier epochs of inflationary dynamics? (4) How big are quantum effects, and which are the most dangerous? and (5) Even if successful, can the mechanism be consistent with cosmological or current observational constraints? It is argued that there are plausible reasons why the mechanism can thread the potential objections, but that a definitive proof that it does depends on addressing well-defined technical points. These points include identifying what fixes the size of the extra dimensions, checking how topological obstructions renormalize and performing specific calculations of quantum corrections. More detailed studies of these issues, which are well within reach of our present understanding of extra-dimensional theories, are currently underway. As such, the jury remains out concerning the proposal, although the prospects for acquittal still seem good. (An abridged version of this article appears in the proceedings of SUSY 2003.)